Orbital Mechanics: Find Eqns of Motion w/ Initial Conditions

[Timothy S]

Hello,

After searching on the internet, I have come to the conclusion that there is no completely general way to calculate the position of an orbiting body. My question is whether there is a way to find the equations of motion with respect to time of a satellite orbit given only the initial tangential velocity, distance from the central mass, and mass of the satellite. If there is, I would appreciate a derivation of the equation.

Thank you.

 

[rumborak]

What you are referring to is called the two-body problem: https://en.wikipedia.org/wiki/Two-body_problem

 

[dreamermatt]

you are looking for paticular object?

 

[dean barry]

If you ignore the mass of the satellite, its easy, its rotation rate = v / r (radians per second)

If you had the mass of the orbited body:
Using the attached word document, given both masses, and the centre to centre distance, you can derive what you need, if not you may get some mileage from it anyway.