Source of Centripetal Force for Planets

The centripetal force that keeps a planet in orbit around the sun is provided by the gravitational force between the two celestial bodies. This force is known as the gravitational centripetal force. The gravitational force is the attractive force between any two masses, which depends on their masses and the distance between them. In the case of a planet orbiting the sun, the centripetal force is directed towards the sun, keeping the planet in its elliptical path.

Gravitational Centripetal Force:
The gravitational centripetal force can be explained by Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it can be expressed as:

F = (G * m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.

Dependence on Mass and Distance:
The centripetal force required for a planet to remain in orbit around the sun depends on two main factors: the mass of the planet and the distance between the planet and the sun.

1. Mass: The more massive the planet, the greater the gravitational force acting on it. Consequently, a larger centripetal force is needed to balance the gravitational force and maintain the planet's orbit. This is why larger planets, such as Jupiter, require a stronger centripetal force compared to smaller planets like Earth.

2. Distance: The distance between the planet and the sun also plays a crucial role. As the distance increases, the gravitational force decreases, requiring a smaller centripetal force to maintain the planet's orbit. This is evident in the planetary orbits, where the outer planets, like Neptune, have larger orbits and require a smaller centripetal force compared to inner planets like Mercury.

Conclusion:
In conclusion, the source of the centripetal force that a planet requires to orbit the sun is the gravitational force between the two bodies. This force depends on the masses of the planet and the sun, as well as the distance between them. The gravitational centripetal force acts as the inward force, allowing planets to maintain their elliptical orbits around the sun.

∆ source of the centripetal force is gravitational force between the earth and the sun.

∆ This force depends upon the mass of earth and sun and distance between the both.