Correct formula for height of a satellite from Earth's surface is

Question

Correct formula for height of a satellite from Earth's surface is _____. [2024]

Smart Achievers · Accepted Answer

(1)

$\frac{m v^{2}}{(R + h)} = \frac{G M m}{{(R + h)}^{2}} \Rightarrow v = \sqrt{\frac{G M}{R + h}}$

$Now T = \frac{2 π (R + h)}{\sqrt{\frac{G M}{R + h}}}$

$\Rightarrow T = \frac{2 π {(R + h)}^{3 / 2}}{\sqrt{G M}} = \frac{2 π {(R + h)}^{3 / 2}}{R \sqrt{g}}$

$\Rightarrow T^{2} R^{2} g = 4 π^{2} (R + h^{3})$

$\Rightarrow {(\frac{T^{2} R^{2} g}{4 π^{2}})}^{1 / 3} - R = h$

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