Question

A space station is set up in space at a distance equal to earth's radius from the surface of earth. Suppose a satellite can be launched from the space station also. Let $v_1$ and $v_2$ be the escape velocities of the satellite on the earth's surface and space station respectively, then

• A. $v_2=v_1$
• B. $v_2<v_1$
• C. $v_2>v_1$
• D. $1,2$ and $3$ are valid depending on the mass of satellite.

Answer 1

The correct option is B $v_2<v_1$

The escape velocity for an object at a distance $r$ from the center of the earth is given by

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

Escape velocity at earth's surface $(r=R)$ will be

$v_1=\sqrt{\frac{2GM}{R}}$

Escape velocity from orbit $(r=2R)$ will be

$v_2=\sqrt{\frac{2GM}{2R}}$

So, we can see clearly, $v_2<v_1$

So, option $\left(b\right)$ is correct.