A space station is set up in space at a distance equal to earth's radius from earth's surface. Suppose a satellite can be launched from space station. Let V1 and V2 be the escape velocites of the satlhte on earth's surface and space station respectively. Then

Question

A space station is set up in space at a distance equal to earth's radius from earth's surface. Suppose a satellite can be launched from space station. Let V1 and V2 be the escape velocites of the satlhte on earth's surface and space station respectively. Then (A) V2=V1 (B) V2 (C) V2>V1 (D) No relation

Tardigrade Admin · Accepted Answer

For an object to escape from an orbit, its total energy must be zero. For space station:

T . E = \frac{1}{2} m v_{2}^{2} + (- \frac{GM m}{2 R}) = 0

⟹ v_{2} = \frac{GM}{R}

where

R

is the radius of earth. For earth's surface :

v_{1} = \frac{2 GM}{R}

Hence

v_{1} > v_{2}

Q. A space station is set up in space at a distance equal to earth's radius from earth's surface. Suppose a satellite can be launched from space station. Let $V_{1}$ and $V_{2}$ be the escape velocites of the satlhte on earth's surface and space station respectively. Then

$V_{2} = V_{1}$

$V_{2}$

$V_{2} > V_{1}$

No relation

For an object to escape from an orbit, its total energy must be zero. For space station: $T . E = \frac{1}{2} m v_{2}^{2} + (- \frac{GM m}{2 R}) = 0$ $⟹ v_{2} = \frac{GM}{R}$ where $R$ is the radius of earth. For earth's surface : $v_{1} = \frac{2 GM}{R}$
Hence $v_{1} > v_{2}$

Q. A space station is set up in space at a distance equal to earth's radius from earth's surface. Suppose a satellite can be launched from space station. Let V1​ and V2​ be the escape velocites of the satlhte on earth's surface and space station respectively. Then

V2​=V1​

V2​

V2​>V1​