How long would it take the moon to orbit the earth if it was 3 times closer?
Interesting photo and video of what the moon looked like from earth so long ago. The video says 5 minutes to cross the sky.
https://slate.com/technology/2014/05/close-encounter-what-if-the-moon-orbited-much-closer-to-earth.html
Sorry about the late reply.
This is actually easy to do, just use Kepler’s famous Third Law:
P squared / R cubed = a constant for any planet or sun.
where P = orbital period
and R = orbital diameter.
Example - Mars’ orbit is 1.52x Earth’s; So if you cube 1.52, then take the square root, you get that Mars’ orbital period is 1.87x Earth’s, or 684 days.
So in this case, cube 0.3333, then take the square root, and multiply it by the Moon’s current period (about 29 days), and you get - just under 6 days for 1 orbit back then.