# Trigonometric identity

Probably it was the book “Astronomy Made Simple”. It was a plot of radial velocity of stars versus distance from the galactic center. And it was flat. At far distances the velocity curve flattened out. And this was not as it should be, the astronomers said.

One idea was this meant that there was more matter than one would guess from just counting visible stars at a far distance from the galactic center. But why couldn’t it be a different law of gravity?

When you go on r/physics these days, you see lots of questions like this. But this was back in the days of information underload. A kid, in his upstairs bedroom, on the floor could sit and wonder how one would have to modify Newtons one over distance squared law to get this curve.

Certainly I knew of Newton’s gravitational force, but I’m not sure why I wanted to do a numerical simulation. Probably this came from reading the back pages of Scientific American’s “Computer Recreations” column. But certainly there was no Runge and no Kutta. There wasn’t even trigonometry.

So what do you do when you want to make a simulation of two stars in orbit around each other but you don’t know how to resolve vectors or trig.

You would guess. Instead of sine being opposite over hypotenuse, you might think that maybe it is something like opposite over opposite plus adjacent?

The orbits were not elliptical.

Halcyon days. May you strive to be Aeolus and give others the space to safe from storms. That’s how you start down the path towards learning trig.