A projectile is fired from the surface of the earth to the moon. Neglecting the

Question

A projectile is fired from the surface of the earth to the moon. Neglecting the orbital motion of the moon, what is the minimum velocity of impact on the surface of the moon? With what speed must the projectile be launched upward from the earth if it is to arrive at the moon with this minimal velocity? Take into account the gravitational pull of both the moon and earth.

Hint: Re/R= 0.0166, Rm/R=4.53 x 10^-3 and Mm/Me=1/81.6, where R is the center-to-center distance from the earth to the moon, Re and Me are the radius and the mass of the earth, and Rm and Mm are the radius and mass of the moon.

Explanation / Answer

a) As the projectile comes from outside the gravitational field of the Moon, the minimum velocity of impact on the surface of the moon, would be the escape velocity of the Moon, or 2.38 km/s
b) Slightly less than the escape velocity of the Earth. The speed must be enough to arrive at the point where the Moon's gravity and that of the Earth have the same size. I know that this speed is about 10.8 km/s, but the calculation is a bit longish.

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