There are mainly three different paths taken by an object thrown with some velocity
elliptical - lower velocities as compared to escape velocity will result in elliptical paths
parabolic and hyperbolic - velocities greater than escape velocities will result in open ended paths like these
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The gravity of the sun is the main force why earth keeps rotating around the earth. There is no other force to change its course and even if there is, it is not enough to change the orbit.
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All the satellites are launched at some special velocity called as escape velocity. This is the least required velocity to get out of the gravitational pull of earth. Now, when out in space, there must be a perfect balance between momentum and gravity. If a satellite is very close to earth and does not have sufficient momentum , it will FALL DOWN. Therefore, satellites which are near the surface of earth need to have very high speed so that their high momentum can counteract the gravity and they keep on rotating in an orbit
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