From: Frank Reed
Date: 2016 Dec 5, 00:07 -0800
David C, you wrote:
"It is many many years since I studied differential calculus so I doubt I could work out d lat/d t for the above formula."
So don't differentiate! Simulate the small changes instead. A good simulation is almost always going to be more useful than a differential calculation (though a differential calculation will put you on the right track much more efficiently than "blind" simulation). There are many tools you can use to simulate the variability, but I would suggest starting with the USNO celestial navigation web tool: http://aa.usno.navy.mil/data/docs/celnavtable.php. It's old and it's old-fashioned, but it's all safe and reliable. Start with any initial conditions you like. Then to test "differential sensitivity", just bump those conditions up or down in the appropriate variable. You can get a handle on these things very quickly. How much does one second matter? Just try it out! This isn't cheating. Though differential analysis by proper calculus is important, in the real world this sort of thing is mostly done by what's technically called "finite differencing" today. Really that just means simulate it for slightly different input conditions.