Artificial Satellite Basics

Satellite refers to any project that is orbiting earth, sun or other planetary bodies. Satellites can be artificial or natural. The artificial satellites basically work on principle of projectiles. The only force that works on satellites is gravity. Once launched in an orbit, gravity is the only force governing the motion of the satellite.

 Important Concepts

• Selection of tangential speed is very much important in case of launch artificial satellite launches. They are projected with such a speed that the “radius” of their curved path is “greater” than the radius of earth. However, not such a high speed that the satellite leaves the orbit and gets lost in space.
• The speed of an artificial satellite does NOT depend upon its mass. This implies that at a particular distance from earth, all objects would move at same speed of revolution.
• Higher the orbit is, lower is its speed, so when a satellite moved from higher orbit to lower orbit, its speed increases.
• If we throw the satellite of a speed lesser than 7900 meters per second or 28500 kilometers per hour, it will simply fall on earth. The speed higher than this will produce an elliptical orbit. However if this speed is more than 11.2 kilometers per second, it will escape the earth’s gravitation field and will never come back.
• Equator or the places near to equator are found suitable for launching the satellites as it will save efforts.
• Satellites are launched in Eastward direction, it also saves efforts.

Basics

When we throw a stone with some speed in the horizontal direction, it will follow a curved path and fall on the ground. When we throw the stone with a greater speed, it will follow a curved path that is even bigger than the previous one. Thus, greater is the speed, greater is the radius of the curved path as shown below:

Now, if we have such a powerful device to throw this stone with such a tremendous speed that radius of the curved path it follows becomes little bigger than the radius of earth, we cannot expect it to return to earth. Rather, it will keep on revolving around the earth. This is how the artificial satellites work. They are projected with such a speed that the “radius” of their curved path is “greater” than the radius of earth.

Gravitational pull of earth would provide the necessary centripetal force that is needed to keep it in its particular orbit. Here, we should note that speed of the satellite is carefully chosen so that it provides necessary force to keep it revolving. This implies that:

From the above formula, we first note that there is no place for m , which means that the speed of an artificial satellite does NOT depend upon its mass. This implies that at a particular distance from earth, all objects would move at same speed of revolution.

But the above formula says that v is dependent upon r. The above formula now we derive again as follows:

F (Gravitational) = F (centripetal)

In the above formula, G is the universal gravitational constant and M is the mass of earth. We arrive at v as follows:

Here we come to two conclusions:

Here we conclude that higher the orbit is, lower is its speed. When we whirl a small string with an small object tied at one of its and also allow to get it rolled around our finger, we find that the smaller the radius of the circle is, higher is its speed.

So, when a satellite moved from higher orbit to lower orbit, its speed increases.

Since, g= 9.8 square meters per second and radius of earth is 6.4 x 10⁶ meters, we conclude that

Thus, if we throw the satellite of a speed lesser than 7900 meters per second or 28500 kilometers per hour, it will simply fall on earth. But the speed higher than this will produce an elliptical orbit. However if this speed is more than 11.2 kilometers per second, it will escape the earth’s gravitation field and will never come back.

This value of 11.2 kilometers per second is known as escape velocity and it explains why we have the gaseous atmosphere which does not go away from earth. On moon the escape velocity is 1.9 kilometers per second and molecules of any gas formed on moon would have velocity more than this value and that is why moon has not gaseous atmosphere.

Launching a satellite needs tremendous forces, because providing it an speed of 28500 kilometers per second is not an easy task.

Launching a satellite on Equator versus Poles

Earth is not round and we all know that its radius on poles is smaller than its radius on equators. The away we move from centre of earth, lower is the gravitational force and this is the reason that the gravitational pull is minimum at Equator. So, Equator or the places near to equator are found suitable for launching the satellites as it will save efforts.

Launching a satellite in eastward versus westward direction

We know that Earth rotes from west to east, the satellites are launched in Eastward direction so that the speed of earth’s rotation which comes nearly 462 meters per second will provide it additional push. (40000 x 1000 ÷24÷60÷60=462 (though exact speed is 465.1 meters per second))