How to calculate angle between two objects in orbit

Question

So I have 2 objects in orbit around the same body, and I have all the orbital elements associated with each body. How do I calculate the angle between them both or figure out when they are a certain angle apart using only the all the orbital elements I have?

Answer 1

I presume you're talking about Newtonian mechanics with only one spherical body of non-negligible mass (let's say the Sun), and the others in elliptical orbits. Now unfortunately if these ellipses are not circles the position as a function of time is not available in "closed form": you have to solve an equation

$$ t = \dfrac{a^{3/2}}{\mu^{1/2}} (E - e \sin(E)) $$

to get the eccentric anomaly $E$ as a function of time $t$, and then the coordinates of the body can be obtained from that. However, if the eccentricity $e$ is small, this is well approximated by a series in powers of $e$.

Once you have the positions, you get the angle using the Law of Cosines, as others have mentioned.