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Classical Mechanics

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Difficult

Equatorial Boost

CLMECH-F54FIN

The hard part about launching satellites is getting the satellite moving at a fast enough speed to enter orbit, not getting it high enough. To use a little less energy, most satellite's are launched from locations near the Earth's equator, to use the Earth's rotational speed as a boost (this is why NASA launches from Florida or Houston).

How much energy, is needed to launch a satellite with mass $M_S=100 kg$ into a circular orbit of height $h=4.02 \times 10^{6} m$ from the Earth's equator?

You may treat the Earth as a perfect sphere, with radius $R_E = 6.37 \times 10^6 m$, and mass $M_E = 5.97 \times 10^{24} kg$.

You may use the SI value for the gravitational constant $G=6.674\times 10^{−11} N⋅m^2/kg^2$

A

$9.6 \times 10^{10} J$

B

$8.9 \times 10^6 J$

C

$7.3 \times 10^8 J$

D

$4.3 \times 10^9 J$

E

$9.6 \times 10^{9} J$