Starfleet Academy
Graduation Exam
(ASE
166MlSpring
1992)
From the groundtrack shown below:
a. Determine the inclination of the spacecraft's orbi
b. Determine the period of the orbit.
C.
identify whether the orbit is circular or ~ l l i ~ t i c .
(B)
Starfleet Command has decided to launch an Earth-observing satellite to update
the current Earth-surface height model using radar altimetry measurements.
The mission will require a nodal spacing of 5 degrees and the satellite
orbit must repeat itself in 1 sidereal day. Calculate the orbital ~ e r i o d
required to complete this mission.
$5-3
2 ( A ) List at least 5 types of perturbing forces felt by spacecraft in Low-Earth Orbit.
(B) Orbit perturbing forces can cause 3 types of time-dependent variations in
orbit elements (2 of which are closely related). LiSt the 3 types and show
&ketch) the time varying behavior of an element (say Q ) that is experiencing
all 3 types of variations. Which type of variation is most important for longterm analysis?
As one of the first settlers to reach the robotically-constructed Mars base at
Utopia Planitia you are faced with a serious dilemma. Your NUKE power supply
is not operating properly and you must launch a satellite into orbit 40 collect
solar energy which can then be beamed (using microwave technology) down
to the base. The satellite must be placed in a solar svnchronous Martian orbit
(orbits Mars with the orbital plane always facing the Sun). The orbit p e r i o d
must be 4 hours and the orbit can have an eccentricity of 0.5. What
inclination is needed for the required orbit? Use the following data:
r~~~~ = 3397.2 km
p~~~~ = 42828.287 krn3/s2
P M a r S = orbital period of Mars about the Sun = 686.98 solar days
J2hfars = 0.001 962 8
aMars = 227 941 040 km
psun = 1.327 124 38 x lo1 km3/s2
f
5
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3 ( A ) A space probe is to bc launchcd from Fcdcration Starbasc Earth-1 in LEO (300
km alt.) to flyby Saturn (on thc sunlit sidc) whcrc i t will photograph and
rcturn data on a large storm developing in the atmosphcrc. Thc probe must
pass within 200 km (altitude) of Saturn's surficc to obtain accuratc
measurements. Assumc all orbits lie in the same plane (LEO, Earth, Saturn,
Given the following data:
Starbase Earth-1:
...).
alt. = 400 km
RE = 6378.145 krn
p~ = 398 600.44 km3/s2
a~ = 149 597 927 km
g~ = 9.81 m/s2
- .
Saturn:
Sun:
Compute: (1) The AV needed to leave Earth orbit.
(2) The eccentricity of the hyperbolic flyby orbit at Saturn.
(3) The turning angle of the flyby orbit at Saturn.
(B)
Assume the NOMAD-class probe has an initial mass of 500 kg and its propulsion
system has an Isp = 1000 seconds. Using the AV from part (1). calculate how
much of the probe's initial mass is fuel (kg).
4 ( A ) Six orbit elements can be used to describe an orbit in space.
(1)
(2)
List and define (name) the six classical orbital elements.
Label the elements shown in the figure (4 angles).
(B) Fill in the table of properties for the four types of conic section orbits:
(State whether each quantity is less than zero, equal to zero, or greater than
zero.)
Conic
Circle
Ellipse
Parabola
Hyperbola
Energy
Semi-major axis
a 7 0 lC\n:k)
Eccentricity
e=O
Jwf\
)
r
a.
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p
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