Question

Word has spread about your amazing Physics skills and NASA is offering you a job at Johnson Space Center’s Mission Control Unit located just South East of Houston, TX. Your first mission involves placing the newest reconnaissance satellite— a more diplomatic military term for a spy satellite— at a stable orbit around Earth. At what distance from the center of Earth do we need to position the satellite along the imaginary line connecting both the center of Earth and the center of the Moon that it observes apparent weightlessness? You can assume that Earth and Moon are perfect spheres with a homogeneous mass distribution such that they can be approximated as simple point masses. The distance between Earth and Moon is d = 384,400km, and the Moon’s mass is approximately 1/81th of the Earth’s mass (mMoon = 1 81mEarth). Is this stable point closer to Earth or closer to the Moon? Hint: You do not need numerical values for the gravitational constant γ, Earth’s mass, or the mass of the satellite mSatellite! All values required to find the solution are given in the text!

Answer 1