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Imagine a planet is alone in a two dimensional universe. It has a mass m_{p}. Suddenly, the planet's moon appears out of nowhere. It appears with a distance r from the planet, has a mass m_{m}and velocities v_{x}in the x-direction and v_{y}in the y-direction. The distances r_{x}and r_{y}are also known. A gravitational force F from the planet acts on the moon. F_{x}and F_{y}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 v_{x}and v_{y}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?

Thank you in advance for all answers!

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# B Calculating Orbital Velocity in 2D

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