A satellite is fitted with a station keeping rocket capable of producing thrust of 500N. Its speed is 500Km/hr. Mission control wishes to increase the radius of orbit by a factor of 0.5. For how long should the rocket be fired to achieve this? (The weight of the satellite and rocket is 200kg, neglect the weight of fuel used during the burn)
F= Gm1m2/r^2 (although m2 is not known)
F/m1 = Gm2/r^2
V^2/r = Gm2/r^2
m1v1 + F*t = m1v2
The Attempt at a Solution
My idea was to try and find the velocity of orbit at 1.5r, but I am not sure how i can do that without using the mass of the body that the rocket is orbiting about. After that my idea was to use the above momentum formula and rearrange for t? Its really the calculation of the new velocity that I am stuck on.