Question

A space station is set up in a space at a distance equal to the earth's radius from the surface of the earth. Suppose a satellite can be launched from the space station. Let ${\nu }_1$ and ${\nu }_2$ be the escape velocities of the satellite on the earth's surface and space station, respectively. Then

• A. ${\nu }_2={\nu }_1$
• B. ${\nu }_2<{\nu }_1$
• C. ${\nu }_2>{\nu }_1$
• D. (a), (b) and (c) are valid depending on the mass of satellite.

Answer 1

The correct option is B ${\nu }_2<{\nu }_1$

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

For space station: $T.E=\frac{1}{2}m{\nu }_2^2+(-\frac{GMm}{2R})=0$

$⟹{\nu }_2=\sqrt{\frac{GM}{R}}$ where R is the radius of earth.

For earth's surface : ${\nu }_1=\sqrt{\frac{2GM}{R}}$

Hence ${\nu }_1>{\nu }_2$