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

Kepler's Three Laws & Newton's Inverse Square Law

1. Kepler's Laws of Planetary Motion

First Law (Law of Ellipses): All planets move in elliptical orbits with the Sun at one of the foci.

Second Law (Law of Equal Areas): A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

Third Law (Law of Harmonies): The square of the time period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
(T² ∝ R³)

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2. How These Laws Helped Newton

Kepler’s third law showed that the time a planet takes to orbit the Sun depends on its distance from the Sun. Newton analyzed this motion and realized that an invisible force must be acting between the planets and the Sun. Using the relationship from Kepler’s third law, Newton derived the inverse square law of gravity, which states that the gravitational force between two masses is inversely proportional to the square of the distance between them.

Newton’s Law of Gravitation:
F = G × (m₁ × m₂) / r²
Where:
G = Gravitational constant
m₁ and m₂ = masses of objects
r = distance between their centers

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3. Animated Elliptical Orbit (Kepler’s First & Second Laws)

The blue planet speeds up near the Sun and slows down farther away, sweeping equal areas in equal times.