Question

Two planets move around the sun. The periodic times and the mean radii of the orbits are $T _ { 1 } , T _ { 2 }$ and $r _ { 1 } , r _ { 2 }$ respectively. The ratio $T _ { 1 } / T _ { 2 }$ is equal to

• A. $\left( r _ { 1 } / r _ { 2 } \right) ^ { 1 / 2 }$
• B. $r _ { 1 } / r _ { 2 }$
• C. $\left( r _ { 1 } / r _ { 2 } \right) ^ { 2 }$
• D. $\left( r _ { 1 } / r _ { 2 } \right) ^ { 3 / 2 }$

Answer 1

Answer: (D)

$\left( r _ { 1 } / r _ { 2 } \right) ^ { 3 / 2 }$

Answer 2

$T ^ { 2 } \propto r ^ { 3 } \Rightarrow \frac { T _ { 1 } } { T _ { 2 } } = \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 3 / 2 }$