Question

write the three laws given by Kepler. how did they help Newton to arrive at the Inverse Square Law of Gravity?

Answer 1

Kepler first law state that the orbit of a planet is an ellipse with the at one of focii
Kepler second law state that the line joining the plane and sun sweep equal areas in equal interval of time
Kepler third law state that the square of period of revolution around the sun is directly proportional to the cube of mean distance of planet from the sun

how?
distance travelled by planet=2πr
distance of planet from the sun =r
time taken =t
$v = \frac{2\pi \: r}{t} \\ f = \frac{mv {}^{2} }{r } \\ f = \frac{m( \frac{2\pi \: r}{t}) }{r } \\ f = \frac{4.m\pi {}^{2}r }{ {t }^{2} } \\ multipliming \: and \: dividing \: by \: {r}^{2} \\ f = \frac{4.m {\pi}^{2} {r}^{3} }{ {t}^{2} } \times {r}^{2} \\ according \: kepler \\ third \: law \: \\ f = \frac{4.m {\pi}^{2} }{ {r}^{2} } \times k \\ f = \frac{4.m {\pi}^{2} }{k}$