How much does the mass of the earth effect moon gravity?

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SUMMARY

The mass of the Earth does exert a gravitational influence on the Moon, but this effect is significantly diminished due to the distance between the two bodies. Gravity on the Moon is measured at 1.622 m/s², and when standing on the Moon, the gravitational force experienced from the Earth varies depending on the observer's position. Using Newton's law of universal gravitation, specifically the equation F = Gm1m2/r², one can calculate the gravitational forces acting on a 1 kg test mass on the Moon's surface, noting that no gravitational force is felt at the Moon's center.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Basic knowledge of gravitational acceleration
  • Familiarity with the concept of gravitational forces
  • Knowledge of the Moon's mass and distance from Earth
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  • Research the implications of gravitational forces in celestial mechanics
  • Explore the effects of distance on gravitational attraction
  • Learn about tidal forces and their relationship to Earth-Moon interactions
  • Study gravitational effects in different locations on the Moon's surface
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Astronomers, physics students, and anyone interested in gravitational effects between celestial bodies.

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As I understand it, the effect of gravity is greatly diminished over long distances. Even so, the mass of the moon is sufficient to exert an influence on earth, for example on tides. My question is, to what extent does the mass of the Earth influence gravity on the moon. Gravity on the moon is quoted as being 1.622m/sec squared. But how much is that effected if you're standing on the moon with the Earth directly above your head, compared to standing on the opposite side of the moon with the Earth directly underfoot?
 
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Try applying Newtons law to a nominal 1kg test mass on the surface of the moon. There will be two forces one due to the moon and the other due to the earth. The general equation is...

F = Gm1m2/r2
 
If you were in a cave in the centre of the moon you would not notice any gravitational force.
 

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