AE-641
Problems Set 6
1. The orbit of a spacecraft around Earth (J2=0.00108263) has
the elements i=28.8o, e=0.732,
and T=10.6 hr. Find the rotation of apsides and regression of
nodes. (Ans. 0.59o/day, -0.365o/day).
2. The mean daily motion of Mars is 0.5240o/day. Design a
photographing orbit for Mars.
Give the possible altitude and inclination. (For Mars: =42828.3
km3/s
2, R0=3397 km,
J2=0.001964.) (Sample answer: For 300 km altitude,
i=92.6495o).
3. What is the maximum radius for a circular, sun-synchronous
Earth orbit? (Ans.12352.679 km).
4. A satellite of frontal area 10 m2 and mass 200 kg is placed
in a 200 km high circular Earth
orbit, where its drag-coefficient is 2.2. Assuming an
exponential atmosphere with 0=1.752
kg/m3 and scale-height 6.7 km, estimate the life of the
satellite in orbit. (Ans. 73.46 mean solar
days).
5. Estimate the rotation of apsides and regression of nodes due
to Moons gravity on a
geosynchronous satellite.
6. Estimate the rotation of apsides and regression of nodes due
to Suns gravity on a
geosynchronous satellite.
7. Can an Earth satellite have its regression of nodes due to
Earth oblateness exactly
cancelled by that due to the Moon, thereby leaving the orbital
plane fixed in space? If so,
calculate the necessary orbital elements of the satellite.
