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Yes this question is on the internet and has a lot of answers but they all suggest orbital velocity in an ideal circular orbit. I want it for an elliptical orbit. I have a few questions and explanations:

So the basic concept of sending something in a circular orbit from the focus involves taking an object to a height h and the giving it a perfect horizontal velocity without any vertical velocity at that height, which is given by $$v_o=\sqrt{\frac{GM}{R+h}}=\sqrt{\frac{GM}{h}}$$ (since the star is a point) (Please correct me if I'm wrong). Well for an elliptical orbit having a point star at one of its foci the idea according to me is giving a body any velocity at any angle(except $\pi/2 rad$) should put it into orbit. Am I right here?

If the above explanation is right then why can't we throw an object from earth into orbit? My explanation for this doubt is that due to the Earth having a diameter ,the object needs a specific velocity and angle for the orbit to not intersect with the planet.

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Suppose you throw the object hard enough for it to orbit the earth in an ellipse. The point where you are throwing it is on the ellipse. It has a large upward velocity at that point, so the ellipse is coming up from below the surface.

The orbit will carry it back to that point. Except that it will crash into the Earth somewhere, and try to burrow through the earth to the launch point.

The best you could do would be to make the orbit horizontal at that point. Then it will just skim the surface on each orbit. Without an atmosphere, that would be possible. But remember to duck every orbit!

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