Question

A satellite of mass m = 2.00 ×103 kg is launched into a circular orbit of orbital period T = 4.00 hours. Newton's gravitational constant is G = 6.67 ×10−11 N∙m2/kg2, and the mass and radius of the Earth are respectively M⨁ = 5.97 ×1024 kg and r⨁ = 6.37 ×106 m. Answer the following questions.

What is the total mechanical energy (kinetic energy + potential energy) of the satellite in orbit? Take the gravitational potential energy of the satellite when it is infinitely far away from the Earth to be zero.

What was the launch speed v0 of the satellite? Neglect the kinetic energy of the satellite due to the rotation of the Earth before launch.

If the satellite is launched straight up instead of into orbit with the launch speed you found in question 7, what is the maximum distance from the Earth's center rmax that the satellite will reach?

Answer 1