49Let us consider the following equations..
1. GMmr2 = mv2r
Suppose the solution to this is given v=vo
2. Now, we all know about escape velocity.
Now suppose we are "throwing" a satellite from a "heavenly body" to orbit it with a velocity v from at a distance r from the centre...
case 1: If v≥vescape , then the satellite never comes back.
case 2: If v=vo of equation, it follows a circular path.
case 3: If v<vescape but v≠vo then the satellite moves in an elliptical path. (This can be proved mathematically)..
a) In case of v<vo, the satellite will fall back to earth's surface following elliptical path (and not parabolic path as in projectile motion)
b) In case vo<v<vescape the satellite undergoes revolution aroung heavenly body following elliptical path...
1I think that due to the gravitational pull of the both the sun and the moon, the earth revolves in an elliptical orbit. Then there is the Jupiter with its strong gravity pulling everything near it. Due to this reasons the earth may not complete a circular orbit and instead of that move in an elliptical orbit.
1once i had derived that an electron moves around the neucleus in an elleptical orbit. simillarly we can prove that the path of earth is also elleptical