I'm working on a game idea that includes objects orbiting around a common center point. I would like to have some way of knowing (mathematically) when two given objects/bodies will be at the same circumferential position (in radians) in their respective orbits.
What is known:
The movement of objects is 2 dimensional
All objects follow a circular orbital path around a common center point.
The distance of the orbiting object from the center point is known, but may vary from object to object.
The time it takes for any given object to complete one full revolution is known in seconds. This will also vary from object to object.
The starting point of any given object is known in radians. This will also vary from object to object.
All objects begin moving/orbiting at the same time.
All objects are circles and their positions on the coordinate plane are dictated by their center points.
All objects will continue their orbits indefinitely.
No external forces are acting on the objects.
Let's assume we are only comparing two objects at a time.
Object 1 is at a radius of 180 pts from the common center point and is located at 0.5 radians. It completes one full revolution in 3 seconds.
Object 2 is at a radius of 220 pts and is located at 0 radians. It completes one revolution in 5 seconds.
The objects are orbiting in the same direction.
What am I trying to figure out?
How can I, for example, determine the first 5 points when/where the two orbiting objects will cross paths. That is, each time a single straight line can be drawn from the common center point through the center points of both objects.
If any additional information is needed to calculate or if this isn't as straight forward as I'm imagining it to be, just let me know and I will do my best to provide additional info. Thanks ahead of time, really appreciate any help you guys can provide. :)