Previously, the plan was to generate a star, then find the furthest reach of its gravitational pull. Since that gravitational pull is technically infinite, I was hoping to find some examples of systems in the observed universe that could serve as a baseline.

For example, if the largest system we’d observed was a star with a mass of 𝑚1 and an orbiting body with an aphelion of 1kLY and a mass of 𝑚2, I could use that data to write a formula that scaled depending on the mass of the planet.

Stars with a mass of… - 𝑚1 would have a maximum feasible planet distance of 1kLY. - √𝑚1 would have a maximum feasible planet distance of √ 1kLY. - 𝑚1² would have a maximum feasible planet distance of 1k ² LY. It’s more complex than that, but you get the drift.

As it turns out, I couldn’t find any really good examples of systems that embody the necessary criteria. Time for a new approach, I guess. 😞

A lot of folx recommended Kepler’s First Law of Planetary Motion. Unfortunately, you really need to know the planetary details (like mass and size) before you can use Kepler’s First Law to determine an orbital path.

So Kepler’s First Law has been ruled out. I need to figure out the location at which I’ll be generating a planet, *then* I’ll generate a planet with properties that are feasible for that location. After noodling on that fact for a while, I think I’ve found a solution!

The solution is to set some arbitrary boundaries for the outer reaches of a planetary system, then generate planets within that boundary. E.g. if the boundary is 10kLY, then no planet can be more than 10kLY from its star.

The next step is to figure out an elliptical orbital velocity for that planet. This is relatively simple using the Vis-viva equation. Cool side note: This also allows me to fiddle with the value of the semi-major axis to create parabolic and hyperbolic orbits. 🤩

The biggest benefit here is that I don’t need to make a realistic boundary to the system. I can generate a planet at *any distance from the star,* then generate a realistic orbit for it. A star’s gravitational force is infinite, after all! 🥳

To figure all this out, I’ll start by plugging in some bunk values for the furthest a planet can be from its star and generating multiple systems within that boundary. Then I’ll render them, and the one that makes the most interesting systems wins!

It *does* make me sad that this decreases the realism of my simulation. I recognize that there will always be a limit to how realistic I can get, but I was really thought I could nail this part. 😞 Freaking physics. 🗑

On the plus side, I did just find out about COCONUTS-2b (giggle) which is the longest orbital period we’ve observed. It takes 1.1 MILLION YEARS to orbit its star and has a distance of ~6,000AU from its star. I think 6,000AU will be my starting point for that upper boundary. 😁

Also also, BIG UPS to @UncleClapton, @JasonMKlug, @TheRedGamer, @JesseKeyes, and @LadyStarbuck2 for the help they provided in trying to solve an impossible (at least theoretically) problem. ❤️🥰❤️