The Motion of Satellites Around Earth

Any heavenly or human-made body that revolves around a central body, such as the Earth, Sun, or other bodies in the solar system, is known to be a satellite. However, these satellites revolve around and make either circular or elliptical orbits when it comes to Earth. The earth, in this case, is said to be the central body. 

In this study material note, we will be discussing the motion of satellites around earth. The motion of satellites around the planet has the same characteristics as any other body in a circular motion. Let us learn in detail about the topic. 

What are Satellites?

Satellites are objects or bodies that revolve around the heavier body in space. There are two types of satellites: 

• Natural Satellites: Satellites naturally present in space, such as comets and the Moon. 
• Artificial Satellites: Satellites made by humans for various purposes such as weather forecasting, communication, etc.

You can find numerous natural satellites in space, and every planet has at least one of its natural satellites. Where our earth has only one, the Moon, other planets such as Jupiter are known to have 53 natural satellites (moons). 

The Soviet Union, now Russia, launched the first artificial satellite into space on Oct 4, 1957, named Sputnik 1. The launch of Sputnik 1 triggered what was called the Space Race, where nations around the world competed with advancements in space sciences. 

The Motion of Satellite Around Earth

The satellite orbiting the earth has a velocity and acceleration component similar to an object moving on a circular path. While revolving around the earth, satellites make a circular path. 

The tangent to this circular path gives the direction of the satellite’s velocity, whereas acceleration is towards the centre of the circle. 

Various forces act between the Earth and the satellite, making them orbit on a circular path. The net force that acts in the inward direction of the circle makes the satellite accelerate around the Earth. 

The gravitational force that acts between the Earth and the satellite and centripetal force are two main forces causing the motion of satellites around Earth. 

If there is no centripetal force, satellites will keep moving at the same speed and direction. In such a case, the satellite will move on a straight path, and there will be no circular motion. 

However, some satellites move along an elliptical orbit. In that case, unlike the circular motion, the central body is positioned at foci of the ellipse. 

As a result, the velocity component of the satellite acts along the tangent of the ellipse. At the same time, the acceleration acts towards the focus. 

As per Newton’s Second Law of Motion, the direction of the net force will be towards the focus. 

This is because, along with centripetal force and gravitational force, there acts a force component either in the same or opposite direction. 

This component of force changes the speed of the satellite. Hence, satellites with elliptical motion do not have a constant speed.

Orbital Velocity of Satellite 

The velocity with which satellites move around the earth is known as the orbital velocity of satellites. 

Orbital velocity is also known as critical velocity. Finally, the minimum velocity is required to make a satellite move around the earth with stability. 

Let us derive the formula for the orbital velocity of the satellites. 

Let, 

Mass of Earth = M

Mass of Satellite = m

Orbital Velocity = vo

Distance between satellite and earth = h

The radius of Earth = R

The radius of orbit = r

As told earlier, the centripetal force makes the satellite move in the orbital path. The gravitational force balances this centripetal force. 

The centripetal force is given by: 

FC=mvo22

Gravitational force is given by: 

Fg=GmMr2

The satellite moves on the orbital path as long as: 

FC=Fg

mvo22=GmMr2

vo2=GMr

vo=GMr= GMR+h

Since g is the acceleration due to gravity, there its value will be: 

mg= GMmR2 

g= GMR2

GM=gR2

On substituting the value of g in the above (i) equation, we get: 

vo=gR2R+h

If the satellite is very close to the earth, then  R+h ≈ R

vo= gR

This velocity is required to make the satellite move on an orbital path by balancing gravitational pull with the inertia of the satellite. 

If both are not balanced, the satellite will leave the orbital and keep moving in a straight line in space. 

Escape Velocity of Satellite 

The escape velocity of a satellite is defined as the minimum velocity required by the satellite to escape the earth’s gravitational pull. The formula gives it: 

ve= 2GMR=2gR

On comparing the escape velocity and orbital velocity, we get the relationship between them as: 

ve=2vo

Conclusion 

To conclude, we learned that the satellites revolve around the Earth either in a circular or elliptical orbit. The velocity with which satellites orbit around the Earth is known to be orbital velocity. The orbital velocity balances the inertia and gravitational force, thus making the satellite curve around the Earth. 

Its distance from the Earth influences the motion of a satellite around it. At a high altitude, that is, with a greater distance, the satellite remains in the path for a longer period.