# Calculating Orbital Velocity in 2D

Torstein Bjelland
Hi!

Imagine a planet is alone in a two dimensional universe. It has a mass mp. Suddenly, the planet's moon appears out of nowhere. It appears with a distance r from the planet, has a mass mm and velocities vx in the x-direction and vy in the y-direction. The distances rx and ry are also known. A gravitational force F from the planet acts on the moon. Fx and Fy are known, as well as the angle α (see figure in attachment). All variables mentioned above are known.

Here is my question: How do you calculate vx and vy at any point in the moon's trajectory without knowing the semi-major axis, orbital period or what type of orbit the moon is going to enter in the first place?

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