<p>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.)</p>

CC BY-SA 4.0
2021-02-19T08:20:36.283Z
just calculate the acceleration (centrifugal force) for a circular motion with the moon's radius and the orbital radius and compare... what stops you?
planetmaker
CC BY-SA 4.0
2021-02-19T10:00:42.427Z
I'm confused (as usual), but do gyroscopes detect *acceleration*? I think you mean to say *rotation*, no?
uhoh
CC BY-SA 4.0
2021-02-20T05:17:18.063Z
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 omega*omega*R (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?
Gilbert Vidal
<the-moon><rotation>
Accelerations on the Moon due to its orbit and its spin
Gilbert Vidal
# Accelerations on the Moon due to its orbit and its spin

(Asked by: username_0 on 2021-02-19)

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.)

**Tags:** the-moon, rotation
> **Comments:**
> **username_1**: just calculate the acceleration (centrifugal force) for a circular motion with the moon's radius and the orbital radius and compare... what stops you?  
> **username_2**: I'm confused (as usual), but do gyroscopes detect *acceleration*? I think you mean to say *rotation*, no?  
> **username_0**: 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 omega*omega*R (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?  

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## 0 answers

