My relevant knowledge:
This question works in two dimensions, with a two-body problem (see bottom for context).
To my understanding, a two-dimensional orbit has the following orbital elements (3D has 3 more, I believe):
- Semimajor axis: Half the distance from periapsis to apoapsis, in kilometers
- Eccentricity: The variation of the orbit from a perfect circle, unitless from 0 to 1
- Rotation/Longitude of Periapsis: The angle from the periapsis to a reference direction with the orbited body as the vertex, in radians
Given a burn of ΔV (meters per second) in either the prograde, retrograde, radial, or anti-radial direction, how can I calculate the orbital elements of the new orbit? That is, what equations give the effect of a burn in one of those four directions on the semimajor axis, eccentricity, and rotation of the orbit?
If the burn is a combination of two directions (say, <-100, 200> which is to say a burn that changes velocity 100m/s in the retrograde direction and 200m/s in the radial direction), do I simply use the equations separately and combine the effects by, say, multiplication?
This is not homework - just a personal project. I'm a beginner to orbital physics, attempting to write a space simulator program in Java based on the patched conic approximation. My simulator stores the motion of a body using the three elements I listed, as well as if the direction is clockwise or counter-clockwise. The position of the body is stored as the mean anomaly along the orbit. I simulate the actual motion on the screen by using the orbital period to find the change in mean anomaly over the time that has passed. And to retrieve the actual velocity of the body I just have to calculate it using the orbital elements and the mass of the orbited body.
This is the best approach I could come up with for programmatically simulating orbital mechanics. If you have any suggestions for an improved way of storing the motion and position of bodies in the patched conic approximation, or an improved idea on changing the orbital elements with velocity changes in one of the four directions, feel free to let me know.