Calculating distances with an elliptical orbit

[iLoveBigData]

Wasn't sure exactly what the title of this post should be.

Working on a side project using machine learning and the solar system (using n-body simulator).

Let's say I have two bodies with coordinates:

Body1: x=-1.42790218981 y=1.4003882805 z=0.0
Body2: x=0.983274588755 y=0.0477301860159 z=0.0

and their respective orbits are:

B1: a=2.00000001449 e=7.84859710126e-09 inc=0.0 Omega=0.0 omega=2.75273162508 f=-0.386809335815

B2: a=1.36522588428 e=0.41230308113 inc=0.0 Omega=0.0 omega=1.24417006229 f=-1.19566606343

Can I figure out the coordinates of Body2 anywhere along the orbit? I'm trying to find how the smallest distance between the two bodies if they continue pursuing their orbits?

Please let me know if I need to clear up some details.

 

[sunrah]

Assuming you know the mass of the central star you can easily find the period and angular velocity of B2 using Kepler's third law. Unless masses B1 and B2 are very big, you can probably neglect these. This will allow you to find the coordinates of B2 after some time t seeing as you know the orbits. Of course you can do the same for B1.

If you want to find the separation distance r_s between the two bodies at a given time. Then I might calculate position of B1 and B2 using polar coords, i.e. r₁ = r(θ₁) and r₂ = r(θ₂) where θ is angular displacement. then use the law of cosines
r_s² = r₁² + r₂² - 2r₁r₂cos(θ₂-θ₁). perhaps this will work.