Gravitation - Newton's universal law of gravitation

Do you know that there is a force of gravity between you and your pc/laptop/phone right now? The force of gravity exists between any two objects with mass. In this topic, we explore not only how to calculate the magnitude of the force of gravity between any two objects, but we will also study gravity in the context of Kepler’s laws of planetary motion and the orbits of man-made satellites.

Newton's universal law of gravitation

As mentioned earlier, the force of gravity exists between any two objects that have mass. What’s even more interesting is that the magnitude of gravitational force you are exerting on the Earth is exactly the same as the magnitude of gravitational force the Earth is exerting on you! In other words, you are pulling the Earth just as strongly as it is pulling you.

Why then do we accelerate towards the Earth, rather than the Earth towards us? Hint: it has something to do with mass.

Watch the video for a detailed explanation.

Gravitational acceleration / gravitational field strength

In your earlier years, you would have learnt that Weight, W = mg. Weight is the force of gravity acting on an object.

Watch out: DO NOT confuse between g and G! G is the gravitational constant. It has a fixed value. g is the gravitational acceleration experienced by an object due to a gravitational force. g can also be defined as the gravitational field strength of a gravitational field. It is the force per unit mass acting on an object in the gravitational field.

g is not constant and is inversely proportional to the square of the distance between the two centres of mass of two bodies. This is similar to the relationship in newton’s universal law of gravitation.

It is very important to understand that the formula for weight (W) is based on the weight of the smaller object, i.e. the force of gravity acting on the smaller object exerted by the larger object. From this, we can see that the mass of the smaller object does not affect the gravitational acceleration experienced by it.

This means that no matter what mass the object has, the gravitational acceleration experienced by the object is the same. Let’s put this into context. The gravitational acceleration experienced by a lorry and a motorcycle on the road is exactly the same!

Centripetal Force

Centripetal force is a force that acts on an object in circular motion. Centripetal force is a force that acts on an object and causes it to move in circular motion. The direction of the centripetal force is always towards the centre of the circular path of motion. We have a new term to explore here – linear speed. Linear speed is the speed of the object along its circular path.

Formula for centripetal force.

Remember that although the speed of an object in circular motion may be constant, its velocity cannot be constant! Can you identify the reason for this?

It is because the direction of the object is constantly changing. Since it moves with changing velocity, it is accelerating. 

When an object in space is in orbit around another object, gravity acts as the centripetal force. The motion in an orbit is circular motion.

Watch the video for a detailed explanation.

Mass of the Earth and the Sun

You can imagine that there is no way to actually measure the mass of the Earth or the Sun! So how do we know their masses?

Using our knowledge of centripetal force and a few other details, we can calculate the mass of the Earth and the Sun.

The mass of the larger body, M (the Earth or the Sun) can be calculated if we know the following details:
r – orbital radius (distance between the centres of mass of the the larger body and the smaller body)
T – orbital period