The speed of a satellite orbiting Earth is given by v = √(GM/d). Escape speed from Earth is given by v = √(2GM/d), where in both cases G is the gravitational constant, M is Earth's mass, and d is distance from Earth's center. If a satellite's kinetic energy were doubled it could
A)orbit at twice its distance from Earth.
B)orbit at four times the distance from Earth.
C)escape Earth.

Question

Quizplus · Accepted Answer

The kinetic energy of a satellite in orbit is given by KE = (1/2)mv^2, where m is the mass of the satellite and v is its orbital speed. If the kinetic energy is doubled, we have 2KE = mv^2, which means v must increase by a factor of sqrt(2). However, the only way for the satellite to achieve this increased speed is to receive an external force, which cannot happen while in orbit around Earth. Therefore, the satellite cannot remain in orbit and will escape Earth's gravitational pull.

The Speed of a Satellite Orbiting Earth Is Given by V