The first and foremost reason for why all planets move around the sun is that sun has very strong gravitational force and makes the planets to move around it Just as the moon revolves around the earth because of earth’s gravitational force. So here again the question arises that if it is due to gravity then why planets have an elliptical orbit? As the pull must be same throughout the rotation of planets or they should completely move towards the sun rather than revolving. This happens because earth velocity’s direction makes the angle of 90 degree to the force of sun’s pull. Earth would start moving in a straight line if there will be no sun. This is the gravity of the sun which makes the earth and other planets to revolve around it.

This can be better understood with example. Let us suppose a man with supernatural powers stand on Mt. Everest and he throws the ball up with great speed because it is thrown by the man with great powers so it passes the horizon before coming back. We know that our earth is curved so it keeps on moving and continuously “falling” but will not reach the earth because the ball has reached in the atmosphere, the earth has curved surface and the part from where the ball has been thrown will move away if the football can reach back to earth because the earth is in continuous rotation. This is the process how the planets move in an orbit.
Always a force is required to move an object, to stop it or to change its direction. Planets does fly off in the space but they revolve around the sun because of sun’s strong gravitational force.