PHYS 361
Homework due Thursday, October 28
20 Points
Start early
Note: Use of external resources such as similar examples in other textbooks, web based
solutions, instructor’s solution manual, programs and calculators with symbolic
manipulation, or similar aids that do not originate from your brain are expressly
forbidden. Collaboration is encouraged. Division of labor on all assignments is
outlawed.
1. In the following two derivations, full credit is not available for skipped steps.
a. Using information on pages 300 and 301, derive the expressions for the apsidal
distances (Equations 8.44). Put them in terms of energy, E, and angular momentum, ℓ.
b. Starting from Equation 8.45, derive Equation 8.49.
2. A satellite is in an elliptical orbit about the earth. At the instant that it is moving with
speed, v, it receives a short engine boost in the direction of motion which changes the
speed by v. Find an expression for the change in length of the major axis, a, in terms of
v, v, a, G and Mearth.
3. Symon, Chapter 3, Problem 52.
4. Find the equation of the trajectory for an earth satellite that has a perigee of 600 km
and an apogee of 1,200 km. Use the center of the earth as the origin. Graph the
trajectory by hand. Use the Earth as the origin and indicate the perigee, the apogee and
the semi-minor axis length. How far is the satellite from the surface of the earth when it
crosses the semi-minor axis?