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Explain how Newton verified his law of gravitation.

Answer» <html><body><p></p>Solution :The gravitational force <a href="https://interviewquestions.tuteehub.com/tag/experienced-13456" style="font-weight:bold;" target="_blank" title="Click to know more about EXPERIENCED">EXPERIENCED</a> by the apple <a href="https://interviewquestions.tuteehub.com/tag/due-433472" style="font-weight:bold;" target="_blank" title="Click to know more about DUE">DUE</a> to Earth.<br/>`F=-(GM_(E)M_(A))/(R^2)` <br/>`M_(A)` - Mass of the apple, `M_(E)` - Mass of the Earth and R - Radius of the Earth.<br/>Equating the above equation with Newton's <a href="https://interviewquestions.tuteehub.com/tag/second-1197322" style="font-weight:bold;" target="_blank" title="Click to know more about SECOND">SECOND</a> law, we get<br/>`M_(A)a_(A)=-(GM_(E)M_(A))/(R^2)` <br/>Simplifying the above equation we get,<br/>`a_(A)=-(GM_(E))/(R^2)` <br/>`a_(A)` is the acceleration of apple that it equal to 'g'.<br/>Similarly the force experienced by Moon due to Earth is given by<br/>`F=-(GM_(E)Mm)/(R_(m)^(2))` <br/>`R_(m)` - distance of the Moon from the Earth,<br/>`M_(m)` - Mass of the Moon.<br/>The acceleration experienced by the Moon is given by,<br/>`a_(m)=-(GM_(E))/(R_(m)^(2))` <br/>The ratio between the apple's acceleration to Moon's acceleration is given by<br/>`(a_A)/(a_m)=(R_(m)^(2))/(R^2)` <br/>From the Hipparchrus <a href="https://interviewquestions.tuteehub.com/tag/measurement-19276" style="font-weight:bold;" target="_blank" title="Click to know more about MEASUREMENT">MEASUREMENT</a>, the distance to the Moon is 60 times that of Earth radius. `R_(m)=60R` <br/>`(a_(A))/(a_(m))=((60R)^(2))/(R^2)=3600` <br/>The apples's acceleration is 3600 times the acceleration of the Moon.<br/> The same result was obtained by Newton <a href="https://interviewquestions.tuteehub.com/tag/using-7379753" style="font-weight:bold;" target="_blank" title="Click to know more about USING">USING</a> his gravitational formula.</body></html>


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