I want to put a 1500 g satellite into orbit around a spherical asteroid with a mass of 3x10^13 kg and a density of 5000 kg/m^3. Since it has no atmosphere, I foolishly decide to do this by building a horizontal runway 10 m off the ground and driving my wheeled satellite along it like a remote controlled car. It will start from rest, get up to speed on the runway, and then begin orbiting when the runway ends. It will make an elliptical orbit with it's closest approach bringing it back down to touch the runway. I calculate (possibly incorrectly) that the take-off speed needs to be 1.7 m/s.
1) What is the radius of the asteroid?
2) What is the magnitude of the gravitational force acting on my satellite when it's on the runway?
3) If the coefficient of friction between the runway and satellite is .8 what will be the maximum acceleration of the satellite?
4) How far will the satellite have to drive along to reach its speed of 1.7 m/s if it accelerates at the maximum rate?
5) Will this speed actually put it into an elliptical orbit above the astroids surface, put it into a hyperbolic orbit, or will it hit the surface?