Question

What is the source of the centripetal force that a planet requires revolving around the Sun? On what factors does that force depend?

Answer 1

Hint:Centripetal force is defined as a force which acts on a body which is moving circularly. It acts towards the center of the motion of a body and orthogonally to the position of the body. The centripetal force tends to attract the body towards the center of its motion.

Complete answer:
The net force which acts on a body to keep it in a circular motion is known as centripetal force. Centripetal force depends on the gravitational force between the Sun and the planet. The gravitational force is the main reason which allows the planets to revolve around the Sun and also develops centripetal force.From Newton’s Law of Motion we know that,
$F = ma$
where, $F = $ force, $m = $ mass of the body and $a = $ acceleration.
In case of circular motion,
Acceleration is known as centripetal acceleration, as ${a_c}$.
${a_c} = r{\omega ^2}$
where $r = $ radius of curvature for the motion of the body and $\omega = $ angular velocity.
So, the centripetal force can be written as,
${F_c} = mr{\omega ^2}$

Gravitational force is formulated as,
${F_g} = \dfrac{{GMm}}{{{r^2}}}$
where $M = $ mass of the larger body, $m = $ mass of the smaller body, $G = $ Universal gravitational constant, $r = $ distance between the smaller and the larger body.
The factors on which the gravitational force depends are:
(i) The mass of the Sun.
(ii) The mass of the planet.
(iii) The distance between the Sun and the planet.

Note: It must be noted that it has to be uniform circular motion in order to achieve the centripetal force equal to the weight of the body. The centripetal force causing rotation can be proved by Newton’s First Law which states that a body will continue to move in a straight line if it is not worked upon by an external force.