Weightlessness

NOTE: please can somebody check this because I am not totally sure if I have got it right. Thankyou -- sodium

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Weightlessness is the experience of apparently having no weight.

We experience weight on the earth because of the reaction of the floor to our weight. A particle in a container in free-fall experiences weightlessness. This is because there is no reaction to the particles weight from the container, as it is being pulled down with the same force. The acceleration of the container equals the acceration of the particle, which equals the acceleration caused by gravity. So weightlessness is when the acceleration of a body is equal to the acceleration caused by gravity.

A body orbiting the earth has the force of gravity pulling on it. This force is inversely proportional to the square of the distance of the body from the centre of the earth:

 (where f = force, r = distance from body to centre of earth, m mass of body, 
  a = acceleration of body, v = velocity of body)

 f = 1/r2

Acceleration is equal to the force divded by the mass of a body:

 a = f/m

So the acceleration caused by gravity for this particle is equal to:

 a = 1/r2m 

Although the body orbitting the earth is travelling at a constant speed, it has not got a constant velocity. Velocity is a vector quantity depending on both speed and direction. Because the direction is constantly changing the velocity is actually accelerating. This acceleration is in the direction of the gravitational attraction of the body to the earth - towards the centre of the earth - and is equal to:

 a = v2/r

For weightlessness to occur, this acceleration has to equal the acceleration caused by gravity:

 v2/r = 1/r2m

 v2 = 1/rm

This shows that the weightlessness depends on the velocity the body is travelling, the radius of the orbit and the mass of the body.

/talk?