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To answer the question one needs to ask what forces act on an orbiting body.
In the Newtonian model these forces are a centripetal force acting along the radius of the orbit and a tangential force.
The orbit is essentially a balancing act between the forces.
The existence of the tangential force depends on the angular velocity of the orbiting body not being constant. (The angular velocity is the number of revolutions per unit time.)
It can be shown using high school maths for circular motion, there is no tangential force acting on an object if the angular velocity does not change. So in the absence of external forces acting tangentially on the object such as the thrusters of an artificial satellite or the gravitational pull of an external body, a circular orbit is unstable.
For an elliptical orbit tangential forces do exist for the simple reason the radius or distance between the orbiting and central body varies along the orbit. The angular velocity changes according to the distance as defined by Kepler's laws of planetary motion.
Note that the Newtonian model is only an approximation. A much more detailed explanation can be given using General Relativity.
General Relativity helps to explain why Mercury's orbital plane also rotates around the Sun, a feature unexplained by Newtonian gravity.
Regards
Steven
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