how did Kepler law help newton to arrive at the inverse square law of gravity?
Answers
Explanation:
Albert Einstein is best known for his equation E = mc2, which states that energy and mass (matter) are the same thing, just in different forms. He is also known for his discovery of the photoelectric effect, for which he won the Nobel Prize for Physics in 1921
Answer:
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 them