This article gives information about mathematical details which come up when one tries to build a realistic space simulation game with realistic physics. Focus here is on physics of various kinds, not graphics or networking because these topics are well treated at other places.
Example code is given in C#, because the language is high level and easy to understand and fast enoguh for copy and paste.
How to compute the thrust of multiple thrusters to fullfill the goal to accelerate in a direction or increase the rotational velocity?
This is a problem of mathematical optimization, which is related to operational research. One good method is to use optimization in the form of https://en.wikipedia.org/wiki/Linear_programming , more specifically the simplex algorithm .
TODO< deeper explaination how it relates to thrust vectors and the target vector > .
TODO< add basic implementation in C# >.
How to find the timing and strenght of acceleration for the goal of a given spatial position together with the velocity?
This is another optimization problem which may be solved with different algorithms.
One simple algorithm is to use a variant of rapidly exploring random tree (RRT). Important here is that the vertices in the tree correspond to a tuple of (velocity, position) and possibly other important properties. Not just the location alone!
TODO< explain further with pseudo code >
ref https://www.ieee-jas.net/en/article/doi/10.1109/JAS.2021.1004252
https://en.m.wikipedia.org/wiki/Proportional_navigation
https://github.com/PtrMan/gameProjectPsiDelta/blob/master/scripts/aiUtils.gd#L9-L45
https://publications.scss.tcd.ie/theses/diss/2010/TCD-SCSS-DISSERTATION-2010-067.pdf
see https://en.wikipedia.org/wiki/Tidal_heating
https://en.wikipedia.org/wiki/Tidal_locking
https://www.omnicalculator.com/physics/luminosity
https://forum.spaceengine.org/viewtopic.php?t=458&start=15#p36682
https://forum.spaceengine.org/viewtopic.php?t=79&start=780
https://astronomy.stackexchange.com/questions/39994/what-is-the-rgb-curve-for-blackbodies
Physics > chemistry > how to compute if there is a ocean on a planet with a given temperature and pressure (?)?
use of https://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation ?
see https://forum.spaceengine.org/viewtopic.php?t=350#p31060
https://forum.spaceengine.org/viewtopic.php?t=311 various sourcecode without license