Orbital Motion: Definition and Expression

In today's article, we are going to talk about orbital motion and its expression. In physics, Orbital motion can be defined as the motion in a circular path or orbit is called Orbital motion. For instance, the Earth and other planets like Mercury, Venus or Jupiter follow a circular orbit around the sun. 

So, in simple words, the movement of planets or other artificial satellites in a circular path is considered to be orbital motion.

How to derive an expression for the orbital motion:

Before deriving an expression for orbital motion, you must be clear that there is no difference between orbital motion and orbital velocity.

Let's derive an expression for orbital motion.

Take a satellite which revolves around the Earth in a circular path. For further clarification, we have shown you a figure below.

 "m" shows mass, whereas "v" manifests the satellite's speed. In the same way,  "M" in the figure can be considered as the Earth's mass, and the orbit's radius is shown as "r".

So, centripetal force will be responsible for the motion of a satellite around the Earth. The magnitude is given by:

In the same way, the gravitational force of attraction provides the centripetal force between the sun and the Earth. So, we use the law of gravitation by Newton, as given below.

Now, compare the equation of both forces.

The final relation will become,

or,

This relation manifests that the satellite's mass is not essential in explaining the satellite's orbit. So, any satellite that orbits at a distance, i.e. "r" from the centre of the Earth possesses the orbit speed, i.e., 

                            

Moreover, it can be concluded that if any satellite owns less speed than this value. It will not orbit around the Earth and will fall on the Earth ultimately.