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}}$

Column-$I$	Column-$II$
$(1)$ Polar satellite	$(a)$ Telecommunication
$(2)$ Geostationary satellite	$(b)$ Spying
	$(c)$ Weather forecasting

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

Similar Questions

The correct formula for the height $h$ of a satellite from the Earth's surface is:

$A$ geostationary satellite is orbiting the earth at a height of $6R$ above the surface of the earth,where $R$ is the radius of the earth. The time period of another satellite at a height of $2.5R$ from the surface of the earth is

The orbital velocity of a planet revolving close to the Earth's surface is:

Match the types of satellites in Column-$I$ with their applications in Column-$II$.

Column-$I$ Column-$II$

$(1)$ Polar satellite $(a)$ Telecommunication

$(2)$ Geostationary satellite $(b)$ Spying

$(c)$ Weather forecasting

Two satellites are revolving around the Earth with orbital velocities $v_1$ and $v_2$ at radii $r_1$ and $r_2$ respectively,where $r_1 > r_2$. Then:

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