During the full moon, a powerful cannon mounted on the moon is aimed at the center of the Earth’s disk and fires a projectile

During the full moon, a powerful cannon mounted on the moon is aimed at the center of the Earth’s disk and fires a projectile that travels at a speed of 80 km / s. Will the projectile reach the Earth’s surface?

The projectile was launched from the surface of the Moon, which itself moves relative to the Earth in orbit at a speed of 1 km / s. As a result, the projectile will fly not in the direction of the center of the Earth, but at an angle of about 0.7 ° to this direction. But this angle is less than the angular radius of the Earth as seen from the Moon (about 1 °). The gravitational influence of the Earth and the Sun will turn the trajectory of the projectile from a straight line into a hyperbola, which will further bring the trajectory closer to the center of the Earth. The projectile will hit the surface of the Earth, unless, of course, it burns up in its atmosphere. The movement of the Earth in orbit at a speed of about 30 km / s will not affect the result in any way, since the entire Earth-Moon system, including the projectile, participates in this movement.

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