You have a summer job at a laboratory associated with the oversight of the Global Positioning System (GPS). The space-based part of the system consists of about three dozen satellites. Just before the summer, a new GPS satellite was launched but, due to a rocket-engine failure, it did not achieve its proper near-circular orbit around the Earth. It now moves in an elliptical orbit with its apogee at 2.65 ✕ 104 km, which is the radius of the circular orbit of a correctly positioned GPS satellite, and its perigee at 6.70 ✕ 103 km. Your boss wonders if the satellite can still be used in some way. Normal GPS satellites appear over the same point on the Earth about twice a day. Your boss asks you to calculate (a) how many times a day the satellite reaches its perigee and to determine (b) if the perigee point is regularly over a fixed point on the Earth's surface.