When describing a circular orbit, 185 mi above the surface of the earth, a space

Question

When describing a circular orbit, 185 mi above the surface of the earth, a space shuttle ejects at point A an inertial upper stage (IUS) carrying a communication satellite to be placed in a geosynchronous orbit at an altitude of 22,230 mi above the surface of the earth. Determine (a) the velocity of the IUS relative to the shuttle after its engine has been fired at A, (b) the increase in velocity required at B to place the satellite in its final orbit.

When describing a circular orbit, 185 mi above the surface of the earth, a space shuttle ejects at point A an inertial upper stage (IUS) carrying a communication satellite to be placed in a geosynchronous orbit at an altitude of 22,230 mi above the surface of the earth. Determine (a) the velocity of the IUS relative to the shuttle after its engine has been fired at A, (b) the increase in velocity required at B to place the satellite in its final orbit.

Explanation / Answer

R = 185 mi = 185 * 1609 = 297665 m

GM = gR^2 = 9.8 * 297665^2 = 8.68 *10^11 m^3/s^2

rA = (3960*1609) + (297665 = 6234875 m

rB = (3960*1609) + (22230*1609) =42135790 m

spped V at A = sqrt(GM/rA) = sqrt (6.65*10^-11*6*10^24/623487^2) = 3.2 m/s

speed at BVb = sqrt(GM/rB) = sqrt (6.65*10^-11*6*10^24/42135790^2 = 0.4732 m/s

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