Question

A satellite of mass $1000kg$ is supposed to orbit the earth at a height of $2000km$ above the earth's surface. Find its kinetic energy.

Answer 1

Given data

$massm=1000kg$

$Heighth=2000km$

$velocity=?$

$K.E=?$

We know that

speed of the satellite in its orbit

$v=\sqrt{\frac{GM}{r+h}}=\sqrt{\frac{g{r}^2}{r+h}}$

$\Rightarrow v=\sqrt{\frac{9.8\times (6400\times {10}^3{)}^2}{{10}^6\times (6.4+2)}}$

$\Rightarrow v=\sqrt{\frac{9.8\times 6.4\times 6.4\times {10}^6}{8.4}}$

$v=6.9\times {10}^{3}m/s=6.9km/s$

Now kinetic energy of satellite

$K.E.=\frac{1}{2}m{v}^2$

$=\frac{1}{2}\times 1000\times (6.9\times {10}^3{)}^2$

$=\frac{1}{2}\times 1000\times (47.6\times {10}^6)$

$=2.38\times {10}^{10}J$