Question

Two satellites P and Q are moving in different circular orbits around the Earth (radius 𝑅). The heights of P and Q from the Earth surface are $ℎ_P$ and $ℎ_Q$, respectively, where $ℎ_P = \frac{𝑅}{3}$. The accelerations of P and Q due to Earth’s gravity are $𝑔_P$ and $𝑔_Q$, respectively. If $\frac{𝑔_P}{𝑔_Q} = \frac{36}{25}$, what is the value of $ℎ_Q?$

• A. $\frac{3𝑅}{5}$
• B. $\frac{𝑅}{6}$
• C. $\frac{6𝑅}{5}$
• D. $\frac{5𝑅}{6}$

Answer 1

Answer: (A)

$\frac{3𝑅}{5}$

Answer 2

Given $h_p=\frac{R}{3}$
$h_q=?$
gravitational acceleration at height
$g_{ht}=\frac{GM}{(R+h)^2}$

$\frac{g_P}{g_Q}=\frac{36}{25}$

$=\frac{\frac{GM}{(R+h_p)^2}}{\frac{GM}{(R+h_Q)^2}}$

when $h_P=\frac{R}{3}$
on solving we get
$h_Q=\frac{3R}{5}$