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A satellite orbits the earth at a height...

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg, mass of the earth `= 6.0xxl0^24 kg`, radius of the earth = `6.4 xx 10^6 m`, G = `6.67 xx 10^11 N m^2kg^2`.

Text Solution

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`h= 400km = 400 xx 10^(3)= 0.4 xx 10^(6)m`
`R= 6.4 xx 10^(6)m`, Mass of earth, `M= 6 xx 10^(24) kg`
Mass of satellite, m=200kg, `G= 6.67 xx 10^(-11) Nm^(2) kg^(-2)`
Now, `E= -(GMm)/(2(R+h)) or, E= - (6.67 xx 10^(-11) xx 6 xx 10^(24) xx 200)/(2(6.4 xx 10^(6) + 0.4 xx 10^(6)))=-5.89 xx 10^(9)J`
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