Moon and an apple are accelerated by the same gravitational force due to Earth. Compare the acceleration of the two.

Explanation

The gravitational force experienced by the apple due to Earth
`F = - (GM_(E )M_(A))/(R^(2))`
Here `M_(A)-` Mass of the apple , `M_(E ) - ` Mass of the Earth and R - Radius of the Earth
Equating the above equation with Newton.s 2nd law
`M_(A) a_(A) = - (GM_(E)M_(A))/(R^(2))`
Simplifying the above equation we get ,
`a_(A) = - (GM_(E))/(R^(2))`
Here `a_(A)` is the acceleration of apple that is equal to .g. . Similarly the force experienced by Moon due to Earth is given by
`F = - (GM_(E )M_(m))/(R_(m)^(2))`
Here `R_(m)- ` distance of the Monn from the `M_(m) ` - Mass of the Moon. The acceleration experienced by the Moon is given by
`a_() = - (GM_(E ))/(R_(m)^(2))`
The ratio between the apple.s acceleration to Moon.s acceleration is given by
`(a_(A))/(a_(m))=(R_(m)^(2))/(R^(2))`
From Hipparchrus measurements , the distance to the moon is 60 times that of earth radius .
`R_(m) = 60 R `
`(a_(A))/(a_(m)) = ((60R)^(2))/(R^(2)) = 3600 `
The apple.s acceleration is 3600 times the acceleration of the Moon .
The same result was obtained by Mewton using his gravitational formula . The apple.s acceleration is measured easily and it `9.8 "ms"^(-2)` . Moon orbits the Earth once in 27.3 days and by using the centripetal acceleration formula ,
`(a_(A))/(a_(m)) = (9.8)/((0.00272)) = 3600`
which is exactly what he got through his law of gravitation .