Gravitational Force

Gravitational Force – A Universal Law

Ever wondered how do planets revolve around the Sun?  The Earth attracts the Moon, and the Moon attracts the Earth, so shouldn’t they both just collide. Why doesn’t the moon fall? Why does it keep revolving around the Earth?

The answer to all such questions lies in the understanding of gravitation. The universal force of attraction which is acting between objects is known as gravitational force.

According to Newton’s universal law of gravitation, the force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them. This relation can be given as:

\(F~∝~\frac{(m_1 m_2)}{r^2}\)

where,

\(F\) is the gravitational force between two bodies

\(m_1\) is the mass of the first body

\(m_2\) is the mass of the second body

\(r\) is the distance between the centers of two bodies

The force exerted by two bodies with mass \(m_1\) and \(m_2\), whose centers are \(r\) units apart is given as:

\(F~=~G\frac{(m_1 m_2)}{r^2}\)<

Newton’s cannonball is a ‘thought experiment’ given by Newton which leads to the hypothesis that force of gravity is universal, and it plays the major role in planetary motion.

According to this thought experiment, he assumed a cannon on the top of the very high mountain peak. The following cases can arise if the canon is loaded with gunpowder and fired.

  • If the speed of cannon is low, it falls on the Earth following a projectile motion.
  • If at that particular altitude, the speed of cannon is equal to the orbital speed, the cannonball will go on circling the Earth about a fixed orbit.
  • If the speed of the cannon ball is higher than the orbital velocity but is insufficient to leave the Earth i.e. less than the escape velocity of the Earth then, the cannon ball continues to revolve around Earth in elliptical orbit.
  • If the speed is equal to escape velocity or greater than that, the cannon ball leaves the Earth in a parabolic or hyperbolic trajectory.

Gravitational Force

Now, coming back to our original question how do planets revolve around the sun? Well, the gravity of sun keeps the planets around it in fixed orbits. Due to the same reason, the moon orbits the Earth due to the Gravitational pull of the Earth on the moon. But if the sun is attracting the Earth, why doesn’t it fall into it or why doesn’t the moon collides with the Earth?

The reason behind this is that Earth has a velocity perpendicular to the gravitational force exerted by the sun. Thus, the planets move sideways in addition to getting attracted by the sun which keeps them moving in specified orbits. Similarly, the moon revolves around the Earth without falling into it.


Practise This Question

120x sin1x1x2dx=