Some communication and weather satellites are launched into circular orbits above the Earth's equator so they are synchronous (from the Greek syn-, same, and chronos, time) with the Earth's rotation. That is, they remain "fixed" or "hover" over one point on the equator. At what altitude are these geosynchronous satellites?

THINKING IT THROUGH. To remain above one location at the equator, the period of the satellite's revolution must be the same as the Earth's period of rotation, that is, \(24 \mathrm{~h}\). Also, the centripetal force keeping the satellite in orbit is supplied by the gravitational force of the Earth, \(F_{\mathrm{g}}=F_{c}\). The distance between the center of the Earth and the satellite is \(r=R_{\mathrm{E}}+h .\left(R_{\mathrm{E}}\right.\) is the radius of the Earth and \(h\) is the height or altitude of the satellite above the Earth's surface.)