General Astronomy, 29:61
Fall, 2005
Sixth Homework Set...October 10, 2005.
Due October 17, 2005

Show calculations and give reasons for your answers. Be sure to put the answers in the right physical units.

(1) A satellite is in a highly elliptical orbit around the Earth, and its orbital plane is the Earth's equatorial plane. The semi-major axis is $3.5 R_{\oplus}$ ($1 R_{\oplus}=$ 1 Earth radius) and the eccentricity is 0.57. How high above the surface of the Earth is the satellite at perigee (closest approach to Earth)?

(2) Keep thinking about the satellite in problem #1. You are observing the satellite at perigee. In 6 minutes, it goes through an angle of $7^{\circ}$. What angle will it move through at apogee? Hint: Make the assumption (unjustified) that the angles you measure are the same that would be observed at the center of the Earth.
It will help if you draw a diagram of the orbit before you start. That diagram will also help you with problems 3,4, and 5 below.

(3) Read this whole question through before trying to come up with the answer. Think about your satellite TV dish. The satellite TV system receives signals transmitted from a spacecraft in outer space. To receive the signal, the antenna has to point directly at the spacecraft. Small satellite TV antennas have no capability of pointing at different directions in the sky, like astronomical telescopes; they are bolted to the side of a building. The spacecraft that sends the transmissions, on the other hand, is moving on an orbit in space. Given all the above, what can you conclude about the orbital period of the spacecraft as it orbits the Earth? Be sure and explain your answer.

(4) Following on question #2, why must TV satellite orbits be highly circular, i.e. possessing a very low eccentricity?

(5) What is the radius of the orbit of a TV satellite? Hint: You need the answer to # 2.

(6) At times of solar maximum, there is a vastly greater probability of solar flares and coronal mass ejections (CMEs) than at solar minimum. Let's assume you are in charge of choosing the date for a future manned spacecraft mission to Mars. What are some favorable dates to choose for the voyage. Hint: You need to use some material in the online diagrams and illustrations.