Can You Achieve a Circular Orbit with Non-Perpendicular Launch Velocities?

[m00npirate]

If you are at the distance R from a planet and you want to achieve a circular orbit your velocity must be Sqrt[Gm/R] perpendicular to the radius vector.

But what if you launch at an angle (ie no longer perpendicular to the radius)? Is it still possible to achieve a circular orbit if the perpendicular component is still Sqrt[Gm/R]?

 

[mathman]

Mt guess is that you will end up with some sort of ellipse.

 

[Meir Achuz]

You will definitely have a non-circular ellipse.