The GPS satellites

You may discuss these problems with other students, but every student needs to submit their
own work. Please be sure to show your work for partial credit. Use scientific notation
throughout your answers. Units are always required. Make sure that you have consistent units
when multiplying or dividing quantities.
GPS satellites are in “medium Earth orbit” or MEO. They have an altitude (above Earth’s
surface) of 20,200 km, and circular orbits. In the following, it may be helpful to remember that
gravity acts as if there is a point of mass at Earth’s center.

1. What are the linear speed and orbital period of GPS satellites in this orbit? (2 pts)
2. On the Earth, you measure a time interval of exactly 1.0 days (86,400 seconds). Ignore
   gravity for the moment. Relative to you on the surface of the Earth, is time passing more slowly
   or more rapidly on the GPS satellites? What interval would you observe to have passed aboard
   the satellites? (2 pts)
3. Now ignoring relative velocities, does time pass more slowly or more rapidly aboard the
   satellites than it does for you on Earth’s surface? If a full day passes for you, how much time
   would the satellites perceive to have passed? (2 pts)
4. What is the Hulse-Taylor binary, and what does it tell us about General Relativity? (4 pts)