How to calculate the orbit of a satellite knowing its speed and the mass of the planet?

Question

Physics

I am creating a primitive spaceship simulator. It is necessary to display the ship's orbit around the planet. The magnitudes and velocity vectors, positions and masses of two bodies (ship and planet) are known. It was not possible to find a formula for obtaining the parameters of the orbit from the speed of the satellite and the mass of the planet.

Answer 1

You can start reading here: https://en.wikipedia.org/wiki/Osculating_orbit
Or use the formula of gravitational attraction and Newton's second law and calculate the state in finite time increments.