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Question -

A satellite orbits the earth at a height of400 km above the surface. How much energy must be expended to rocket thesatellite out of the earthтАЩs gravitational influence? Mass of the satellite =200 kg; mass of the earth = 6.0 ├Ч1024┬аkg; radius of theearth = 6.4 ├Ч106┬аm; G = 6.67 ├Ч 10тАУ11┬аN m2┬аkgтАУ2.



Answer -

Mass of the Earth,┬аM┬а= 6.0├Ч 1024┬аkg

Mass of the satellite,┬аm┬а=200 kg

Radius of the Earth,┬аRe┬а= 6.4 ├Ч 106┬аm

Universal gravitational constant, G = 6.67 ├Ч10тАУ11┬аNm2kgтАУ2

Height of the satellite,┬аh┬а=400 km = 4 ├Ч 105┬аm = 0.4 ├Ч106┬аm

Totalenergy of the satellite at height┬аh
Orbital velocity of the satellite,┬аv┬а=
Total energy of height,┬аh

The negative signindicates that the satellite is bound to the Earth. This is called bound energyof the satellite.

Energy required to sendthe satellite out of its orbit = тАУ (Bound energy)

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