Right the 3 law of keepler how did they help newton to arrive at the inverse square law of gravity
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Answers
Answer:Three laws by Kepler:
(law of elipses). An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time (Law of equal areas). ... Facts like planets move on ellipses will continuously accelerate helped newton to from his law of gravitation
Explanation:
Newton used Kepler's third law of planetary motion to arrive at the inverse-square rule. He assumed that the orbits of the planets around the Sun are circular, and not elliptical, and so derived the inverse-square rule for gravitational force using the formula for centripetal force. This is given as:
F=
r
mv
2
.... {i) where, m is the mass of the particle, r is the radius of the circular path of the particle and v is the velocity of the particle.
Newton used this formula to determine the force acting on a planet revolving around the Sun. Since the mass m of a planet is constant, equation (i) can be written as:
F α
r
v
2
... (ii)
Now, if the planet takes time T to complete one revolution around the Sun, then its velocity v is given as:
v=
T
2πr
... (iii) where, r is the radius of the circular orbit of the planet
or, v α
T
r
... (iv) [as the factor 2π is a constant]
On squaring both sides of this equation, we get:
v
2
α
T
2
r
2
... (v)
On multiplying and dividing the right hand side of this relation by r, we get:
v
2
α
r
1
r ... (vi)
According to Kepler's third law of planetary motion, the factor
T
2
r
3
is a constant.
Hence, equation (vi) becomes:
v
2
α
r
1
... (vii)
On using equation (vii) in equation (ii) we get:
F α
r
2
1
Hence. the gravitational force between the sun and a planet is inversely proportional to the square of the distance between