A 250kg science platform is designed to operate in a circular orbit 2.00×106m above the surface of Mars. The radius of Mars is 3.39×106m, and the mass of Mars is 6.42×1023kg.
(1) Calculate the speed the platform must have to maintain the desired orbit.
(2) Determine the mechanical energy (kinetic plus gravitational potential) of the platform–Mars system while the platform is in orbit. State clearly whether the energy is positive, negative, or zero and interpret the sign.
(3) If mission planners wish to raise the platform to a new circular orbit that is 1.00×106m higher, calculate the additional energy that must be provided to the platform–Mars system.
(4) Briefly explain, without further calculation, whether the orbital speed in the higher orbit will be greater than, less than, or equal to the speed found in part (a). Cite the relevant physical principles in your explanation.