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=`6.0xx10^(24)`kg, radius of the earth=`6.4xx10(6)`m, G=`6.67xx10^(-11)Nm^(2)Kg^(-2)`.

Explanation

Mass of the Earth, `M=6.0xx10^24kg`

`m=200kg`

`R_e=6.4xx10^6m`

`G=6.67xx10^-11Nm^2kg^-2`

Height of the satellite, `h=400km=4xx10^5m`

Total energy of the satellite at height , `h=1/2mv^2+(-(GM_em)/(R+h))`

Orbital velocity of the satellite,`v=sqrtfrac(GM_e)(R_e+h)`

Total energy at height, `h=1/2frac(GM_em)(R_e+h)-frac(GM_em)(R_e+h)`

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