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 = R 3 . The accelerations of P and Q due to Earth’s gravity are g P and g Q , respectively. If g P g Q = 36 25 ,…

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 = R 3 . The accelerations of P and Q due to Earth&rsquo;s gravity are g P and g Q , respectively. If g P g Q = 36 25 , what is the value of h Q ?

Aicharya · Accepted Answer

Acceleration due to gravity at any height from the Earth's surface is given by, $g = \frac{G M}{r^{2}}$ , where $r =$ distance from the centre of the Earth.
Now, we can write
$\frac{g_{P}}{g_{Q}} = \frac{\frac{G M}{{(r_{P})}^{2}}}{\frac{G M}{{(r_{Q})}^{2}}} \Rightarrow \frac{36}{25} = {(\frac{r_{Q}}{r_{P}})}^{2} \Rightarrow \frac{r_{Q}}{r_{P}} = \frac{6}{5} \Rightarrow r_{Q} = \frac{6}{5} \times (R + \frac{R}{3}) \Rightarrow R + h_{Q} = \frac{8}{5} R \Rightarrow h_{Q} = \frac{3}{5} R$

Two satellites P and Q are moving in different circular orbits around the Earth(radius R ). The heights of P…

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