Question

Time period of a satellite revolving round a planet in an orbit of radius $R$ is $T$. Periodic time of a satellite moving in an orbit of radius $9R$ will be.

• A. $27T$
• B. $81T$
• C. $729T$
• D. $3T$

Answer 1

Answer: (A)

$27T$

Using Kepler's $3$rd law, $[\frac{T_2}{T_1}{]}^2=[\frac{R_2}{R_1}{]}^3$

Given: $R_2=9R{R}_1=R{T}_1=T$

$[\frac{T_2}{T}{]}^2=[\frac{9R}{R}{]}^3⟹T_2=27T$