Just watched your fuel harvesting tutorial, so added a request about tugs, curious how you got your fuel stations to Saturn.
https://youtu. be/4iZCmx4youA
The easy math for any ship is: speed = [50000 x power]/[total tonnage]. In words, an engine power of 10% of the displacement of a ship means a speed of 5000 km/s.
10% = 5000km/s,
5% = 2500km/s,
1% = 500km/s
etc.
There is one snag: You can easily factory-build space stations so large that your tug will not be able to overtake celestial objects, which have their own orbital speeds around the star. For example, Steve's tug in the default game has an engine power of 4500. If you try to tow a 5 million ton orbital habitat, you will achieve a speed of 44km/s, which is not enough to overtake and reach Mercury. Your tug will chase the planet forever. Other systems might have faster planets still.
In fact I was (as usual) wrong.
As 1. 9 isnt out yet i decided this is an interesting problem you posed. Then I numerically solved it for a circular orbit and also for an elliptical for kicks. See:
https://puu. sh/FDKft/b845a4e560. gif
After looking at this for a bit I realized it looks like its approaching some limiting circle if the speed is slower than the orbiting speed of the target
After a day of googling I found out a bunch of stuff. These curves are called "Pursuit curves" to the well-initiated and the original problem dates to the 1700s while the case for a circular orbit was actually first solved in 1921.
The original pursuit problem was posed by French mathematician and hydrographer Pierre Bouger in 1732. It was published in the French
"M´emoires de l’Acad´emie Royale des Sciences" and deals with a pirate ship pursuing a merchant vessel.
In this paper
https://mse. redwoods. edu/darnold/math55/DEproj/sp08/mseverdia/pursuit. pdf they find that the limit circle has a very simple formula too, its simple the multiplier of the projectiles speed relative to the targets speed times the radius of the orbiting circle of the target as concluded here
https://puu. sh/FDKkO/63bf1dc0c5. png .
Cool beans
. (also sorry for spamming spess muhreen)