Recap: Under constant-acceleration, travel time is proportional to square root of distance. So, I created a square-root projection of our solar system to see if such a 2D projection is a useful visualisation tool. Object sizes (radii) and object distances both use square-root scaling, but with different origins. See figure for more explanation.
Changes from Version 1: The radii in the previous version was double what it should have been. Fixed here. I also included what straight-line constant-g trajectories would look like in this square-root projection. All the trajectories depicted here are actually straight-lines! The square-root projection makes them warp (especially around the origin, i.e. the Sun). Also included the solar system in one-dimension because that was a major request. The figure is now in a much higher resolution, i.e.,1920 x 1080, with pictures of the actual bodies and not just circles.
Is this a useful projection? My objective in sharing in this community is to get feedback on whether or not this is a useful tool for visualising the solar system, especially in a scenario where we have regular spaceflights at an inter-planetary scale. So far, despite the warping around the Sun, I kinda feel like this is a pretty good projection for visualisation purposes, but I am obviously biased so would appreciate feedback. Linear projections are too "empty" for easy human comprehension, and logarithmic projections don't let us appreciate how far away outer planets are. I think square-root hits a pretty useful middle-ground.
I wish I could label this under "Discussion" because that is the purpose of this image, not just to display but to get feedback about the usefulness of such a 2D projection. Sorry for reiterating, but I wanted to make my reason for posting absolutely clear.
by thauyxs
1 Comment
But we don’t move things through the solar system under constant acceleration.