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 `= 6.0xx 10^(24)` kg, radius of the earth `= 6.4 xx 10^(6) m, G = 6.67 xx 10^(-11) Nm^(2) kg^( 2)`  

Explanation

`implies` Height of satellite from the surface of earth,
h = 400 km
`= 0.4 xx 10^(6) m`
Mass of satellite m = 200 kg
Radius of earth `R_e = 6.4 xx 10^(6) m`
Mass of earth Me = `6 xx 10^(24) kg`
` G = 6.67 xx 10^(-11) Nm^(2)//kg^(2)`
Energy required to send the satellite out of its orbit = - (Bound energy)
`=(GM_Em)/((2R_E+h))`
`= (6.67 xx10^(-11)xx6xx10^(24)xx200)/(2[6.4xx10^6+0.4 xx10^6])`
`=(6.67 xx10^(15)xx12)/(2xx6.8 xx10^6)`
`= 5.885 xx10^9`
`= 5.9 xx 10^(9) J`