Moonfall is a movie coming out in 2022. It creates a scenario where the Moon’s orbit is changed and set on a collision course with the Earth. It is fun to work out the orbital mechanics.

Let us assume that the Moon is in a circular orbit around the Earth. It is actually more influenced by the Sun than the Earth, but the circular orbit approximation is sufficient for our purposes. A mysterious force changes the orbit from circular to elliptical so that at closest approach it hits the Earth. The transfer orbit has an eccentricity of 0.9673 and a semi-major axis of 195000 km. The new orbital period is 9.9 days so it will hit the Earth in 5 days!

What kind of force is needed? The required velocity change is 0.83 km/s so a force of 6 x 1016 N applied over 10 seconds is required. To get an idea of how large that force really is, the Space Launch System (SLS) Block 2 vehicle produces about 10 million pounds of thrust [1], which is approximately 50 x 106 N (50 MN). Hence it would take 1.2 billion SLS rockets firing for 10 seconds to perform such a re-direction of the Moon! An image of the SLS is shown below (image from [1]).

As the Moon approaches the Earth it is going to raise the tides. A simple formula (really only valid when the Moon is far from the Earth) is

where is the gravitational constant for the moon, is the gravitational constant for the Earth, r is the distance between the Earth and Moon and a is the radius of the Earth. The distance during the approach and the wave height are shown in the following plot.

By around 3 days the tides started getting really big! We’d expect the Moon’s gravitational force also to pull on the solid part of the Earth’s surface, causing all sorts of trouble.



This entry was posted in Aerospace, General and tagged , by Michael Paluszek. Bookmark the permalink.

About Michael Paluszek

Michael Paluszek is President of Princeton Satellite Systems. He graduated from MIT with a degree in electrical engineering in 1976 and followed that with an Engineer's degree in Aeronautics and Astronautics from MIT in 1979. He worked at MIT for a year as a research engineer then worked at Draper Laboratory for 6 years on GN&C for human space missions. He worked at GE Astro Space from 1986 to 1992 on a variety of satellite projects including GPS IIR, Inmarsat 3 and Mars Observer. In 1992 he founded Princeton Satellite Systems.

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