Would the Moon really only travel in a straight line then? What about the other planets and their forces of gravity? Wouldn't they prevent this rectilinear and undisturbed motion of the Moon?

  • $\begingroup$ There is no such thing as a centripetal force. There is something called centripetal acceleration, which just describes a very specific type of acceleration, namely that of circular curves. The only macroscopic forces present in the Earth-moon system are gravity, radiation pressure (very weak), and particle pressure (almost non-existent from dust and solar wind particles). $\endgroup$ – honeste_vivere Jul 25 '18 at 14:07

If the Earth just disappeared, the Moon would continue around the Sun on pretty much the same path it has now.

To see this, consider the velocity of the Earth/Moon system around the Sun:

$2\pi \times 150 \times 10^6 \text{ km} / 365 \text{ days} = 2.6 \times 10^6 \text{ km}/\text{day}$

versus the Moon's speed around the Earth:

$2\pi \times 385 \times 10^3 \text{ km} / 29 \text{ days} = 83 \times 10^3 \text{ km}/\text{day}$

The motion around the Sun is a factor of $30$ faster; the Moon's motion around the Earth is just a small perturbation on that.

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