Two space shuttles A and B orbit the earth along the solid trajectory in Figure 9. Hoping
Question:
Data From Exercise 20
Show that a planet in an elliptical orbit has total mechanical energy E = −GMm/2a, where a is the semimajor axis. Use Exercise 19 to compute the total energy at the perihelion.
Data From Exercise 19
The perihelion and aphelion are the points on the orbit closest to and farthest from the sun, respectively (Figure 8). The distance from the sun at the perihelion is denoted rper and the speed at this point is denoted vper. Similarly, we write rap and vap for the distance and speed at the aphelion. The semimajor axis is denoted a.
Prove that
(a) Use Conservation of Energy (Exercise 17) to show that
Data From Exercise 17
The total mechanical energy (kinetic energy plus potential energy) of a planet of mass m orbiting a sun of mass M with position r and speed v = ΙΙr'ΙΙ is
(b) Show thatusing Exercise 13.
Data From Exercise 13
(c) Show that using Exercise 15. Then solve for vper using (a) and (b).
Data From Exercise 15
Step by Step Answer: