A planet orbiting the Sun has speed v = √(GM/d). Escape speed from the Sun is v = √v(2GM/d), where G is the gravitational constant, M is Sun's mass, and d is the distance from the Sun. Noting that this tells us that escape speed is √2 times orbital speed, which planet would fly out of the solar system by a 1.5 increase in orbital speed?
A)Mercury.
B)Venus.
C)Earth.
D)all of the above
E)none of the above

Question

Quizplus · Accepted Answer

Increasing the orbital speed by a factor of 1.5 means the new speed is 1.5 times the original orbital speed. Since the escape speed is √2 times the orbital speed, and 1.5 is less than √2 (approximately 1.414), a 1.5 increase in speed is not enough to reach escape velocity for any planet. Therefore, no planet would fly out of the solar system with a 1.5 increase in orbital speed.

A Planet Orbiting the Sun Has Speed V = √(GM/d)