One of the functions of the space shuttle is to release communications satellites at low altitude. A booster rocket is fi red at B, placing the satellite in an elliptical transfer orbit, the apogee of which is at the altitude necessary for a geosynchronous orbit. (A geosynchronous orbit is an equatorial plane circular orbit whose period is equal to the absolute rotational period of the earth. A satellite in such an orbit appears to remain stationary to an earth-fixed observer.) A second booster rocket is then fi red at C, and the final circular orbit is achieved. On one of the early space-shuttle missions, a 1500-lb satellite was released from the shuttle at B, where h₁ = 170 miles. The booster rocket was to fi re for t = 90 seconds, forming a transfer orbit with h₂ = 22,300 miles. The rocket failed during its burn. Radar observations determined the apogee altitude of the transfer orbit to be only 700 miles. Determine the actual time t′ which the rocket motor operated before failure. Assume negligible mass change during the booster rocket firing.

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В -h2 = 22,300 mi h = 170 mi