Why Does an Object Travel in an Elliptical Orbit Due to Gravitational Force?

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An object travels in an elliptical orbit due to the gravitational force acting as a centripetal force, with the Earth located at one of the foci of the ellipse. When thrown, an object follows a parabolic path initially, but this is part of a larger elliptical trajectory. The gravitational force varies in magnitude as the object moves along its orbit, yet it can still be classified as a centripetal force. This classification holds true even as the force changes, as long as it continuously directs the object toward the center of the gravitational pull. Understanding these dynamics is essential for comprehending orbital mechanics.
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If we throw an object in straight line this objects travels in parabolic path until it hits the ground.
But in fact this parabola is only a part of an ellipse that object would travel in and center of the Earth is one of the foci points

I understand that object can circle around the Earth with certain speed due to gravitational force acting as centripetal force.

But why does object travel in elliptical orbit?

Could we still call gravitational force that causes this a centripetal force?

thank you
 
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So basicly you could still call a force acting on object going in elliptical motion a centripetal force, even if it is changing its magnitude?
 

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