A satellite is in low earth orbit, but for one reason or another, its orbit is decaying. This means the satellite is losing altitude. Assume the orbit is circular. (radius of earth = 6400km, mass of earth = 6e24kg).
1) The satellite is in low earth orbit, and the radius of the orbit is 300km above the surface of the earth. What is the orbital period?
2) The boundary between medium and high earth orbit is a region where geosynchronous satellites lie. These satellites orbit the earth with the same period as the rotation period of the earth. What is the distance to the surface of the earth?
3) If the period is decaying by 5% per day, how fast is the altitude changing?
Use the drag force equation to find the relationship between the orbital decay rate in terms of the orbital radius, the density of air , and the effective cross-sectional area to mass ratio.