If the earth has a radius of 6 x 10^6 meters, how high above earth's surface does a geosynchronous satellite have to be, if it has a mass of 100kg and gravity acts on the satellite with a force of 4.23 x 10^8 Newtons? What is its linear speed? (Assume the orbit is circular)
The Attempt at a Solution
After reading through the problem, I realized that there has to be some clarification on some points. I'm fairly certain that the geosynchronous idea means that if somebody stood on the earth, the satellite would remain directly above them. That means that the satellite is rotating at the same speed as the earth (in terms of the circumference of its orbit). However, since the radius is larger (we don't actually know it, that's something I need to solve for), its linear speed must be significantly faster than the speed of the earth. So then, I found some equations on the internet, but it seems that I'd need the values for the mass of the earth as well to solve it. Is there something I'm missing? Thanks!