Question

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

• A. $\frac { 3 } { 2 } v$
• B. $\sqrt { \frac { 3 } { 2 } } v$
• C. $\sqrt { \frac { 2 } { 3 } } v$
• D. $\frac { 2 } { 3 } v$

Answer 1

Answer: (C)

$\sqrt { \frac { 2 } { 3 } } v$

Answer 2

$v = \sqrt { \frac { G M } { R + h } }$

For first satellite $h = 0$, $v _ { 1 } = \sqrt { \frac { G M } { R } }$

For second satellite $h = \frac { R } { 2 }$,

$v _ { 2 } = \sqrt { \frac { 2 G M } { 3 R } }$

$v _ { 2 } = \sqrt { \frac { 2 } { 3 } } v _ { 1 } = \sqrt { \frac { 2 } { 3 } } v$