Question 237: Gravitation

Question

A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

Accepted Answer

Gravitational force applied on the satellite,
= $${{GMm} \over {{{\left( {R + x} ight)}^2}}}\,\,$$
For satellite, gravitational force = centripetal force
$$	herefore$$ $${{m{v^2}} \over {\left( {R + x} ight)}} = {{GMm} \over {{{\left( {R + x} ight)}^2}}}\,\,$$
where $$v$$ is the orbital speed of satellite.
also $$\,\,g = {{GM} \over {{R^2}}}$$ $$ \Rightarrow GM = g{R^2}$$
$$	herefore$$ $${v^2} = {{g{R^2}} \over {R + x}} $$
$$\Rightarrow v = {\left( {{{g{R^2}} \over {R + x}}} ight)^{1/2}}$$

Answer

$${{g{R^2}} \over {R + x}}$$

Answer

$${{gR} \over {R - x}}$$

Answer

$${gx}$$

Answer

$${\left( {{{g{R^2}} \over {R + x}}} \right)^{1/2}}$$

Gravitation

A satellite of mass $m revolves around the earth of radius R at a height x from its surface. If g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

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