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)

A satellite orbits the earth at a height of 400 km above the surface.

1.	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)
Answer» Solution :`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 = `6xx 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`