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Calculating the gravitational field strength felt by our Moon, caused by our Earth and Sun, I found that the magnitude of the Sun's gravitational field is felt as greater by the Moon than the Earth's.

Using the equation g=GM/r^2

where G is the universal gravitational constant, M is the Mass of the object producing the gravitational field, and r is the distance away from that object (i.e. distance between centers of the Earth and Moon, and the Sun and Moon).

My calculations yielded:

g of Sun on Moon = 0.00590 N/kg

g of Earth on Moon = 0.00262 N/kg

This concerned me for obvious reasons. If the Sun's gravitational field is more influential for the Moon than the Earth's, then why does the Moon remain in orbit around the Earth?

I expect I am missing something important. Any help is appreciated. Especially a thorough explanation of the theory, principles, and an overview of the mathematics involved.

kulan
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    The Center of Mass of the Earth-Moon system orbits the Sun – FGSUZ Jan 17 '20 at 17:05
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    FWIW: You can't feel gravity. The strength of Earth's gravity up where the astronauts are orbiting in the space station is almost as strong (more than 90%) as gravity at sea level. What you feel, standing on the ground, that astronauts don't feel, is the contact force of the ground pushing up on your feet, and stopping you from following the path that gravity and inertia want you to follow--stopping you from falling to the center of the Earth. The astronauts, in orbit, do follow the path that gravity and inertia want them to follow. An orbit actually is a kind of continuous "falling." – Solomon Slow Jan 17 '20 at 23:37

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the moon orbits both Earth and the Sun. Since the Earth orbits the Sun, and the moon orbits the Earth, it necessarily also orbits the Sun.

These two motions of the moon almost do not interfere with one another, because its orbit about the Sun is almost identical to the Earth's orbit around the Sun (because they are approximately the same distance from the Sun), so everything is fine!

  • FWIW, if you plot the solar orbits of the Moon & Earth on the same diagram, they look very similar: the Moon's orbit differs from the Earth's by only a few pixels at most on a modern hi-res screen. – PM 2Ring Jan 17 '20 at 17:15