Back in News #3 and the subsequent video I talked about reference frames. As this update builds on that idea, I’ll recap. It is often useful for course planning to draw the universe as if something that is in motion isn’t. If you draw the solar system from the reference frame of the sun, the course of the moon makes a wobbly spiral around the course of the earth, which isn’t very useful for flying from the earth to the moon. If you draw the solar system from the perspective of the earth, then the moon makes an orderly circle that’s much easier to deal with. The sun also makes a circle around the earth then! And the other planets make weird curly paths.
Incidentally, these kinds of weird shapes are related to the various complicated systems people came up with to explain the motion of the planets in the sky when they thought the earth was motionless. In any case this relatively simple form of reframing the view can be quite useful for many kinds of courses, but there’s another step further beyond that’s useful, the rotating reference frame.
Consider the Lagrange points. To recap them as well: For every sufficiently massive object in a circular orbit around a star or planet these five points of relative stability exist, three along the line between the two bodies, two along the orbit of the smaller body at a 60 degree angle to that line. These locations have been used for space missions both completed and proposed and have influenced the locations of large populations of asteroids, so they’re worth consideration.
If you draw the motion of the earth-moon L-points from the perspective of earth you get circles. If you draw them relative to the moon, you get circles. Neither of these are great for helping you see how your course relates to these points.The solution is to draw the universe as if neither is moving. You create a rotating reference frame where the universe rotates around your primary object once for every orbit the secondary makes. (The implementation for ASR actually just rotates the universe so the secondary is always to the direct right of the primary, but the difference is probably only significant for notably elliptical orbits) This has the following effects:
- The secondary appears to stay motionless, if it’s orbit is perfectly circular. Otherwise it’ll wobble around a bit.
- The Lagrange points appear stationary too, plus a little wobble as above.
- Objects orbiting the primary or secondary will generally have recognizable orbits rather than arcane curls
- Objects interacting with the Lagrange points will have quite interesting curls!
If you look at diagrams of the Apollo missions where you get a figure-8 like structure with the ship circling around a static earth and moon, this is an example of a rotating reference frame. I have found that planning similar courses in Atomic Space Race is a lot easier with this tool available. Without it need to either rapidly switch between reference frames or do a lot of scrubbing along the timeline to determine you approach your target after tweaking a transfer burn.
The same advantages manifest when dealing with courses that interact with Lagrange points. A great example from outside of the project is this animation of the motion of asteroids influenced by Jupiter’s Lagrange points, produced by Petr Scheirich. If you drew those all those courses in a normal, sol-centric non-rotating frame you’d just have a huge mess of orbits overlapping Jupiter’s, but in the rotating frame you can clearly see the structure emerge.
If you want to see this in motion in-game, particularly with examples of Lagrange-interacting orbits, here’s a video I made of that.