MAE 4410: Fundamentals of Astronautics
Homework #4
DUE: 03 MAR 2008
1. For a given orbit inclination around the Earth describe what happens to the ground track
for the following orbits as the semi-major axis is increased.
a. Non-rotating Earth
b. Rotating Earth
2.
A geosynchronous satellite with an inclination of 30º has a ground track that looks like a
“figure-8”. Describe why the ground track has this shape.
3. Sketch the ground track of a spacecraft with the following COEs
Semi-major axis, a = 7980 km
Eccentricity, e = 0
Inclination, i = 25º
a. What is the nodal displacement (ΔN) of the ground track?
b. What is the highest (and lowest) latitude that the spacecraft’s ground track
reaches?
c. What shape does the ground track have? Is it symmetric?
4. Calculate the period for the following 5 orbits.
Orbit
#2
Orbit
#3
Orbit
#4
Orbit
#1
5. Given the following ground track of a direct orbit shown below, determine the
following: inclination, period, and draw an arrow to the approximate location of
perigee.
i = ______
ω= ______
Period = _________
Orbit
#5
6. (True / False) All circular orbits will always exhibit hinge symmetry.
7.
(True / False) Semi-synchronous satellites such as the GPS with orbital period of
12-hours will have a figure eight ground track providing global coverage.
8. (True / False) The following ground track (the dot) could be a valid ground track
for a typical communications satellite providing satellite TV to North America.
9. For an indirect orbit with inclination of 125 º, the ground track will
A. Cannot be drawn on a 2-dimensional Mercator map.
B. Cover between north and south latitude of 35 º.
C. Provide the same global coverage as the 90 º polar orbit.
D. Cover between north and south latitude of 55º and much faster than a direct
orbit with inclination of 55º.
10. Which of the orbital elements cannot be determined by a simple ground track and
requires the location of the star of Aries to be depicted on the map at a known time?
A. Semi-major axis.
B. Inclination.
C. True Anomaly.
D. Argument of Perigee.
E. Right Ascension of the Ascending Node.