I get obsessed with the math of it all, often through the use of mods. Current obsession is a satellite relay network for the Jool system in remote tech (playing Laythe space program). One central satellite around Jool that points to a satellite at the L4 points of each of the moons (5 directional dishes). The L4 satellite (2 directional dishes) pointing back at the planet such that the 3 equatorial omni comms (1 directional 1 omni) are always in its view. That way the only down time is when the Jool satellite swoops down below the planet.
But how much up-time is there in that system? Well first how do you find the function for the ellipse made by an orbit? What is the lowest point in that orbit that the Laythe L4 location can see? what is the area of the curve cut out going from that point on the ellipse to the same height on the other side? What is the overall area of the ellipse and period of the orbit? So how long is its downtime compared to its uptime? (I got around 99.998% uptime)
It’s got geometry, integrals, Kepler, pi. Oh, so much math.