Satellite moves in a circular orbit around the Earth at a speed of 5.1 km/s.Determine the satellite's altitude above the surface of the Earth. Assume the Earth is a homogeneous sphere of radius...

Satellite moves in a circular orbit around the Earth at a speed of 5.1 km/s.

Determine the satellite's altitude above the surface of the Earth. Assume the Earth is a homogeneous sphere of radius 6370 km and mass 5.98 x 10^24 kg. The value of the universal gravitational constant is 6.67259 x 10^-11 N times m^2/kg^2. Answer in units of km.

Asked on by jayjay00

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

We can assume that the altitude of the satellite is x from earth and so it is earths radius R +x  meter distant from the centre of the earth.

The satellites speed is v . We also assume that the gravitational force F is given by:

F = GMm/(r+x)^2 and this is equal to the centrepetal force of the satellite, mv^2/(R+x), where G is the gravitational constant, M =mass of the earth and m is the mass of the satellite. Using the known values, we would detrmine the value of x, the altitude of the satellite.

GMm/(R+x)^2=mv^2/(R+x). Reducinf by m/(R+x) , we get:

GM/(R+x) = v^2 or

R+x = GM/v^2 or

x = GM/v^2 - R

=6.67259*10^-11*5.98*10^24/5100^2  - (6370000)

= 8971056.594 m

=8971.056594 Km.

astrosonu's profile pic

astrosonu | Student | (Level 1) Valedictorian

Posted on

It is 8971.056594 km.

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