What is the time period of a satellite orbiti | vedclass

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(B) The time period $T$ of a satellite at a height $h$ above the Earth's surface is given by the formula:$T = 2\pi \sqrt {\frac{{(R + h)^3}}{{GM}}}$Gi

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$4\sqrt 2 \pi \sqrt {\frac{R}{g}} $

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(B) The time period $T$ of a satellite at a height $h$ above the Earth's surface is given by the formula:$T = 2\pi \sqrt {\frac{{(R + h)^3}}{{GM}}}$Given that the height $h = R$,we substitute this into the equation:$T = 2\pi \sqrt {\frac{{(R + R)^3}}{{GM}}}$Since the acceleration due to gravity at the surface is $g = \frac{GM}{R^2}$,we can write $GM = gR^2$:$T = 2\pi \sqrt {\frac{{(2R)^3}}{{gR^2}}}$$T = 2\pi \sqrt {\frac{{8R^3}}{{gR^2}}}$$T = 2\pi \sqrt {\frac{{8R}}{g}}$$T = 2\pi \cdot 2\sqrt{2} \sqrt {\frac{R}{g}}$$T = 4\sqrt{2} \pi \sqrt {\frac{R}{g}}$

What is the time period of a satellite orbiting at a height $R$ above the Earth's surface?

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