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Cat Flynn 2024-04-26 23:16:16 +01:00
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@ -163,6 +163,28 @@ Instead of having to pad the physics budget to account for a worst-case scenario
---
Cheek still smarting, you weigh the ball in your hand.
Looking out past the horizon, you think of the ground below your feet.
You think through the core of your perfectly spherical virtual planet, and out into the space beyond.
You think as far as double-precision floating points can take you - which is, wait, how far?
The distance doesn't really matter anymore, you realise, since the precision is the same for an ellipse a metre across as it is for an astronomical unit.
The limit now is double-precision time.
Idly bouncing the ball in one hand, you work out what that means.
To be accurate to a single frame, you want be able to represent units of time as short as a frame, or 0.01 seconds.
There are about ten million seconds in a year, or billion frames: looking good so far, that's only 10 significant figures, there are a few more to go yet.
In a thousand years, the smallest step we can represent is still less than a microsecond, so you keep going.
After a million years, the minimum increment finally creeps up to half a millisecond, which sounds about right.
With a grin, you add a healthy number of zeroes, aim, and throw.
You watch the ball disappear over the horizon - it does so much more quickly than last time, and sit down.
You turn around, sit down, and looking at your watch, start to crank up the passage of time itself.
You watch as the ball comes back around... and around, and around, and around again, until it becomes a steady blur over your head.
It stays that way, and you start to think about double doubles.
You've come a long way, but what's a million years, when you're a planet?
---
I don't know how Kerbal Space Program computes positions on elliptical orbits - if you do, [please get in touch!](mailto:me@ktyl.dev) - but I would be surprised if they used Newton-Raphson.
In practice, Kepler's laws are limited in their utility for complex, real-life astrodynamical systems, as they don't take into account tidal effects, irregular gravitational fields, atmospheric drag, solar pressure or general relativity.
They also cannot model Lagrange points, which are fundamental to many modern spacecraft such as JWST, or Weak Stability Boundary transfers as used by modern robotic lunar probes such as SLIM.