## Saturday, April 30, 2016

### Orbital Velocity and Escape Velocity of a body from a planet

Orbital velocity

Orbital velocity is the minimum velocity that has to be given to a body on a planet so that it can go to a certain height from the planet and there it starts rotating around that planet. Orbital velocity of a body around the planet depends on the mass of the planet and its radius. But it is independent of the mass of that body. It means the orbital velocity is same weather you want to orbit a small ball or a big and heavy body.

To determine orbital velocity of a body, we need to use the concept of centripetal force. Centripetal force is the resultant force acting on a body towards its center. It does not come from out side and the total effective force acting towards the center in a system is actually treated as centripetal force. When a body is revolving around the earth, centripetal force is nothing but the gravitational force between the body and the planet. By equating them, we can derive the equation for the orbital velocity of a body as shown in the video below.

For a body to revolve around the earth near to the earth, we shall give an orbital velocity approximately equal to 7.9 Km/sec. This is generally given to the artificial satellites send by us into the space. They further satisfy conditions like having a time period of 24 hours, rotates from west to east and if it is at a height of 36000 KM from the surface of the earth, they are called geostationary satellites.

Orbital velocity is independent of the angle with which we project the body into the space.

Escape Velocity

Escape velocity is the minimum velocity that we shall give to a body on the planet so that in escapes away from the gravitational pull of the planet and never comes back to the planet. It goes into the space and gets away from the influence of the planet. This is also independent of the mass of the body that is escaping from the planet.

For the planet earth, escape velocity is approximately 11.2 Km/sec. It means if we give that much velocity to any body from the surface of the earth, it escapes away from the gravitational pull of the earth and never returns back to the earth.

It is proved in the following video lesson that the escape velocity is root two times the orbital velocity. It means 1.414 times more. It means for a body all ready orbiting around the earth, if you increase its speed by 0.414 or 41.4 %, it escape from the earth influence and goes to space.

What kind of gases present around a planet depends on its escape velocity and that escape velocity further depends on the mass of the planet and its radius.

For example RMS velocity of oxygen gas molecules is more than the escape velocity of the moon and hence all oxygen escaped from the moon. It could not do the same from the earth as the escape velocity of the earth is more than the RMS velocity of the oxygen gas. The same is the explanation for the hydrogen gas availability around the sun. The escape velocity of the sun is so large such that hydrogen cannot escape from its influence and acting like a basic source for nuclear fission in it.

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