See below and explain fully. When it orbited the Moon, the Apollo 11 spacecraft\

Question

See below and explain fully.

When it orbited the Moon, the Apollo 11 spacecraft's mass was 7300 kg, and its mean distance from the Moon's center was 2.34785 Times 106 m. Find the orbital speed of the spacecraft. Assume its orbit to be circular and the Moon to be a uniform sphere of mass 7.36 Times 1022 kg. The gravitational constant is 6.67259 Times 10-11 N middot m/kg2. Answer in units of m/s What is the minimum energy required for the craft to leave the orbit and escape the Moon's gravitational field? Answer in units of J

Explanation / Answer

G M m / d^2 = m v^2 / d

v = sqrt [G M / d]

= sqrt [(6.67259 * 10-11 * 7.36 * 10^22) / (2.34785 * 10^6)]

= 1446.28 m/s

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The total energy E = K + U = 1/2 m v^2 - G M m / d

= - G M m / 2d

= - (6.67259 * 10-11 * 7300 * 7.36 * 10^22) / (2 * 2.34785 * 10^6)

= - 0.76 * 10^10 J

Emin = mod E

= 0.76 * 10^10 J

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