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Explain how Newton verified his law of gravitation. |
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Answer» Solution :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. |
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