Thursday, May 16, 2019
Unfortunately, like all knowledge, it's use it or lose it. I haven't done differential equations since leaving college. Nor calculus. I know the theory behind them but not the mechanics. I can still do algebra fairly well.
In this novel I'm writing (the second of a planned trilogy that is a prequel to Treasure of the Black Hole), I found an occasion when being able to differential equations would be helpful. But, of course, I don't remember how.
So, instead, I did an Excel spreadsheet.
Here's the situation. The bad guys fired missiles at the good guys. The missiles were accelerating at 100 times the force of gravity (gees). The good guy's ship was accelerating at ten gees toward the missiles. Even though this was taking place in three-dimensional space, I simplified it to being on a line. The captain of the good guys ship asked "How long until the missiles are in firing range." And that's when I realized I had to do the math.
The ship and the missiles were approximately 1 AU apart (98 million miles). I set up a spreadsheet that would at each second calculate how far the missiles had gone and what speed they were going and did the same for the ship, calling its velocity and acceleration negative. I ignored relativity (even though the missiles would be going 5% the speed of light when they were close to the ship).
So I set up my equations (which used the data from the previous equation to do the math) and copied them down (and down and down) until the ship and the missiles were close together on my line. And that happened at 16,653 seconds. or about 4 hours 36 minutes.
And all that work because one character asked a question.