Explain how Newton verified his law of gravitation.

Explanation

The gravitational force experienced by the apple due to Earth.
`F=-(GM_(E)M_(A))/(R^2)`
`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 second law, we get
`M_(A)a_(A)=-(GM_(E)M_(A))/(R^2)`
Simplifying the above equation we get,
`a_(A)=-(GM_(E))/(R^2)`
`a_(A)` is the acceleration of apple that it equal to 'g'.
Similarly the force experienced by Moon due to Earth is given by
`F=-(GM_(E)Mm)/(R_(m)^(2))`
`R_(m)` - distance of the Moon from the Earth,
`M_(m)` - Mass of the Moon.
The acceleration experienced by the Moon is given by,
`a_(m)=-(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 the Hipparchrus measurement, the distance to the Moon is 60 times that of Earth radius. `R_(m)=60R`
`(a_(A))/(a_(m))=((60R)^(2))/(R^2)=3600`
The apples's acceleration is 3600 times the acceleration of the Moon.
The same result was obtained by Newton using his gravitational formula.