Question

Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity? Answer the question

Answer 1

1: The orbit of a planet is an ellipse with the sun at one of the foci.2: The line joining the planet and the sun sweeps equal areas in equal intervals of time.3: The square of its period of revolution around the sun is directly proportional to the cube of the mean distance of a planet from the sun. 

Answer 2

Dear Student,

◆ Kepler's Laws of planetary motion-

• Kepler described 3 different laws of planetary motion-

1. Kepler’s Law of Orbits –

• The Planets move around the sun in elliptical orbits with the sun at one focus.

2. Kepler’s Law of Areas –

• The line joining a planet to the Sun sweeps out equal areas in equal interval of time.

3. Kepler’s Law of Periods –

• The square of the time period of the planet is directly proportional to the cube of the semimajor axis of its orbit.

◆ Inverse square law of gravity -

• Kepler’s 3rd law of planetary motion led Newton to establish the inverse-square rule for gravitational force between two bodies.
• The square of the time period of the planet is directly proportional to the cube of the semimajor axis of its orbit. i.e. T² ∝ r³

Newton understood that centripetal force for rotation of planets is caused by gravitational force.

Fg = Fc

Fg = mv²/r = mrw²

Substitute, w = 2π/T

Fg = mr(2π/T)²

Fg = mr.4π²/T²

But by Kepler's law, T² ∝ r³

Fg ∝ mr.4π²/r³

Fg ∝ m4π²/r²

Fg ∝ 1/r² ...(taking m4π² = constant)

Therefore, gravitational force is inversely proportional to square of distance.

Hope that is helpful...