How do Satellites orbit the earth?

Have you ever wondered how satellites orbit the earth?  Just how do they stay up there?  It’s the same reason that the earth does not fly off into space.  Satellites orbit the earth, just as the earth orbits the sun.  It all has to do with gravity, and we have Isaac Newton to thank for the discovery of gravitational attraction.

Newton published the law of gravitation in 1687.  This law basically says that everything in the universe is attracted to everything else by a force.  This force is related to the masses of two objects that are attracted to each other.  This force also has a relation that is opposite to how far they are from each other, squared.  Confused yet?  Maybe an example would help.

The law of gravitation can also be written in the form of an equation, Fg = (Gm1m2)/r^2. In this equation, Fg is the degree of the gravitational force between the two objects and it is determined by multiplying the two masses of the objects, m1 and m2, by G, which is the gravitational constant that has a value of 6.67×10^-11 N m^2/kg^2.  You then divide this answer by the distance between the two objects.  And then you square it.

Let’s say that you would like to figure out the gravitational force between you and the earth.  First, you need the two masses, m1 and m2.  Your mass can be m1, and let’s just say for example sake that you weigh 70 kg.  And the mass of the earth, m2, is 5.98 x 10^24 kg.  Then we will have to figure out the distance between you and the earth’s center.  I’ll save you the googling and tell you that it is 6.38 x 10^6 meters.  So you plug all of this into the law of gravitation formula and you find that the force is 685.54 Newtons.

Back to satellites.  We are all very familiar with satellites, but just how do they stay up there in orbit? Keeping the law of gravitation in mind, imagine that you are in a sports car and you are driving very fast towards a cliff.  You dive off the edge of the cliff and you eventually take a parabolic path and eventually land, due to gravity.  You then try this again, but this time you increase your speed. You notice that you now land farther than you did the first time.  Hmm, increasing speed means that you land further?  Well what if you were to drive so fast that you completely miss the earth and end up in orbit?

As you are in the air the earth starts to curve beneath you.  If you were lucky enough to have a launch point that were to clear all obstacles in your way, such as mountains, then you would be able to go right around the earth without having to land.  You are now essentially a satellite.  If there was nothing to slow you down, you would eventually orbit the earth and return to the point where you launched, and then you would continue to orbit, just as satellites do.

This is known as a closed orbit, and all closed orbits are ellipses.  Or you can think of it as a circle, which is a special type of ellipse.  The force that is acting on a satellite which is in orbit is the earth’s gravitational attraction.  As the satellite is orbiting with constant speed, it is falling around the earth.

Author: Claude