Question

Consider three planets. All have the same mass as Earth, but with different radii (from largest to smallest: Planet 1, 2, 3). For which planet is the escape velocity from the surface the largest

Answer 1

Answer:

Planet 3 will have the greatest escape velocity.

Explanation:

Escape velocity is the velocity needed by an object to escape the gravitational field of a body or planet. At the escape velocity, the kinetic energy is equal to the gravitational potential energy.

Escape velocity of an object can be calculated by the below formula where $v_e$ is the escape velocity, $G$ is the gravitational constant, $M$ is the mass of the body to be escaped from and $r$ is the distance between the center of mass of the body being escaped from and the object.

$v_e=\sqrt{\frac{2GM}{r}}$

From the equation, it can be seen that escape velocity $v_e$ is inversely proportional to $r$,the distance between the center of mass of the body being escaped from and the object. Thus, the planet with the smallest radius will have the greatest escape velocity, as the distance between the object on the surface and the center of mass of the body will be the least.

Planet 3 will have the greatest escape velocity.