Question

The rotation period of an earth satellite close to the surface of the earth is 83 minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be

• A. 83 minutes
• B. $83 \times \sqrt { 8 }$ minutes
• C. 664 minutes
• D. 249 minutes

Answer 1

Answer: (C)

664 minutes

Answer 2

For first satellite $r _ { 1 } = R$ and $T _ { 1 } = 83$ minute

For second satellite $r _ { 2 } = 4 R$

$T _ { 2 } = T _ { 1 } \left( \frac { r _ { 2 } } { r _ { 1 } } \right) ^ { 3 / 2 } = T _ { 1 } ( 4 ) ^ { 3 / 2 } = 8 T _ { 1 } = 8 \times 83$ =664 minutes