# Accelerations on the Moon due to its orbit and its spin

A gyroscope is placed on the equator of the Moon. It detects among others 2 accelerations: one due to the orbit and one due to the spin. What is the module of the second one compared to the first one? (the effects due to the tilting of the orbit, the librations, the Sun... are neglected.)

• just calculate the acceleration (centrifugal force) for a circular motion with the moon's radius and the orbital radius and compare... what stops you? Feb 19, 2021 at 8:20
• I'm confused (as usual), but do gyroscopes detect acceleration? I think you mean to say rotation, no?
– uhoh
Feb 19, 2021 at 10:00
• I agree, but there is a problem. Let's put the gyroscope at point B of coordinates (0, 0), the point of the Moon closest to the Earth. The acceleration due to spin is omegaomegaR (omega: angular velocity and R: radius of the Moon). Now suppose that we suddenly double the radius R while keeping the position of point B. The said acceleration should double too. Now the Moon continues its course as if nothing had happened. How could the acceleration of point B double if it keeps its trajectory and speed in the Galaxy? Feb 20, 2021 at 5:17