UNIT- I
INTERPLANETARY TRANSPORT NETWORK
INTRODUCTION
The interplanetary transport network (IPN) is a collection of gravitationally determined pathways through the Solar System that
require very little energy for an object to follow. The ITN makes
particular use of Lagrange points as locations where trajectories through space are redirected using little or no
energy. These points have the peculiar property of allowing objects to orbit around them, despite the absence of
any material object therein. While they use little energy, the transport can
take a very long time.
A low energy transfer, or low
energy trajectory, is a route in
space which allows spacecraft to change orbits using
very little fuel. [1][2] These
routes work in the Earth-Moon system and
also in other systems, such as traveling from Earth to Mars or
between the satellites
of Jupiter. The drawback of such trajectories is that they take
longer to complete than higher energy (more fuel) transfers such as Hohmann transfer orbits
1.2 History
The key to the
interplanetary transport network was investigating the exact nature of these
winding paths near the Lagrange points. They were first investigated by Jules-Henri Poincaré in the 1890s. He
noticed that the paths leading to and from any of these points would almost
always settle, for a time, on the orbit around it. There are in fact an infinite number of paths
taking one to the point and back away from it, and all of them require no
energy to reach. When plotted, they form a tube with the orbit around the point
at one end, a view which traces back to mathematicians Charles C. Conley and Richard P. McGehee in the 1960s. Theoretical work by Edward Belbruno in 1994 provided the first
insight into the nature of the ITN between the Earth and the Moon that was used by Hiten, Japan's
first lunar probe. Beginning in 1997 Martin
Lo, Shane D. Ross, and
others wrote a series of papers identifying the mathematical basis and applying
the technique to the Genesis
solar wind sample return, along with Lunar and Jovian missions. They referred
to an Interplanetary Superhighway (IPS)
As it turns out, it
is very easy to transit from a path leading to the point to one leading back
out. This makes sense, since the orbit is unstable, which implies one will
eventually end up on one of the outbound paths after spending no energy at all.
However, with careful calculation, one can pick which outbound path one
wants. This turned out to be exciting, because many of these paths lead right
by some interesting points in space, like the Earth's Moon or the Galilean moons of Jupiter. That means that for
the cost of getting to the Earth–Sun L2 point, which is
rather low, one can travel to a huge number of very interesting points for a
low additional fuel cost or even for
free.
The transfers are so
low-energy that they make travel to almost any point in the Solar System
possible. On the downside, these transfers are very slow, and only useful for
automated probes. Nevertheless, they have already been used to transfer
spacecraft out to the Earth–Sun L1 point, a useful point
for studying the Sun that was used in a number of recent missions, including
the Genesis mission. The Solar and
Heliospheric Observatory began
operations at L1 in 1996. The network is also relevant to understanding Solar
System dynamics; Comet Shoemaker–Levy
9followed such a trajectory to collide with Jupiter.
1.3 Further
explanation
In addition to orbits
around Lagrange points, the rich dynamics that arise from the gravitational
pull of more than one mass yield interesting trajectories, also known as low energy transfers. For example, the
gravity environment of the Sun–Earth–Moon system allows spacecraft to travel
great distances on very little fuel, albeit on an often circuitous route.
Launched in 1978, the ISEE-3 spacecraft was sent on a mission to orbit around one
of the Lagrange points. The
spacecraft was able to maneuver around the Earth's neighborhood using little
fuel by taking advantage of the unique gravity environment. After
the primary mission was completed, ISEE-3 went on to accomplish other goals,
including a flight through the geomagnetic tail and a comet
flyby. The mission was subsequently renamed the International
Cometary Explorer (ICE).
The first low energy
transfer utilizing this network was the rescue of Japan's Hiten lunar mission in
1991. Another
example of the use of the ITN was NASA's
2001–2003 Genesis
mission, which orbited the Sun–Earth L1 point for over two
years collecting material, before being redirected to the L2 Lagrange point, and
finally redirected from there back to Earth. The 2003–2006 SMART-1 of the European Space Agency used another low
energy transfer from the ITN.
The ITN is based
around a series of orbital paths predicted by chaos
theory and
the restricted three-body
problem leading
to and from the unstable orbits around the Lagrange points – points in space
where the gravity between various
bodies balances with the centrifugal force of an object there. For any two
bodies in which one body orbits around the other, such as a star/planet or
planet/moon system, there are three such points, denoted L1 through L3. For
instance, the Earth–Moon L1 point lies on a line
between the two, where gravitational forces between them exactly balance with
the centrifugal force of an object placed in orbit there. For two bodies whose
ratio of masses exceeds 24.96, there are two additional stable points denoted
as L4 and L5. These
five points have particularly low delta-v requirements, and
appear to be the lowest-energy transfers possible, even lower than the common Hohmann transfer
orbit that
has dominated orbital navigation in the past.
Although the forces
balance at these points, the first three points (the ones on the line between a
certain large mass (e.g. a star)
and a smaller, orbiting mass (e.g. a planet))
are not stable equilibrium points.
If a spacecraft placed at the
Earth–Moon L1 point is given even a
slight nudge towards the Moon, for instance, the Moon's gravity will now be
greater and the spacecraft will be pulled away from the L1 point. The entire
system is in motion, so the spacecraft will not actually hit the Moon, but will
travel in a winding path, off into space. There is, however, a semi-stable
orbit around each of these points. The orbits for two of the points, L4 and L5, are
stable, but the orbits for L1 through L3 are stable only on
the order of months
1.4 Lagrangian points
The Lagrangian points are the five
positions in an orbital configuration where a small object affected only
by gravity can theoretically be part of a constant-shape pattern with
two larger objects (such as a satellite with respect to
the Earth and Moon). The Lagrange
points mark positions where the combined gravitational pull of the two large
masses provides precisely the centripetal force required to orbit with them.
Lagrangian
points are the constant-pattern solutions of the restricted three-body
problem. For example, given two massive bodies in orbits around
their common center
of mass, there are five positions in space where a third body,
of comparatively negligible mass, could be
placed so as to maintain its position relative to the two massive bodies. As
seen in a rotating reference frame matching the angular velocity of
the two co-orbiting bodies, the gravitational fields of two massive
bodies combined with the satellite's acceleration are in balance at the
Lagrangian points, allowing the third body to be relatively stationary with
respect to the first two bodies.
1.4.1 History and concepts
The three
collinear Lagrange points (L1, L2, L3 ) were discovered by Leonhard Euler a few
years before Lagrange discovered the remaining two.
In 1772, the
Italian-French mathematician Joseph Louis Lagrange was working on the famous
three-body problem when he discovered an interesting quirk in the results.
Originally, he had set out to discover a way to easily calculate the
gravitational interaction between arbitrary numbers of bodies in a system,
because Newtonian mechanics concludes that such a system results in the bodies
orbiting chaotically until there is a collision, or a body is thrown out of the
system so that equilibrium can be achieved.
The logic
behind this conclusion is that a system with one body is trivial, as it is
merely static relative to itself; a system with two bodies is the relatively
simple two-body problem, with the bodies orbiting around their common center of
mass. However, once more than two bodies are introduced, the mathematical
calculations become very complicated. It becomes necessary to calculate the
gravitational interaction between every pair of objects at every point along
their trajectory.
Lagrange,
however, wanted to make this simpler. He did so with a simple hypothesis: The
trajectory of an object is determined by finding a path that minimizes the
action over time. This is found by subtracting the potential energy from the
kinetic energy. With this way of thinking, Lagrange re-formulated the classical
Newtonian mechanics to give rise to Lagrangian mechanics.
Common opinion
has been that Lagrange himself considered how a third body of negligible mass
would orbit around two larger bodies which were already in a near-circular
orbit, and found that in a frame of reference that rotates with the larger
bodies, there are five specific fixed points where the third body experiences
zero net force as it follows the circular orbit of its host bodies (planets).
However, that is false.
Actually,
Lagrange considered in the first chapter of the Essai the general three-body problem. From that, in
the second chapter, he demonstrated two special constant-pattern solutions, the
collinear and the equilateral, for any three masses, with conic section orbits.
Thence, if one mass is made negligible, one immediately gets the five positions
now known as the Lagrange Points; but Lagrange himself apparently did not note
that.
In the more
general case of elliptical orbits, there are no longer stationary points in the
same sense: it becomes more of a Lagrangian “area”. The Lagrangian points
constructed at each point in time, as in the circular case, form stationary
elliptical orbits which are similar to the orbits of the massive bodies. This
is due to Newton's second law (Force = Mass times Acceleration, or ), where p = mv (p the momentum, m the mass,
and v the velocity) is invariant if force and position are scaled by the same
factor. A body at a Lagrangian point orbits with the same period as the two
massive bodies in the circular case, implying that it has the same ratio of
gravitational force to radial distance as they do. This fact is independent of
the circularity of the orbits, and it implies that the elliptical orbits traced
by the Lagrangian points are solutions of the equation of motion of the third
body.
Early in the
20th century, Trojan asteroids were discovered at the L4 and L5 Lagrange points
of the Sun–Jupiter system.
FIVE POINTS
A diagram showing the five Lagrangian points in a
two-body system with one body far more massive than the other (e.g. the Sun and the Earth). In such a system, L3–L5 will
appear to share the secondary's orbit, although in fact they are situated
slightly outside it.
The five
Lagrangian points are labeled and defined as follows:
L1
The L1 point
lies on the line defined by the two large masses M1 and M2, and between them.
It is the most intuitively understood of the Lagrangian points: the one where
the gravitational attraction of M2 partially cancels M1 gravitational
attraction.
Example: An
object which orbits the Sun more closely than the Earth would normally have a
shorter orbital period than the Earth, but that ignores the effect of the
Earth's own gravitational pull. If the object is directly between the Earth and
the Sun, then the Earth's gravity weakens the force pulling the object towards
the Sun, and therefore increases the orbital period of the object. The closer
to Earth the object is, the greater this effect is. At the L1 point, the
orbital period of the object becomes exactly equal to the Earth's orbital
period. L1 is about 1.5 million kilometers from the Earth.
The Sun–Earth
L1 is suited for making observations of the Sun–Earth system. Objects here are
never shadowed by the Earth or the Moon. The first mission of this type was the
International Sun Earth Explorer 3 (ISEE3) mission used as an interplanetary
early warning storm monitor for solar disturbances. The feasibility of this
orbit was the result of a PhD thesis by the astrodynamicist Robert W. Farquhar.
Subsequently the Solar and Heliospheric Observatory (SOHO) was stationed in a
Halo orbit at L1, and the Advanced Composition Explorer(ACE) in a Lissajous
orbit, also at the L1 point. WIND is also at L1.
The Earth–Moon
L1 allows comparatively easy access to lunar and earth orbits with minimal
change in velocity and has this as an advantage to position a half-way manned
space station intended to help transport cargo and personnel to the Moon and
back.
In a binary
star system, the Roche lobe has its apex located at L1; if a star overflows its
Roche lobe then it will lose matter to its companion star.
L2
A diagram
showing the Sun–Earth L2 point, which lies well beyond the Moon's orbit around
the Earth
The L2 point
lies on the line defined by the two large masses, beyond the smaller of the two.
Here, the gravitational forces of the two large masses balance the centrifugal
effect on a body at L2.
Example: On the
side of the Earth away from the Sun, the orbital period of an object would
normally be greater than that of the Earth. The extra pull of the Earth's
gravity decreases the orbital period of the object, and at the L2 point that
orbital period becomes equal to the Earth's.
The Sun–Earth
L2 is a good spot for space-based observatories. Because an object around L2
will maintain the same relative position with respect to the Sun and Earth,
shielding and calibration are much simpler. It is, however, slightly beyond the
reach of Earth's umbra, so solar radiation is not completely blocked. The
Herschel Space Observatory, Planck space observatory are already, Chang'e 2 was
until April 2012, and the Wilkinson Microwave Anisotropy Probe [10] was until
October 2010, in orbit around the Sun–Earth L2. The Gaia probe and James Webb
Space Telescope will be placed at the Sun–Earth L2. Earth–Moon L2 would be a
good location for a communications satellite covering the Moon's far side.
Earth–Moon L2 would be "an ideal location" for a propellant depot as
part of the proposed depot-based space transportation architecture.
If the mass of
the smaller object (M2) is much smaller than the mass of the larger object (M1)
then L1 and L2 are at approximately equal distances r from the smaller object,
equal to the radius of the Hill sphere, given by:
where R is the
distance between the two bodies.
This distance
can be described as being such that the orbital period, corresponding to a
circular orbit with this distance as radius around M2 in the absence of M1, is
that of M2 around M1, divided by :
Examples
• Sun and Earth: 1,500,000 km (930,000
mi) from the Earth
• Earth and Moon: 60,000 km (37,000 mi)
from the Moon
L3
The L3 point
lies on the line defined by the two large masses, beyond the larger of the two.
Example: L3 in
the Sun–Earth system exists on the opposite side of the Sun, a little outside
the Earth's orbit but slightly closer to the Sun than the Earth is. (This
apparent contradiction is because the Sun is also affected by the Earth's
gravity, and so orbits around the two bodies' barycenter, which is, however,
well inside the body of the Sun.) At the L3 point, the combined pull of the
Earth and Sun again causes the object to orbit with the same period as the
Earth.
The Sun–Earth
L3 point was a popular place to put a "Counter-Earth" in pulp science
fiction and comic books. Once space-based observation became possible via
satellites and probes, it was shown to hold no such object. The Sun–Earth L3 is
unstable and could not contain an object, large or small, for very long. This
is because the gravitational forces of the other planets are stronger than that
of the Earth (Venus, for example, comes within 0.3 AU of this L3 every 20
months). In addition, because Earth's orbit is elliptical and because the
barycenter of the Sun–Jupiter system is unbalanced relative to Earth (that is,
the Sun orbits the Sun–Jupiter center of mass, which is outside of the Sun
itself), such a Counter-Earth would frequently be visible from Earth.
A spacecraft
orbiting near Sun–Earth L3 would be able to closely monitor the evolution of
active sunspot regions before they rotate into a geoeffective position, so that
a 7-day early warning could be issued by the NOAA Space Weather Prediction
Center. Moreover, a satellite near Sun–Earth L3 would provide very important
observations not only for Earth forecasts, but also for deep space support
(Mars predictions and for manned mission to near-Earth asteroids). In 2010,
spacecraft transfer trajectories to Sun–Earth L3 were studied and several
designs were considered.
One example of
asteroids which visit an L3 point is the Hilda family whose orbit brings them
to the Sun–Jupiter L3 point.
L4 and L5
Gravitational
accelerations at L4
The L4 and L5
points lie at the third corners of the two equilateral triangles in the plane
of orbit whose common base is the line between the centers of the two masses,
such that the point lies behind (L5) or ahead of (L4) the smaller mass with
regard to its orbit around the larger mass.
• The reason these points are in
balance is that, at L4 and L5, the distances to the two masses are equal. Accordingly,
the gravitational forces from the two massive bodies are in the same ratio as
the masses of the two bodies, and so the resultant force acts through the
barycenter of the system; additionally, the geometry of the triangle ensures
that the resultant acceleration is to the distance from the barycenter in the
same ratio as for the two massive bodies. The barycenter being both the center
of mass and center of rotation of the system, this resultant force is exactly
that required to keep a body at the Lagrange point in orbital equilibrium with
the rest of the system. (Indeed, the third body need not have negligible mass).
The general triangular configuration was discovered by Lagrange in work on the
3-body problem.
• L4 and L5 are sometimes called
triangular Lagrange points or Trojan points. The name Trojan points comes from
the Trojan asteroids at the Sun–Jupiter L4and L5 points, which themselves are
named after characters from Homer's Iliad (the legendary siege of Troy).
Asteroids at the L4 point, which leads Jupiter, are referred to as the
"Greek camp", while those at the L5 point are referred to as the
"Trojan camp". These asteroids are (largely) named after characters
from the respective sides of the Trojan War.
Examples
The Sun–Earth
L4 and L5 points lie 60° ahead of and 60° behind the Earth as it orbits the
Sun. The regions around these points contain interplanetary dust and at least
one asteroid, 2010 TK7, detected October 2010 by WISE and announced July 2011.
Watch NASA's animated clip..
• The Earth–Moon L4 and L5 points lie
60° ahead of and 60° behind the Moon as it orbits the Earth. They may contain
interplanetary dust in what is called Kordylewski clouds; however, the Hiten
spacecraft's Munich Dust Counter (MDC) detected no increase in dust during its
passes through these points.
• The region around the Sun–Jupiter L4
and L5 points are occupied by the Trojan asteroids.
• The region around the Sun–Neptune L4
and L5 points have trojan objects.
• Saturn's moon Tethys has two much
smaller satellites at its L4 and L5 points named Telesto and Calypso,
respectively.
• Saturn's moon Dione has smaller moons
Helene and Polydeuces at its L4 and L5 points, respectively.
• One version of the giant impact hypothesis
suggests that an object named Theia formed at the Sun–Earth L4 or L5 points and
crashed into the Earth after its orbit destabilized, forming the Moon.
Stability
• The first three Lagrangian points are
technically stable only in the plane perpendicular to the line between the two
bodies. This can be seen most easily by considering the L1 point. A test mass
displaced perpendicularly from the central line would feel a force pulling it
back towards the equilibrium point. This is because the lateral components of
the two masses' gravity would add to produce this force, whereas the components
along the axis between them would balance out. However, if an object located at
the L1 point drifted closer to one of the masses, the gravitational attraction
it felt from that mass would be greater, and it would be pulled closer. (The
pattern is very similar to that of tidal forces.)
• Although the L1, L2, and L3 points
are nominally unstable, it turns out that it is possible to find stable
periodic orbits around these points, at least in the restricted three-body
problem. These perfectly periodic orbits, referred to as "halo"
orbits, do not exist in a full n-body dynamical system such as the Solar
System. However, quasi-periodic (i.e., bounded but not precisely repeating)
orbits following Lissajous-curve trajectories do exist in the n-body system.
These quasi-periodic Lissajous orbits are what most of Lagrangian-point
missions to date have used. Although they are not perfectly stable, a
relatively modest effort at station keeping can allow a spacecraft to stay in a
desired Lissajous orbit for an extended period of time. It also turns out that,
at least in the case of Sun–Earth-L1 missions, it is actually preferable to
place the spacecraft in a large-amplitude Lissajous orbit, instead of having it sit at
the Lagrangian point, because this keeps the spacecraft off the direct
Sun–Earth line, thereby reducing the impact of solar interference on
Earth–spacecraft communications. Another interesting and useful property of the
collinear Lagrangian points and their associated Lissajous orbits is that they
serve as "gateways" to control the chaotic trajectories of the
Interplanetary Transport Network.
• In contrast to the collinear
Lagrangian points, the triangular points (L4 and L5) are stable equilibria (cf.
attractor), provided that the ratio of M1/M2 is greater than 24.96. This is the
case for the Sun–Earth system, the Sun–Jupiter system, and, by a smaller
margin, the Earth–Moon system. When a body at these points is perturbed, it
moves away from the point, but the factor opposite of that which is increased
or decreased by the perturbation (either gravity or angular momentum-induced
speed) will also increase or decrease, bending the object's path into a stable
, kidney-bean-shaped orbit around the point (as seen in the rotating frame of
reference). However, in the Earth–Moon case, the problem of stability is
greatly complicated by the appreciable solar gravitational influence.
1.5 Trajectory
A trajectory is
the path that a moving the object follows through space as a function of time.
The object might be a projectile or
a satellite, for example.
It thus includes the meaning of orbit—the path of
a planet, an asteroid or
a comet as it
travels around a central mass. A trajectory can be described mathematically
either by the geometry of the path, or as the position of the object over time.
Figure Illustration
showing the trajectory of a bullet fired at an uphill target
Range and height
Trajectories
of projectiles launched at different elevation angles but the same speed of 10
m/s in a vacuum and uniform downward gravity field of 10 m/s2. Points are at
0.05 s intervals and length of their tails is linearly proportional to their
speed. t = time from launch, T = time of
flight, R = range and H = highest point of trajectory
(indicated with arrows).
The range, R, is the greatest distance the object travels along the x-axis in the I
sector. The initial velocity, vi, is the speed at which
said object is launched from the point of origin. The initial angle, θi, is the angle at which said
object is released. The g is
the respective gravitational pull on the object within a null-medium.
The height, h, is the greatest
parabolic height said object reaches within its trajectory
Hard Stuff
In terms of
angle of elevation 
and
initial speed 
:
giving the
range as
This equation
can be rearranged to find the angle for a required range
(Equation II: angle of projectile
launch)
Note that
the sine function
is such that there are two solutions for for a
given range 
. The
angle giving
the maximum range can be found by considering the derivative or 
with
respect to and setting it
to zero.
which has a
nontrivial solution at 
, or 
. The maximum range is then 
.
At this angle
, so
the maximum height obtained is 
.
To find the
angle giving the maximum height for a given speed calculate the derivative of
the maximum height 
with
respect to , that is 
which is zero when 
. So the
maximum height
Unit –ii
2.1 Gravitational keyhole
A gravitational keyhole is a tiny
region of space where a planet's gravity would alter the orbit of a
passing asteroid such that
the asteroid would collide with that planet on a given future orbital pass. The
word "keyhole" contrasts the large uncertainty of trajectory
calculations (between the time of the observations of the
asteroid and the first encounter with the planet) with the relatively narrow
bundle(s) of critical trajectories. The term was coined by P. W. Chodas in
1999. It gained some public interest when it became clear, in January 2005,
that the Asteroid (99942 Apophis would miss the
earth in 2029 but may go through one or another keyhole leading to impacts in
2036 or 2037. This has been ruled out in 2012.
Keyholes for
the nearer or farther future are named by the numbers of orbital periods of the
planet and the asteroid, respectively, between the two encounters There are
even more but smaller secondary keyholes, with trajectories
including a less close intermediate encounter (bank shots). Secondary gravitational keyholes are
searched for by importance
sampling: Virtual asteroid trajectories (or rather their ‘initial’
values at the time of the first encounter) are sampled
according to their likelihood given the
2.2 elliptical
orbit
Due to
observational inaccuracies, bias in the frame of reference stars, and largely
unknown non-gravitational forces on the asteroid, mainly the Yarkovsky effect, its position
at the predicted time of encounter is uncertain in three dimensions. Typically,
the region of probable positions is formed like a hair, thin and elongated,
because visual observations yield 2-dimensional positions at the sky but no
distances. If the region is not too extended, less than about one percent of
the orbital radius, it may be represented as a 3-dimensional uncertainty ellipsoid and the
orbits (ignoring the interaction) approximated as straight lines.
Now imagine a
plane comoving with the planet and perpendicular to the incoming velocity of
the asteroid (unperturbed by the interaction). This target plane is
named b-plane after the collision parameter b,
which is the distance of a point in the plane to the planet at its coordinate
origin. Depending on a trajectory's position in the b-plane its post-encounter
direction and kinetic energy is affected. The orbital energy is directly
related to the length of the semi-major axis and also
to the orbital period. If the post-encounter orbital period of the asteroid is
a fractional multiple of the orbital period of the planet, there will be a
close encounter at the same orbital position after the given numbers of orbits.
According to theory of close encounters, the set
of points in the b-plane leading to a given resonance ratio forms a circle.
Lying on this circle are the planet and two gravitational keyholes, which
are images of the
planet in the b-plane of the future encounter (or rather of the slighly larger
catchment area due to gravitational focusing). The form of the keyholes is a
small circle elongated and bent along the circle for the given resonance ratio.
The keyhole which is closer to the planet is smaller than the other because the
variation of deflection becomes steeper with decreasing collision
parameter b
Accuracy may matter
Relevant
keyholes are those which are close to the uncertainty ellipsoid projected onto
the b-plane, where it becomes an elongated ellipse. The ellipse shrinks and
jitters as new observations of the asteroid are added to the evaluation. If the
probable path of the asteroid keeps close to a keyhole, the precise position of
the keyhole itself would matter. It varies with the incoming direction and
velocitiy of the asteroid and with the non-gravitational forces acting on it
between the two encounters. Thus, “a miss is as good as a mile,” does not apply
to a keyhole of several hundred meter width. However, changing the path of an
asteroid by a mile is not a huge task if the first encounter is still
years away. Deflecting the asteroid after the fly-by would need a much stronger
kick.
For a rapidly
rotating planet as the earth, calculation of trajectories passing close to it,
less than a dozen radii, shall include the oblateness of the planet—its
gravitational field is not spherically symmetric. For even closer
trajectories, gravity
anomalies may be important.
For a large
asteroid (or comet) passing close to the Roche limit, its size,
which is inferred from its magnitude, affects not
only the Roche limit but also the trajectory because the center of
gravitational force on the body deviates from its center of mass resulting in a
higher-order tidal
force shifting the keyhole.
2.3 Hohmann
transfer orbit
The orbital maneuver to
perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the
transfer orbit and a second to move off it. This maneuver was named after Walter Hohmann, the German scientist
who published a description of it in his 1925 book Die Erreichbarkeit
der Himmelskörper (The Accessibility of Celestial Bodies). Hohmann
was influenced in part by the German science fiction author Kurd Laßwitz and his
1897 book Two
Planets.
stage
The diagram
shows a Hohmann transfer orbit to bring a spacecraft from a lower circular
orbit into a higher one. It is one half of an elliptic orbit that
touches both the lower circular orbit that one wishes to leave (labeled 1 on
diagram) and the higher circular orbit that one wishes to reach (3 on
diagram). The transfer (2 on diagram) is initiated by firing the
spacecraft's engine in order to accelerate it so that it will follow the
elliptical orbit; this adds energy to the spacecraft's orbit. When the
spacecraft has reached its destination orbit, its orbital speed (and hence its
orbital energy) must be increased again in order to change the elliptic orbit
to the larger circular one.
Due to
the reversibility of orbits, Hohmann
transfer orbits also work to bring a spacecraft from a higher orbit into a
lower one; in this case, the spacecraft's engine is fired in the opposite
direction to its current path, decelerating the spacecraft and causing it to
drop into the lower-energy elliptical transfer orbit. The engine is then fired
again at the lower distance to decelerate the spacecraft into the lower
circular orbit.
The Hohmann
transfer orbit is theoretically based on two instantaneous velocity
changes. Extra fuel is required to compensate for the fact that in reality the
bursts take time; this is minimized by using high thrust engines to minimize
the duration of the bursts. Low thrust engines can perform an approximation of
a Hohmann transfer orbit, by creating a gradual enlargement of the initial
circular orbit through carefully timed engine firings. This requires a change in velocity (delta-v)
that is up to 141% greater than the two impulse transfer orbit (see also
below), and takes longer to complete.[citation needed]
Calculation
For a small
body orbiting another, very much larger body (such as a satellite orbiting the
earth), the total energy of the body is the sum of its kinetic energy and
potential energy, and this total energy also equals half the potential at the
average distance , (the semi-major
axis):
Solving this
equation for velocity results in the Vis-viva equation,
Where
Is the speed of an orbiting body?
• is the standard gravitational
parameter of the primary body, assuming
is not significantly bigger than
(which makes)
• is the distance of the orbiting body
from the primary focus
• is the semi-major axis of the body's
orbit.
• Therefore the delta-v required for
the Hohmann transfer can be computed as follows, under the assumption of instantaneous
impulses:
Where and
are, respectively, the radii of the departure and arrival circular
orbits; the smaller (greater) of and corresponds to the periapsis distance
(apoapsis distance) of the Hohmann elliptical transfer orbit. The total is then:
Whether moving into a higher or lower orbit,
by Kepler's third law, the time taken
to transfer between the orbits is:
A horseshoe orbit is a type
of co-orbital motion of a
small orbiting body relative to a larger orbiting body (such as Earth). The
orbital period of the smaller body is very nearly the same as for the larger
body, and its path appears to have a horseshoe shape in a rotating reference frame as viewed
from the larger object.
The loop is not
closed but will drift forward or backward slightly each time, so that the point
it circles will appear to move smoothly along Earth's orbit over a long period
of time. When the object approaches Earth closely at either end of its
trajectory, its apparent direction changes. Over an entire cycle the center
traces the outline of a horseshoe, with the
Earth between the 'horns'.
Saturn's moons Epimetheus and Janus occupy
horseshoe orbits with respect to each other (in their case, there is no
repeated looping: each one traces a full horseshoe with respect to the other).
Explanation of
horseshoe orbit
The following
explanation relates to an asteroid which is in such an orbit around the Sun, and is also
affected by the Earth.
The asteroid is
in almost the same solar orbit as Earth. Both take approximately one year to
orbit the Sun.
It is also
necessary to grasp two rules of orbit dynamics:
1.
A body closer to the Sun completes an
orbit more quickly than a body further away.
2.
If a body accelerates along its orbit,
its orbit moves outwards from the Sun. If it decelerates, the orbital radius
decreases.
The horseshoe
orbit arises because the gravitational attraction of the Earth changes the
shape of the elliptical orbit of the asteroid. The shape changes are very small
but result in significant changes relative to the Earth.
The horseshoe
becomes apparent only when mapping the movement of the asteroid relative to
both the Sun and the Earth. The asteroid always orbits the Sun in the same
direction. However, it goes through a cycle of catching up with the Earth and
falling behind, so that its movement relative to both the Sun and the Earth
traces a shape like the outline of a horseshoe.
Stages of the orbit
Figure 1. Plan showing possible orbits along gravitational contours.
In this image, the Earth (and the whole image with it) is rotating
counterclockwise around the Sun.
Starting out at
point A on the inner ring between L5 and
Earth, the satellite is orbiting faster than the Earth. It's on its way toward
passing between the Earth and the Sun. But Earth's gravity exerts an outward
accelerating force, pulling the satellite into a higher orbit which (per Kepler's
third law) decreases its angular speed.
figure 2 : thin horseshoe orbit
When the
satellite gets to point B, it is traveling at the same speed as Earth. Earth's
gravity is still accelerating the satellite along the orbital path, and
continues to pull the satellite into a higher orbit. Eventually, at C, the
satellite reaches a high enough, slow enough orbit and starts to lag behind
Earth. It then spends the next century or more appearing to drift 'backwards'
around the orbit when viewed relative to the Earth. Its orbit around the Sun
still takes only slightly more than one Earth year.
2.5 Gravity assist
The
"assist" is provided by the motion of the gravitating body as it
pulls on the spacecraft. The technique was first proposed as a mid-course
manoeuvre in 1961, and used by
interplanetary probes from Mariner 10 onwards,
including the two Voyager probes'
notable fly-bys of Jupiter and Saturn
Elastic
collision
A gravity
assist or slingshot maneuver around a planet changes a spacecraft's velocity relative
to the Sun, though the
spacecraft's speedrelative to the
planet on effectively entering and leaving its gravitational field, will remain
the same (as it must according to the law of conservation of energy). To a first
approximation, from a large distance, the spacecraft appears to have bounced
off the planet. Physicists call this an elastic collision even
though no actual contact occurs. A slingshot maneuver can therefore be used to
change the spaceship's trajectory and speed relative to the Sun.
A close
terrestrial analogy is provided by a tennis ball bouncing off a moving train.
In the cartoon at right, a boy throws a ball at 30 mph toward a train
approaching at 50 mph. The engineer of the train sees the ball approaching
at 80 mph and then departing at 80 mph after the ball bounces
elastically off the front of the train. Because of the train's motion, however,
that departure is at 130 mph relative to the station.
Over-simplified
example of gravitational slingshot: the spacecraft's velocity changes by up to
twice the planet's velocity
Translating
this analogy into space, then, a "stationary" observer sees a planet
moving left at speed U and a spaceship moving right at
speed v. If the spaceship has the proper trajectory, it will pass
close to the planet, moving at speed U + v relative to the
planet's surface because the planet is moving in the opposite direction at
speed U. When the spaceship leaves orbit, it is still moving
at U + v relative to the planet's surface but in the opposite
direction (to the left). Since the planet is moving left at speed U,
the total velocity of the rocket relative to the observer will be the velocity of
the moving planet plus the velocity of the rocket with respect to the planet.
So the velocity will be U + ( U + v ), that is 2U + v.
This
oversimplified example is impossible to refine without additional details
regarding the orbit, but if the spaceship travels in a path which forms aparabola, it can leave
the planet in the opposite direction without firing its engine, the speed gain
at large distance is indeed 2U once it has left the gravity of
the planet far behind.
This
explanation might seem to violate the conservation of energy and momentum, but
the spacecraft's effects on the planet have not been considered. The linear
momentum gained by the spaceship is equal in magnitude to that lost by the
planet, though the planet's enormous mass compared to the spacecraft makes the
resulting change in its speed negligibly small. These effects on the planet are
so slight (because planets are so much more massive than spacecraft) that they
can be ignored in the calculation.[2]
Realistic
portrayals of encounters in space require the consideration of three
dimensions. The same principles apply, only adding the planet's velocity to
that of the spacecraft requires vector addition, as shown
below.
2 dimensional schematic of gravitational slingshot. The
arrows show the direction in which the spacecraft is traveling before and after
the encounter. The arrows' length shows the spacecraft's speed.
Unit-iii
3.1 Communication network in space
DEFINITIONS FROM OSI BASIC
REFERENCE MODEL
Most
of the CCSDS space communications protocols are defined using the style
established
by
the Open Systems Interconnection (OSI) Basic Reference Model (reference
[2]). This
model
provides a common framework for the development of standards in the field of
systems
interconnection. It defines concepts and
terms associated with a layered architecture
and
introduces seven specific layers. The
concepts and terms defined in this model are
extensively
used in the Blue Books that define CCSDS space communications protocols. If
the
reader is not familiar with this model, an excellent introduction can be found
in a
textbook
on computer networks such as reference
2.2 PROTOCOL LAYERS
2.2.1 SUMMARY
A
communications protocol is usually associated with one of the seven layers
defined in the
OSI
Basic Reference Model (reference [2]).
Although some space communications protocols
do
not fit well with the OSI seven-layer model, this Report uses this model for
categorizing
the
space communications protocols.
The
space communications protocols are defined for the following five layers of the
ISO
Model:
·
Physical Layer;
·
Data Link Layer;
·
Network Layer;
·
Transport Layer;
·
Application Layer.
3.1Physical
layer
Compression
IPSec
Figure
2-1: Space Communications Protocols
Reference Model
Figure 2-2: Some Possible Combinations of Space
Communications Protocols
In
figure 2-1, there are two protocols that do not correspond to a single
layer. CCSDS File
Delivery
Protocol (CFDP) has the functionality of the Transport and Application
Layers.
3.2 PHYSICAL LAYER
CCSDS
has a standard for the Physical Layer called the Radio Frequency and Modulation
Systems
to be used for space links between
spacecraft and ground stations.
The
Proximity-1 Space Link Protocol also contains recommendations for the Physical
Layer
of
proximity space links.
3.2 DATA LINK LAYER
CCSDS
defines two Sub layers in the Data Link Layer of the OSI Model: Data Link Protocol
Sublayer
and Synchronization and Channel Coding Sublayer. The
Data Link Protocol
Sublayer
specifies methods of transferring data units provided by the higher layer over
a
space
link using data units known as Transfer Frames.
The Synchronization and Channel
Coding
Sublayer specifies methods of synchronization and channel coding for
transferring
Transfer
Frames over a space link.
CCSDS
has developed four protocols for the Data Link Protocol Sublayer of the Data
Link Layer:
a)
TM Space Data Link Protocol.
b)
TC Space Data Link Protocol.
c)
AOS Space Data Link Protocol
d)
Proximity-1 Space Link Protocol—Data Link Layer.
The
above protocols provide the capability to send data over a single space link.
CCSDS
has developed three standards for the Synchronization and Channel Coding
Sublayer
Data Link Layer:
a)
TM Synchronization and Channel Coding (reference [8]);
b)
TC Synchronization and Channel Coding (reference [9]);
c)
Proximity-1 Space Link Protocol—Coding and Synchronization Layer (reference
[19]).
TM
Synchronization and Channel Coding is used with the TM or AOS Space Data Link
Protocol,
TC Synchronization and Channel Coding is used with the TC Space Data Link
Protocol,
and the Proximity-1 Space Link Protocol—Coding and Synchronization Layer is
used
with the Proximity-1 Space Link Protocol—Data Link Layer.
2.2.4 NETWORK LAYER
Space
communications protocols of the Network Layer provide the function of routing
Higher-layer
data through the entire data system that includes both onboard and ground
Sub
networks.
CCSDS
has developed two protocols for the Network Layer:
a)
Space Packet Protocol
b)
SCPS Network Protocol (SCPS-NP).
In
some cases, Protocol Data Units (PDUs) of the Space Packet Protocol are
generated and
consumed
by application processes themselves on a spacecraft, instead of being generated
and
consumed by a separate protocol entity, and in these cases this protocol is
used both as a
Network
Layer protocol and as an Application Layer protocol.
PDUs
of a Network Layer protocol are transferred with Space Data Link Protocols over
a
The
following protocols developed by the Internet can also be transferred with
Space Data
Link
Protocols over a space link, multiplexed or not-multiplexed with the Space
Packet
Protocol
and/or SCPS-NP:
a)
Internet Protocol (IP), Version
b)
Internet Protocol (IP), Version
3.4 TRANSPORT LAYER
Space
communications protocols of the Transport Layer provide users with end-to-end
Transport
services.
CCSDS
has developed the SCPS Transport Protocol (SCPS-TP)
Transport
Layer. The CCSDS File Delivery Protocol
(CFDP) (reference [15]) also provides
PDUs
of a Transport Layer protocol are usually transferred with a protocol of the
Network
Layer
over a space link, but they can be transferred directly with a Space Data Link
Protocol
If
certain conditions are met.
Transport
protocols used in the Internet (such as TCP, , and UDP,
can also be used on top of SCPS-NP, IP Version
4, and IP Version 6 over
space
links.
SCPS
Security Protocol (SCPS-SP) and IPSec may
be used
with
a Transport protocol to provide end-to-end data protection capability.
3.5 APPLICATION LAYER
Space
communications protocols of the Application Layer provide users with end-to-end
application
services such as file transfer and data compression.
CCSDS
has developed three protocols for the Application Layer:
a)
SCPS File Protocol (SCPS-FP) (reference
b)
Lossless Data Compression
c)
Image Data Compression
The
CCSDS File Delivery Protocol (CFDP) provides the functionality of the
Application
Layer (i.e., functions for file management), but it also provides functions of
the
Transport
Layer.
Each
project (or Agency) may elect to use application-specific protocols not
recommended
By
CCSDS to fulfill their mission requirements in the Application Layer over CCSDS
space
Communications
protocols.
PDUs
of an Application Layer protocol (excluding CFDP) are usually transferred with
a
Protocol
of the Transport Layer over a space link, but they can be transferred directly
with a
Protocol
of the Network Layer if certain conditions are met.
Applications
protocols used in the Internet can also be used on
top
of SCPS-TP, TCP and UDP over space links.
UNIT – IV
SPACECRAFT PROPULSION
Spacecraft
propulsion is any method used to accelerate spacecraft and artificial
satellites. There are many different methods. Each method has drawbacks and
advantages, and spacecraft propulsion is an active area of research. However,
most spacecraft today are propelled by forcing a gas from the back/rear of the
vehicle at very high speed through a supersonic de Laval nozzle. This sort of
engine is called a rocket engine.
All
current spacecraft use chemical rockets (bipropellant or solid-fuel) for
launch, though some (such as the Pegasus rocket and SpaceShipOne) have used
air-breathing engines on their first stage. Most satellites have simple
reliable chemical thrusters (often monopropellant rockets) or resist jet
rockets for orbital station-keeping and some use momentum wheels for attitude
control. Soviet bloc satellites have used electric propulsion for decades, and
newer Western geo-orbiting spacecraft are starting to use them for north-south
station keeping and orbit rising. Interplanetary vehicles mostly use chemical
rockets as well, although a few have used ion thrusters and Hall Effect
thrusters (two different types of electric propulsion) to great success.
Types
of propulsion
·
Solid propellant
·
Liquid propellant
·
Semi-liquid propellant
·
Chemical propellant
·
Nuclear propellant
4.1 Solid
propellant
All rockets used some form of solid
or powdered propellant up until the 20th century,
when liquid rockets and hybrid rockets offered more efficient and controllable alternatives.
Solid rockets are still used today in model rockets and on larger applications for their simplicity and
reliability.
Since solid-fuel rockets can remain
in storage for long periods, and then reliably launch on short notice, they
have been frequently used in military applications such as missiles. The lower performance of solid propellants (as compared to
liquids) does not favor their use as primary propulsion in modern
medium-to-large launch vehicles customarily used to orbit commercial satellites
and launch major space probes. Solids are, however, frequently used as strap-on
boosters to increase payload capacity or as spin-stabilized add-on upper stages
when higher-than-normal velocities are required. Solid rockets are used
as light launch vehicles for low Earth orbit (LEO) payloads under 2 tons or
escape payloads up to 1100 pounds.
Design
Design begins with the total impulse required, which determines the fuel/oxidizer mass.
Grain geometry and chemistry are then chosen to satisfy the required motor
characteristics.
The following are chosen or solved
simultaneously. The results are exact dimensions for grain, nozzle, and case
geometries:
§ The grain burns at a predictable
rate, given its surface area and chamber pressure.
§ The chamber pressure is determined
by the nozzle orifice diameter and grain burn rate.
§ Allowable chamber pressure is a
function of casing design.
§ The length of burn time is
determined by the grain 'web thickness'.
The grain may or may not be bonded
to the casing. Case-bonded motors are more difficult to design since the
deformation of the case and the grain under flight must be compatible.
Common modes of failure in solid
rocket motors include fracture of the grain, failure of case bonding, and air
pockets in the grain. All of these produce an instantaneous increase in burn
surface area and a corresponding increase in exhaust gas and pressure, which
may rupture the casing.
Another failure mode is casing seal design. Seals are required in casings that have to be
4.2 Liquid
propellant
Another failure mode is casing seal design. Seals are required in casings that have to be
A liquid-propellant rocket or a liquid rocket is a rocket engine that uses propellants in liquid form. Liquids are desirable
because their reasonably high density allows the volume of the propellant tanks
to be relatively low, and it is possible to use lightweight pumps to pump the
propellant from the tanks into the engines, which means that the propellants
can be kept under low pressure. This permits the use of low mass propellant
tanks, permitting a high mass ratio for the rocket.
Liquid propellant rockets can
be throttled in realtime, and have control of mixture ratio; they
can also be shut down, and, with a suitable ignition system or self-igniting
propellant, restarted.
Liquid propellants are also
sometimes used in hybrid rockets, in which they are combined with a solid or gaseous
propellant.
Principle
of operation
All liquid rocket engines have tankage
and pipes to store and transfer propellant, an injector system, a combustion
chamber which is very typically cylindrical, and one (sometimes two or
more) rocket nozzles. Liquid systems enable higher specific impulse than solids and hybrid rocket engines and can provide
very high tankage efficiency.
Unlike gases, a typical liquid
propellant has a density similar to water, approximately 0.7-1.4g/cm³
(except liquid hydrogen which has a much lower
density), while requiring only relatively modest pressure to prevent
vapourisation.
This combination of density and low pressure permits very lightweight tankage;
approximately 1% of the contents for dense propellants and around 10% for
liquid hydrogen (due to its low density and the mass of the required
insulation).
For injection into the combustion
chamber the propellant pressure at the injectors needs to be greater than the
chamber pressure; this can be achieved with a pump. Suitable pumps usually useturbopumps due to their high power and lightweight, although
reciprocating pumps have been employed in the past. Turbopumps are usually
extremely lightweight and can give excellent performance; with an on-Earth
weight well under 1% of the thrust. Indeed, overall rocket engine thrust to weight
ratios including
a turbo pump have been as high as 133:1 with the Soviet NK-33rocket engine.
Alternatively, instead of a pump, a
heavy tank can be used, and the pump forgone; but the delta-v that the stage can achieve is often much lower due to
the extra mass of the tankage reducing performance; but for high altitude or
vacuum use the tankage mass can be acceptable.
A liquid rocket engine (LRE) can be
tested prior to use, whereas for a solid rocket motor a rigorous quality management must be applied during
manufacturing to ensure high reliability.[5] A LRE can also usually be reused for several flights,
as in the Space Shuttle.
Use of liquid propellants can be
associated with a number of issues:
§ Because the propellant is a very
large proportion of the mass of the vehicle, the center of mass shifts significantly rearward as the propellant is
used; one will typically lose control of the vehicle if its center mass gets
too close to the center of drag.
§ When operated within an atmosphere,
pressurization of the typically very thin-walled propellant tanks must
guarantee positive gauge pressure at all times to avoid catastrophic collapse of the
tank.
§ Liquid propellants are subject to slosh, which has frequently led to loss of control of the
vehicle. This can be controlled with slosh baffles in the tanks as well as
judicious control laws in the guidance system.
§ They can suffer from pogo oscillation where the rocket suffers from uncommanded cycles of
acceleration.
§ Liquid propellants often need ullage motors in zero-gravity or during
staging to avoid sucking gas into engines at start up. They are also subject to
vortexing within the tank, particularly towards the end of the burn, which can
also result in gas being sucked into the engine or pump.
§ Liquid propellants can leak,
especially hydrogen, possibly leading to the formation of an explosive mixture.
§ Turbopumps to pump liquid propellants are complex to design, and
can suffer serious failure modes, such as overspeeding if they run dry or
shedding fragments at high speed if metal particles from the manufacturing
process enter the pump.
§ Cryogenic
propellants,
such as liquid oxygen, freeze atmospheric water vapour into very hard crystals.
This can damage or block seals and valves and can cause leaks and other
failures. Avoiding this problem often requires lengthy chilldown procedures
which attempt to remove as much of the vapour from the system as possible. Ice
can also form on the outside of the tank, and later fall and damage the
vehicle. External foam insulation can cause issues as shown by the Space
Shuttle Columbia disaster.
Non-cryogenic propellants do not cause such problems.
§ Non-storable liquid rockets require
considerable preparation immediately before launch. This makes them less
practical than solid rockets for most weapon systems.
4.3 Nuclear
propellant
Nuclear propulsion includes a wide variety of propulsion methods that fulfill
the promise of the Atomic Age by
using some form of nuclear
reaction as their primary power source.
Many types of nuclear propulsion
have been proposed, and some of them (e.g. NERVA) tested, for spacecraft
applications:
Bimodal Nuclear Thermal Rockets - conduct nuclear fission reactions
similar to those employed at nuclear power plants including submarines. The
energy is used to heat the liquid hydrogen propellant. Courtesy of NASA Glenn
Research Center
Nuclear pulse propulsion
§ Project
Orion, first
engineering design study of nuclear pulse (i.e., atomic explosion) propulsion
Nuclear thermal rocket
§ Bimodal Nuclear Thermal Rockets conduct nuclear fission
reactions similar to those safely employed at nuclear power plants including
submarines. The energy is used to heat the liquid hydrogen propellant.
Advocates of nuclear powered spacecraft point out that at the time of launch,
there is almost no radiation released from the nuclear reactors. The
nuclear-powered rockets are not used to lift off the Earth. Nuclear thermal
rockets can provide great performance advantages compared to chemical
propulsion systems. Nuclear power sources could also be used to provide the
spacecraft with electrical power for operations and scientific instrumentation.
§ NERVA - NASA's Nuclear Energy for Rocket Vehicle
Applications, a US nuclear thermal rocket program
§ Project Prometheus, NASA development of nuclear
propulsion for long-duration spaceflight, begun in 2003
§ Project Rover - an American project to develop a nuclear thermal
rocket. The program ran at the Los Alamos Scientific Laboratory from 1955
through 1972.
Ramjet
Nuclear electric
§ RKA
(Russian Federal Space Agency) NPS Development
Anatolij Perminov, head of Russian
Space Agency announced that RKA is going to develop a nuclear powered
spacecraft for deep space travel. Design will be done by 2012, and 9 more years
for development (in space assembly). The price is set to 17 billion rubles (600
million dollars). The nuclear propulsion would have mega-watt class,
provided necessary funding, Roscosmos Head stated.
This system would consist of a space nuclear power and the matrix of ion
engines. "...Hot inert gas temperature of 1500 °C from the reactor turns
turbines. The turbine turns the generator and compressor, which circulates the
working fluid in a closed circuit. The working fluid is cooled in the radiator.
The generator produces electricity for the same ion (plasma)
engine..." [10]
According to him, the propulsion will be able to support human mission to Mars,
with cosmonauts staying on the Red planet for 30 days. This journey to Mars
with nuclear propulsion and a steady accelaration would take 6 weeks, instead
of 8 months by using chemical propulsion - assuming thrust of 300 times higher
than that of chemical propulsion
Analysis
the performance of chemical propellant
,
we note again the existence of a zone AC
The propellants go from a series of liquid
jets issuing through a multiplicity
Of
small injector holes, through breakup of these jets into droplets, impingement
Of jets or droplet streams on each other,
dispersion of the
Droplets
into a recirculating mass of combustion products, evaporation of the
Droplets,
interdiffusion of the vapors and
kinetically controlled combustion. These
Are
obviously complicated processes, and a comprehensive analysis good enough
For
first principles design requires large-scale computation In fact,
the
largest number of existing liquid rocket combustors, those dating from before
1970,
were developed mainly through empirical methods, supplemented by very
Extensive
testing. Improved modeling and computational capabilities have more
Recently
permitted a more direct approach, with fewer hardware iterations, but
Theory
is still far from completely developed in this area, and serves at this point
Mainly
to ascertain trends and verify mechanisms. For an in-depth discussion of
Liquid
propellant combustion, Here we will only review the
Fundamental
concepts which underlie current spray combustion models
COMBUSTION INSTABILITIES IN LIQUID
ROCKETS
rocket
engines is brief,
but nevertheless we shall often
refer to results achieved
in
other systems as well, especially to encourage workers in the field to be aware
of, if not
conversant with, combustion
instabilities in all
types of propulsion
systems.
To begin
to understand the
essential characteristics of combustion
instabilities, it is
best first to
distinguish linear and
nonlinear behavior. Linear
behavior presents only one
general problem, linear
instability, which received
widespread attention
during the 1950s
and 1960s; see,
e.g., the monograph
by Crocco and Cheng
l
and the
comprehensive compilation of works
edited by
Harrje and Reardon.2
Any disturbance may be synthesized as an infinite series
of
harmonic motions. An approximate
analysis developed over many years (see
3
and Culick
and Yang
) allows
one to use
classical acoustic modes
as
the terms
in the series and
to compute the perturbations
of the complex wave
number
for each
mode due to
various contributing processes
in a combustion
chamber. The real
part of the wave
number gives the
frequency shift, and
the
imaginary
part gives the growth (or decay)
constant associated with each mode.
Vanishment
of the imaginary part determines the formal condition for linear
stability, whose dependence
on the parameters
characterizing the system
is then
known.
Two basic nonlinear
problems arise when
dealing with combustion
instabilities: determining the conditions for the existence and stability of
limit cycles for a
linearly
unstable system and finding the conditions under which a linearly stable
system
may become unstable to a sufficiently large disturbance. In the language
of
modern dynamical systems theory, these two problems are identified as
supercritical and subcritical bifurcations, respectively. The term
bifurcation refers to
the
characteristic that the character of the steady behavior of the system suffers
a
qualitative
change abruptly as a parameter of the system is varied continuously.
This
may at first seem an unnecessarily formal description of the phenomenon. In
fact, the framework provided by the approximate analysis and application of
some
of
the ideas of dynamical systems theory forms
a widely useful and
convenient basis for understanding combustion instabilities
Unit -5
5.1 Space travel
According to current
reports in the media, travelling to outer space should become possible for
everyone by the beginning of the next century. In April 1998, the newspaper
Berlin Morgenpost reported that the international Hilton Hotel corporation is planning the
construction of a 5-star hotel, the "Lunar Hilton ," on the Moon. A
team of British architects was commissioned to develop plans for the gigantic
building project. The luxury hotel with 5000 beds and a height of 325 metres
provides its own beach at its private "ocean," and should be equipped
with all the amenities one can expect from a first class hotel.
|
·
|
|
|
|
Fig. 2:
The space tourism roadmap with its four sub-scenarios [ESA98, ESA99]
However,
the short-term realisation of this utopian project of the Hilton Group will most likely take
a little more time, and for the first half of the 21st century it must be
regarded as pure science fiction. Apart from the technical feasibility of
some of the construction plans, economic analyses performed by DLR and
the Technical University of Berlin show that the transportation
of humans and building materials to the Moon would be extraordinarily
expensive, even if very optimistic economic conditions in space operations
are assumed [LAssMANN94, REICHERT97a]. With the announcement of its
spectacular project, the HiltonCorporation competes with three
Japanese corporations, Shimizu, the construction firm
Nishimatsu, and Obayashi, all of which have already invested millions into
futuristic colonising concepts for the moon.
Life-cycle
cost analyses performed in [ESA99, REICHERT97b/c/d] for the planet Mars
indicate, that the transportation of humans would require ticket prices in
the range of hundreds of millions of dollars, even if very favourable
economic conditions in space operations are assumed. In addition, one must
consider that after the successful completion of the Apollo program no
transportation infrastructure is currently available that would allow humans
to be transported beyond the Earth orbital. The creation of such a new
infrastructure would require investments of billions of dollars. The Moon and
Mars are therefore not likely to play a role in international tourism in the
first half of the next century, although Mars represents one of the most
promising travel destination because of its many similarities to Earth and
its potential of possible former life forms.
Fig. 3:
The first humans explore the Martian surface
Therefore
future space tourism will focus for a long time on Earth orbit which can be
reached more easily. Figure 2 shows the expected roadmap for space tourism
for the next decades with its four sub-scenarios. It is likely, that the
space tourism business is initiated by very short suborbital flights,
followed by short Earth orbital tourism in advanced, reusable spacecraft
which allow several orbits around Earth. Before extended stays in space
hotels will become a reality in the far future, touristic trips to existing orbital
facilities (e.g. the international space station) might represent an
intermediate step.
Already
since the mid-sixties, several important analyses of Earth orbital space
tourism have been carried out [EHRICKE67]. Various scenarios of
transportation and accommodation of tourists in space have been analysed in
the frame of industrial research in Japan, increasingly over the last 10
years [COLLINS97, MATSUMOTO97]. In the United States, NASA and the American "Space
Transportation Association" have completed a study of
the feasibility of space tourism with some promising results [O'NEIL97] in
1998. Furthermore, DASA ( DaimlerChrysler Aerospace) investigates touristic
spacecraft and space hotel concepts and supported the first international
symposium on space tourism in the spring of 1997, which took place in Bremen
(Germany) and attracted more than 100 experts from around the world. The
symposium also found a significant echo in the media. Moreover, in 1998/99,
the general feasibility and economics of space tourism played also a
considerable role in an ESA study under the lead of DLR
[ESA98, ESA99, REICHERT98]. All of these activities indicate that space
tourism is gaining more and more attention and significance. Today, it is
already possible to book atmospheric parabolic flights in aeroplanes for the
short-term simulation of zerogravity, and to reserve future passenger flights
into suborbital space, even though the technology for the latter has not been
developed yet.
5.2 THE INDUSTRIAL SIGNIFICANCE OF
FUTURE SPACE TOURISM
According
to an estimate of the World Travel Tourism Council, annual global expenditures
in the terrestrial tourism sector amount to about 3400 billion US dollars for
the year 1995. Tourism thus globally represents one of the largest
industries. If it would be possible to shift only a few percent of the
world-wide terrestrial tourist expenditures to a future space tourism market,
this could double the civil space budgets to 60 billion dollars. This would
create up to half a million new jobs also in the high technology space
industry, if it is assumed that a sales volume of $50000 to $250000 creates
one job.
If a
space tourism business can be established in the future, the scientific and
operational know-how - globally gained after decades of research and
experience in manned space flight (e.g. by astronaut training centers or
institutions of aerospace medicine) - could be applied to the space flight
preparation and medical supervision of future space tourists. Furthermore,
touristic spaceflights could be planned, controlled and monitored by existing
space operation centers in Europe, the USA or Russia. As soon as a space
tourism market is established, large commercially oriented industrial
conglomerates will cooperate in strategic alliances to operate and expand the
space tourism business comparable to the terrestrial tourism and
telecommunications industries. The main motivation for an industrial
investment in the space tourism sector will be the potential of very high
achievable profits, which can be expected due to multi-billion dollar market
potential.
5.3
THE MARKET FOR SPACE TOURISM
As soon
as the "space ticket" can be purchased for some $10000 - in the
best of all cases a ticket price comparable to that of a transatlantic flight
with the Concorde - one can expect that a global space tourism market will be
established. This has been confirmed by first national and international
polls and market analyses (e.g. in the US, Japan, Europe) which indicate that
a remarkable segment of clients would be already willing to make considerable
financial commitments for short trips into space. For example, 4.3% of all
Germans are willing to pay several $10000 - which is roughly comparable to an
annual income - for a space trip [ABITZSCH97]. This could be a ticket price
which might be achievable with future generations of spacecraft, and it is
comparable to the cost of a vacation on a cruise ship which already attracts
a steady clientele. Figure 4 shows the expected number of passengers for a
space trip as a function of the ticket costs according to international polls
performed in the US, Japan, and Europe. With current costs of several ten
million dollars to transport a human into space, space tourism is not
affordable and finds no acceptance in the public.
However,
with declining space travel ticket prices the situation will change. Once a
ticket price of $ 1000 is obtainable, a passenger volume of about 20 million
is expected, and even with a ticket price of $ 50000 a passenger rate of 1
million per year can be expected. [ABITZSCH97]. Nevertheless, the above
mentioned polls have to be critically assessed with respect to their accuracy
and credibility. Therefore, more detailed and representative polls and market
research in this area have to be carried out.
Fig. 4:
Expected passengers as a function of the cost/price per ticket [ABITZSCH97]
Generally,
any average person in good health and with appropriate preparation is able to
go on a space trip. NASA, for example, just recently
decided to send 77-year old former astronaut and Senator John Glenn into
space with the Space Shuttle (Fig. 5). He took part in important medical
research experiments from which especially the older generation will profit.
Fig. 5:
A space trip at the age of 77 years: Ex-astronaut and US-Senator John Glenn
[NEWSWEEK]
5.4 FUTURE MANNED SPACE
TRANSPORTATION SYSTEM
The fact
that tourist space travel has not been established yet is mostly due to the
high costs of manned space travel. The transportation of a passenger into
orbit, for example with the Russian rocket launcher Soyuz still costs several
$10 million. Therefore, alternative and less expensive space transportation
system concepts have to be identified.
Already
in 1979, a manned Space Shuttle was proposed in [DURST79], with a cabin
module designed to offer a seat capacity for 74 passengers (fig. 6). The
costs for this design were calculated in 1997 to be $3.6 million per
passenger, assuming a launch rate of 12 flights per year [KOELLE97].
Fig. 6:
A modified Space Shuttle with a seat capacity of 74 Passengers [DURST79]
A
further reduction of the costs is only expected by the development of
advanced, reusable single-staged spacecraft. An example of such a spacecraft
is the Japanese design for the single staged Kankoh-Maru launcher (fig. 7)
[COLLINS97]. This model with a capacity of 50 passengers is propelled by
oxygen/hydrogen engines and is supposed to be operated like regular airplanes
on conventional airports.
Fig. 7:
The Japanese Kankoh-Maru single
stage vehicle in comparison with a Boeing 737
and 747 aircraft [COLLINS97]
The
launch costs for this design are estimated in [KOELLE97] to be $300000 per
passenger (assuming 10 launches per year) and and in [ESA98] to be about
$50000 to $100000 (optimistically assuming 1 launch per day). The
illustration shows the Japanese single staged launcher in comparison to
a Boeing 747 and 737.
A
further considerable cost reduction - ticket prices ranging from $10000 to $100000
- can therefore be only expected by the development of future generations of
launchers, which have extremely high launch rates, are fully reusable and are
operated with a minimum maintenance effort, comparable to today's aircraft
fleets in the commercial airline business. The X-33 Space Shuttle Successor
(fig. 8) - a one billion-dollar development program initiated by NASA, can be considered as a first
step to lower the transportation cost into space by using a single stage to
orbit launching system for the first time.
 Fig. 8: The American X-33concept[NASA
According
to the American company Zegrahm suborbital flights will play a major role,
already in the next decade, as a precursor to initiate touristic space trips.
These short space trips either consist of a vertical ascent into space or end
after one orbit around Earth with a landing at the departure airport.
Although the advanced technology for suborbital flights is not developed yet,
it is already possible to make reservations for such space trips for the
beginning of the next decade at a ticket price of about $100000. However, the
past experience shows, that the new development of high technology launchers
generally requires long periods of research and testing and also investments
typically in the range of several billion dollars. Taking these circumstances
into account, the cost calculations and especially the short time frame for
the first suborbital flights already for the beginning of the next decade
appears very optimistic. Moreover, the first X-prize (promising $10 million
prize for the first private manned rocket, which is launched to an altitude
of 100 kilometer) candidates ran out of business.
Another
project aims at the same objective: the proposed Ascender spaceplane (fig. 9) which is
designed to perform several flights per day with a crew of 4 members. Ascender is equipped with two
Williams-Rolls FJ44 turbofans and a Pratt & Whitney RL10 rocket engine.
After take-off from a conventional runway it performs a subsonic ascent to an
altitude of 8 kilometre on jet power by using its two turbofans (fig. 10).
Afterwards the rocket engine is ignited which lifts the spaceplane to an
altitude of about 100 km. After re-entry into the atmosphere the spaceplane
returns to the departure runway. The price per passenger is estimated
[ASHFORD97] to be $ 5000 within the next 10 to 20 years. This cost estimate
must be critically assessed, and appears too optimistic, especially in
comparison with military jets with one flight hour costing up to several $10000.
Furthermore, up to now, the RL10 rocket engine is not designed to be operated
fully reusable and several times a day.
Fig. 9:
The suborbital Ascender spaceplane
[ASHFORD97]
Fig. 10:
A typical ascent/descent trajectory of the Ascender spaceplane
[ASHFORD97]
This
might significantly increase the cost per flight and indicates that a costly
development program has to be initiated to modify the RL10 engine according
to the requirements of the Ascender spaceplane. Finally, Ascender s maximum take-off weight of only about 4000 kg seems very
optimistic and too low to fulfil the mission requirements. Nevertheless, the
generalAscender spaceplane approach looks promising and could result in an
important technological development program, which leads to a single stage to
orbit precursor
5.5 SPACE CRAFT OF EUROPE
For this
reason a first rough return on investment analysis has been carried out for
the suborbital scenario in [ESA98, ESA99]. Space tourism is expected to be
carried out by commercial companies which expect a profit from their
business. Furthermore, in general, initial investments for the development
and production have to be refinanced. Figure 11 shows the profit as a
function of the operational year including and excluding financing costs,
assuming a fare per passenger of $50000. If the financing costs are
neglected, a first profit can be achieved in the 9th operational year which
increases to about $36.6 billion in the 30th operational year. Considering
financing costs, the date of the first profit shiftes to the 11th year and
increases to about $34 billion in the 30th operational year. This decreased
profit is caused by financing costs, which sum up to about $2.5 billion
within the 30 year life cycle. The date of the first profit could be even
shifted to earlier years, if the repayment of the development and production
costs is spread over a longer period. Because of the relatively early return
of i nvestment and the high achievable profits, the suborbital flights
scenario generally looks very promising from an economic standpoint. This is
also confirmed by the fact, that international polls ind icate, that the
assumed ticket price of $50000 could lead to more than one million passengers
per year [ABITZSCH97]. Due to the fact, that the fleet of 10 spaceplanes is
only capable of transporting 43800 passengers per year, a further extension
of the suborbital flights business seems very likely with decreasing ticket
costs. However, it should kept in mind that the achieved profit mainly
depends on low operation costs per flight (currently not state of the art) and
the ability to realise the Ascender spaceplane with very low
mass budgets as designed by [ASHFORD97].
Fig. 11:
Return on investment analysis for the suborbital flights scenario [ESA98]
A
completely different design approach is implemented in the concept of the
single stage ALLTRA-M1 rocket (fig. 12) of the German FAR
research group, which could also represent a promising X-prize candidate
[FAR99]. A capsule, which can accommodate up to 3 crew members is mounted on
top of the rocket, which is able to reach an altitude of at least 100
kilometres during a vertical ascent. The ALLTRA-M1 rocket
has a total mass of only about 10 tons and has almost the dimensions of a
garage. The rocket is equipped with a hybrid propulsion system, in which
liquid oxygen (in the central tank) is burned up with ordinary solid plastics
in the lateral boosters. The hybrid propulsion system represents an
interesting propulsion alternative between the classical solid and
liquid/liquid propulsion systems. Its simple design, generous production
tolerances and environmentally friendly and inexpensive fuels, possibly
produced from recycled materials, make them a good candidate for low-cost
high power propulsion systems. Thus a complete refuelling of the ALLTRA-M1 rocket
costs only about $5000 and a 2-staged rocket concept could even reach a
stable orbit around Earth. However, the overall economy, the atmospheric
re-entry with acceptable G-loads, the soft landing and the general
reusability still have to be demonstrated for the ALLTRA-M1 rocket
in further studies.
Fig. 12:
The ALLTRA-M1 hybrid rocket [FAR99]
5.6 TOURISM IN SPACE HOTELS
In order
to provide longer touristic stays in Earth orbit, concepts for space hotels
have been investigated world-wide. In Japan, several designs for large-scale
space hotels were analysed in the context of industrial studies like
the Shimizu space hotel illustrated in
fig. 13 [MATSUMOTO97]. It has a total mass of 8000 tons and offers all
amenities and entertainment opportunities, one can expect from such a giant
hotel complex. It is difficult to imagine from a current standpoint, that
this giant hotel complex can be financed, built up and constructed in the
near future. However, this sophisticated hotel concept might represent the
second generation of space hotels maybe in the second half of the 21st
century.
Fig. 13:
The Japanese space hotel concept by Shimizu [MATSUMOTO97]
A
different design philosophy is considered in the Space Hotel Berlin concept
(fig. 14), which was evaluated to some extend at DLR in the context of
an ESA study [ESA98, ESA99]. For
this concept, mainly existing technologies are used by connecting modified
habitat modules derived from the International Space Station (e.g. COF) as
"apartments" to a circular ring-structure.
Fig. 14:
The rotating Space Hotel Berlin concept in Earth Orbit [REICHERT98,
ESA99]
Rotating
the circular structure with different velocities creates a wide variety of
artificial gravity levels. With regard to mass and costs, the Space
Hotel Berlin is about comparable to the International Space
Station . In case of a 100 percent rate of capacity utilization,
first rough life cycle cost analyses indicate that the accommodation of
tourists seems possible at a price of about $100000 per overnight stay. This
depends on the assumed life time of the space hotel complex, ranging from 10
to 30 years [ESA98, ESA99]. However, these costs do not include financing
cost (for refinancing the development and production phase), a profit for a
commercial company and the expensive Earth to LEO transportation of
the tourists. This means, that a space hotel can be realized at the earliest,
as soon as future generations of launchers provide extreme cost-efficient
tickets, which are decreased by a factor of about hundred. Moreover.
Figure
15 shows the major subsystems of one basic element, of which the Space
Hotel Berlin concepts consists
during the first build-up phase. The central subsystem is a cylindrical
"apartment"-module with a large panoramic window which is capable
to accommodate about 4 tourists. Connected to the module is a solar array
which provides in combination with a rechargeable battery pack sufficient
electrical energy for the flight phases when the space hotel enters into the
Earth's shadow for about 40 minutes. Furthermore, a multifunctional
connecting node, which can be entered by humans, is docked at the apartment
module. This node provides five further docking ports which can be used, if
needed in subsequent build-up phases, to connect additional apartment
modules. For safety reasons each node has its own rescue capsule, which can
be used in emergencies for the immediate return of the tourists back to
Earth. With respect to the main apartment axis, the connecting node is 30o
aligned, which causes the circular structure of the Space Hotel
Berlin with a capacity of about 50 tourists.
Fig. 15:
The basic element of the Space Hotel Berlin concept [REICHERT98, ESA98]
Figure
16 shows an artist view of the Space Hotel Europe concept,
which is derived from the circular structure of the Space Hotel Berlin to
simplify the rendezvous/docking man oeuvres and to improve the living
conditions.
Fig. 16:
TheSpace Hotel Europe concept [ESA99]
6. THE
FASCINATION OF SPACE TRAVEL
The
fact, that a significant portion of the public is willing to spend a lot of
money on space trips proofs that these are regarded as very promising and
fascinating. The confrontation with the high technology of space missions,
the heroic myth of astronauts, and the possibility of orbiting planet Earth
in just a little more than 80 minutes with a speed of about 30000 kilometers
per hour (compared to the 80 days needed a hundred years ago) will represent
for each tourist an unforgettable adventure and event. Furthermore, for the
first time in his life, the tourist in a space hotel will experience an
entirely different environment. Depending on the rotational velocity of
the Space Hotel Berlin various levels of artificial gravity
can be obtained, ranging from customary terrestrial gravity (1G) to Mars
gravity (1/3 G) and even Lunar gravity (1/6 G), i.e. a human being will weigh
only one sixth of his or her earthly weight. In the central node of the Space
Hotel Berlin there will be nearly zero gravity. Here the tourist can
experience weightlessness. How does one behave if one can not get from A to B
in a normal way and "above" or "below" are without meaning?
Many of the questions that astronauts were asked - how they manage eating,
sleeping, and personal hygiene - can be explored by tourists themselves. The zero
gravity area also offers fascinating opportunities for entirely new sorts of
entertainment, games and sports. For example a ball game in zero-gravity and
three-dimensional space. Or one can imagine a swimming pool. The water would
not be in a basin, but would float as wobbly water bubbles in space, some of
which are several meters in diameter, and one can swim and dive through them.
One can imagine that some tourists may want to use the zero-gravity zones for
future medical therapies: This could represent a first step towards a future
space hospital. Furthermore, the Coriolis force, which only appears within
rotating systems, will baffle the tourist, since it will push him, like a
magic force, into a certain direction, depending on his direction of
movement. Probably, the predominant part of the vacation will be spent with
the breathtaking view each tourist will have from the panoramic window of
each apartment onto the blue home planet from a distance of 400 kilometres.
Even if initially concentrating on his home city and country, soon the
tourist will discover earth with its thin and precious atmosphere and a wide
variety of picturesque structures on its surface as a totality without
national borders. On the other hand, the view of the infinite expanse of
outer space will dramatically symbolise that we owe our human existence,
history and future a singular, beautiful, tiny "grain of sand"
which we call Earth.
After
returning to Earth, the consciousness of many tourists may have changed; it
will be expanded and globalised with many potentially positive social
consequences, which could help, for example, to lower the dangers for
environmental pollution, local conflicts, and war. Once space tourism is
affordable to the broad public, space activities - especially manned space
programs - will develop and increase in a way that is hardly imaginable
today. A wide variety of space station concepts have been investigated for
decades (fig. 17) and first concepts for gigantic, circular cities in orbit
are available. Perhaps many humans increasingly will harbour the wish to
visit the more remote planetary worlds of Mars and of the Earth's Moon some
day, according to the Russian space pioneer Ziolkowksy who proclaimed around
the year 1900: "Earth is the cradle of humanity, but one cannot always
remain in the cradle."
Fig.17: Wernher
von Braun`s
ring-shaped space station of 1952
The
cover picture and some artist views in the text are provided by ALLTRA. You
are invited to visit the complete space gallery of ALLTRA
|
Glossary
Absolute Brightness
(Absolute Magnitude)
A measure of the
true brightness of an object. The absolute brightness or magnitude of an object
is the apparent brightness or magnitude it would have if it were located
exactly 32.6 light-years (10 parsecs) away. For example, the apparent
brightness of our Sun is much greater than that of the star Rigel in the
constellation Orion because it is so close to us. However, if both objects were
placed at the same distance from us, Rigel would appear much brighter than our
Sun because its absolute brightness is much larger.
Angular Resolution
The ability of
an instrument, such as a telescope, to distinguish objects that are very close
to each other. The angular resolution of an instrument is the smallest angular
separation at which the instrument can observe two neighboring objects as two
separate objects. The angular resolution of the human eye is about a minute of
arc. As car headlights approach from a far-off point, they appear as a single
light until the separation between the lights increases to a point where they
can be resolved as two separate lights.
Angular Size
The apparent
size of an object as seen by an observer; expressed in units of degrees (of
arc), arc minutes, or arc seconds. The moon, as viewed from the Earth, has an
angular diameter of one-half a degree.
Apparent Brightness
(Apparent Magnitude)
A measure of the
brightness of a celestial object as it appears from Earth. The Sun is the
brightest object in Earth's sky and has the greatest apparent magnitude, with
the moon second. Apparent brightness does not take into account how far away
the object is from Earth.
Arc Minute
One arc minute
is 1/60 of a degree of arc. The angular diameter of the full moon or the Sun as
seen from Earth is about 30 arc minutes.
Arc Second
One arc second
is 1/60 of an arc minute and 1/3600 of an arc degree. The apparent size of a
dime about 3.7 kilometers (2.3 miles) away would be an arc second. The angular
diameter of Jupiter varies from about 30 to 50 arc seconds, depending on its
distance from Earth.
Astronomer
A scientist who
studies the universe and the celestial bodies residing in it, including their
composition, history, location, and motion. Many of the scientists at the Space
Telescope Science Institute are astronomers. Astronomers from all over the
world use the Hubble Space Telescope.
Astronomical Unit (AU)
The average
distance between the Earth and the Sun, which is about 150 million kilometers
(93 million miles). This unit of length is commonly used for measuring the
distances between objects within the solar system.
Baseline
The distance
between two or more telescopes that are working together as a single instrument
to observe celestial objects. The wider the baseline, the greater the resolving
power.
Blueshift
The shortening
of a light wave from an object moving toward an observer. For example, when a
star is traveling toward Earth, its light appears bluer.
Celestial Sphere
An imaginary
sphere encompassing the Earth that represents the sky. Astronomers chart the
sky using the celestial coordinates of the sphere to locate objects in the
cosmos. This sphere is divided into 88 sections called constellations. Objects
are sometimes named for the major constellation in which they appear.
Collecting Area
The area of a
telescope’s primary light-collecting mirror. A telescope’s light-gathering
power rises with an increase in its collecting area.
Constellation
A geometric
pattern of bright stars that appears grouped in the sky. Ancient observers
named many constellations after gods, heroes, animals, and mythological beings.
Leo (the Lion) is one example of the 88 constellations.
Cosmic Abundances
The relative
proportions of chemical elements in the Sun, the solar system, and the local
region of the Milky Way galaxy. These proportions are determined by studies of
the spectral lines in astronomical objects and are averaged for many stars in
our cosmic neighborhood. For example, for every million hydrogen atoms in an
average star like our Sun, there are 98,000 helium atoms, 360 carbon atoms, 110
nitrogen atoms, 850 oxygen atoms, and so on.
Declination (DEC)
One of two
celestial coordinates required to locate an astronomical object, such as a
star, on the celestial sphere. Declination is the measure of angular distance
of a celestial object above or below the celestial equator and is comparable to
latitude. To familiarize yourself with declination, hold out your arm in the
direction of the North Star (Polaris). You are now pointing at plus 90 degrees
declination. Move your arm downward by 90 degrees. You are now pointing at 0
degrees declination.
Degree of Arc
One degree of
arc is 1/360 of a full circle. The apparent sizes of objects as seen from Earth
can be measured in degrees of arc. The angular diameter of the full moon or the
Sun as seen from Earth is one-half of a degree.
Differentiation
The separation
of heavy matter from light matter, thus causing a variation in density and
composition. Differentiation occurs in an object like a planet as gravity draws
heavier material toward the planet’s center and lighter material rises to the
surface.
Diffraction Grating
A device that
splits light into its component parts or spectrum. A diffraction grating often
consists of a mirror with thousands of closely spaced parallel lines, which
spread out the light into parallel bands of colors or distinct fine lines or
bars.
Ellipse
A special kind
of elongated circle. The orbits of the solar system planets form ellipses.
Field of View (FOV)
A telescope’s
viewing area, measured in degrees, arc minutes, or arc seconds. A telescope
that can just fit the full moon into its complete viewing area has a field of
view of roughly 30 arc minutes.
Geocentric
An adjective
meaning “centered on the Earth.” Most early civilizations had a geocentric view
of the universe.
Infrared Telescope
An instrument
that collects the infrared radiation emitted by celestial objects. There are
several Earth- and space-based infrared observatories. The Infrared Telescope
Facility, an Earth-bound infrared telescope, is the U.S. national infrared
observing facility at the summit of Mauna Kea, Hawaii. A planned space-based
infrared observatory is the Space Infrared Telescope Facility (SIRTF).
Interferometer
An instrument
that combines the signal from two or more telescopes to produce a sharper image
than the telescopes could achieve separately.
Jets
Narrow,
high-energy streams of gas and other particles generally ejected in two
opposite directions from some central source. Jets appear to originate in the
vicinity of an extremely dense object, such as a black hole, pulsar, or
protostar, with a surrounding accretion disk. These jets are thought to be
perpendicular to the plane of the accretion disk.
Kepler’s Laws
Three laws,
derived by 17th century German astronomer Johannes Kepler, that describe
planetary motion.
Kepler’s first
law: The orbits of planets are ellipses, with the Sun at one focus. Therefore,
each planet moves in an elliptical orbit around the Sun.
Light Curve
A plot showing
how the light output of a star (or other variable astronomical object) changes
with time.
Light-Year
The distance
that a particle of light (photon) will travel in a year — about 10 trillion kilometers
(6 trillion miles). It is a useful unit for measuring distances between stars.
Luminosity
The amount of
energy radiated into space every second by a celestial object, such as a star.
It is closely related to the absolute brightness of a celestial object.
Megaparsec (MPC)
Equals one
million parsecs (3.26 million light-years) and is the unit of distance commonly
used to measure the distance between galaxies.
North Celestial Pole (NCP)
A direction
determined by the projection of the Earth’s North Pole onto the celestial
sphere. It corresponds to a declination of +90 degrees. The North Star,
Polaris, sits roughly at the NCP.
Observable Universe
The portion of
the entire universe that can be seen from Earth.
Optical Telescope
A telescope that
gathers and magnifies visible light. The two basic types of optical telescopes
are refracting (using lenses) and reflecting (using mirrors). The Hubble Space
Telescope is an example of a reflecting telescope.
Parallax
The apparent
shift of an object’s position when viewed from different locations. Parallax,
also called trigonometric parallax, is used to determine the distance to nearby
stars. As the Earth’s position changes during its yearly orbit around the Sun,
the apparent locations of nearby stars slightly shift. The stars’ distances can
be calculated from those slight shifts with basic trigonometric methods.
Parsec (PC)
A useful unit
for measuring the distances between astronomical objects, equal to 3.26
light-years and 3.085678 * 1013 kilometers, or approximately 18 trillion miles.
A parsec is also equivalent to 103,132 trips to the Sun and back.
Period-Luminosity Law
A relationship
that describes how the luminosity or absolute brightness of a Cepheid variable
star depends on the period of time over which that brightness varies.
Photometer
An instrument
that measures the intensity of light. Astronomers use photometers to measure
the brightness of celestial objects.
Photometry
A technique for
measuring the brightness of celestial objects.
Proper Motion
The apparent
motion of a star across the sky (not including a star’s parallax), arising from
the star’s velocity through space with respect to the Sun.
Radial Motion
The component of
an object’s velocity (speed and direction) as measured along an observer’s line
of sight.
Recessional Velocity
The velocity at
which an object moves away from an observer. The recessional velocity of a
distant galaxy is proportional to its distance from Earth. Therefore, the
greater the recessional velocity, the more distant the object.
Redshift
The lengthening
of a light wave from an object that is moving away from an observer. For
example, when a galaxy is traveling away from Earth, its light shifts to the
red end of the electromagnetic spectrum.
Reflector
A type of
telescope, also known as a reflecting telescope, that uses one or more
polished, curved mirrors to gather light and reflect it to a focal point.
Refractor
A telescope,
also known as a refracting telescope, that uses a transparent lens to gather light
and bend it to a focus.
Revolution
The orbital
motion of one object around another. The Earth revolves around the Sun in one
year. The moon revolves around the Earth in approximately 28 days.
Right Ascension (RA)
A coordinate
used by astronomers to locate stars and other celestial objects in the sky.
Right ascension is comparable to longitude, but it is measured in hours,
minutes, and seconds because the entire sky appears to pass overhead over a
period of 24 hours. The zero hour corresponds to the apparent location of the
Sun with respect to the stars on the day of the vernal (spring) equinox
(approximately March 21).
Roche Limit
The smallest
distance at which two celestial bodies can remain in a stable orbit around each
other without one of them being torn apart by tidal forces. The distance
depends on the densities of the two bodies and their orbit around each other.
