One method for estimating the travel time from the Earth to the Moon is to use K

Question

One method for estimating the travel time from the Earth to the Moon is to use Kepler's third law to find half the period of an orbit whose perigee is at the Earth and whose apogee is at the Moon. What is the travel time to the Moon, a distance of 3.84 105 km from the Earth's center, for a spacecraft initially at an altitude of 244 km in the Earth's orbit, assuming it does not use any means of propulsion? (Use 6.67 1011 m for the gravitational constant, 6370 km for the radius of Earth, and 5.98 1024 kg for the mass of the Earth. Enter your answer to at least 6 significant figures.)

Explanation / Answer

ra = 3.84 x 10^5 km

rp = 6371 + 244 = 6615 km

a = (ra + rp) / 2 = 195307.5 km Or 195.31 x 10^6 m

Time period of orbit, T = 2pi sqrt[ a^3 / G M ]

T = 2 pi sqrt[ (195.31 x 10^6)^3 / (6.67 x 10^-11) (5.972 x 10^24)]

T = 859281.4 sec

Time to travel to moon = T/2

= 429640.7 sec .......Ans

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