Height of Satellite
Category : JEE Main & Advanced
As we know, time period of satellite \[T=2\pi \,\sqrt{\frac{{{r}^{3}}}{GM}}\]\[=2\pi \,\,\sqrt{\frac{{{(R+h)}^{3}}}{g{{R}^{2}}}}\]
By squaring and rearranging both sides \[\frac{g\,{{R}^{2}}{{T}^{2}}}{4{{\pi }^{2}}}={{\left( R+h \right)}^{3}}\]
\[\Rightarrow \] \[h={{\left( \frac{{{T}^{2}}g\,{{R}^{2}}}{4{{\pi }^{2}}} \right)}^{1/3}}-R\]
By knowing the value of time period we can calculate the height of satellite from the surface of the earth.
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