I am trying to understand the existence of orbits apart from the elliptical one. I have used the following line of thought.(adsbygoogle = window.adsbygoogle || []).push({});

Consider an object moving from infinity towards a planet. The object has kinetic energy alone at infinity. But it develops a potential energy as it comes closer to the planet. Thereby, its kinetic energy reduces. As it comes sufficiently closer to the planet, its kinetic energy reduces. At the radial distance wherein its speed is equal to the orbital speed of the planet, it starts to move around and orbit the planet. But if its speed throughout somehow manages to be larger than the orbital speed then it continues to move away from the planet, suffering only a light deflection.

Thus, I gather that it is imperative that the speed of the object at all points be larger than the orbital velocity. But then, the gravitational force only always tends to infinity. In other words, the gravitational force always affects the object no matter how far away it keeps on going. My analysis is that, if the change in velocity as the object moves closer and farther away from the planet is negligible, then the object movies in a hyperbola. But if the change is not negligible and not larger enough reduce the speed to the orbital speed, then I guess it moves in a parabola.

I am developing on the mathematics to follow this. But I would like to know if my analysis is right.

Thanks in advance.

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# Orbital and escape velocity

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