Question 221: Gravitation

Question

The time period of an earth satellite in circular orbit is independent of

Accepted Answer

For satellite, gravitational force = centripetal force
$$	herefore$$ $${{m{v^2}} \over {R + x}} = {{GmM} \over {{{\left( {R + x} ight)}^2}}}$$
$$x=$$ height of satellite from earth surface
$$m=$$ mass of satellite
$$ \Rightarrow {v^2} = {{GM} \over {\left( {R + x} ight)}}$$ or $$v = \sqrt {{{GM} \over {R + x}}} $$
We know, $$T = {{2\pi } \over \omega }$$
$$T = {{2\pi \left( {R + x} ight)} \over v} $$  [ as $$\omega  = {v \over r}$$ ]
$$= {{2\pi \left( {R + x} ight)} \over {\sqrt {{{GM} \over {R + x}}} }}$$
which is independent of mass of satellite

Answer

both the mass and radius of the orbit

Answer

radius of its orbit

Answer

the mass of the satellite

Answer

neither the mass of the satellite nor the radius of its orbit

Gravitation

The time period of an earth satellite in circular orbit is independent of

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