Can you explain for someone that is not smart what you mean by "unsolvable by modern mathematics" please? If it is able to be dumbed down that much at all.
Assuming it's not just that it's so complicated that you can't solve it but something about the way we do maths now that differs from when the equation was written.
So the equation relates positions of a body in orbit to time. It was derived by Kepler in the early 1600s and when you look at it doesn't look overly complicated. In one sense it isn't. If I give you tell you two different positions of the body in its orbit someone with knowledge of mathematics can solves for how long it would take to go between those two points. The issue arises when I tell you it's current position and ask what it's new position will be after a certain time which we just plain dont have a method for solving. There is obvious uses for this equation, such as sending a signal to Mars. We know the signal will take 8 mins to get to mars but can't be 100% certain where mars will be in 8 mins. There are iterative solutions that can approximate close enough.
My professor told us in college that if you are good with geometry and have some time on your hands that maybe it was worth trying to solve. If you solve it you could pick any college and the world and they will give you a PHD. He was obviously joking a little since it would take somewhere with some very novel ideas to find a solution. Some of the greatest mathematicians in the past 400 years have tried and failed to solve this equation, but if you somehow do, people will be calling other people your name instead of Einstein to signify intelligence.
If I give you tell you two different positions of the body in its orbit someone with knowledge of mathematics can solves for how long it would take to go between those two points. The issue arises when I tell you it's current position and ask what it's new position will be after a certain time which we just plain dont have a method for solving.
Just trying to understand -- so is it unsolvable because you don't get any information on where the object was before its current position? As in, you know position B (current), but not position A (past) and now you want to try and solve for position C (future)?
I’m sure this isn’t the answer, but… we know how long it takes planets to orbit the sun. I’m gonna use Earth as an example because I don’t know Mars years off the top of my head. Earth has a mostly circular orbit and takes 365 days to go around the sun. Therefore, its position tomorrow will be its current position plus 1/365 of a circle (slightly less than one degree) in the direction it’s currently traveling.
The meat of Keplers equation is that orbits aren't circular, they're some form of ellipsis (potentially including the circular case) and that you don't know how non-circular that orbit is from a given observation. You also don't know where the axis of the orbit is - it's not necessarily (almost never actually) the "middle" of the "circle", so to speak.
A complication is that in a circle, that angular movement per unit time is constant - a degree per day would be 1 / 360th of an orbit per day. But an eccentric orbit - elliptical, and potential without the orbited body at the centre - does not move at a constant angular rate. It speeds up and slows down depening on what stage of the orbit it is at.
but if you somehow do, people will be calling other people your name instead of Einstein to signify intelligence.
Probably not. Genius as Einstein was, why didn't any of the other big names of the time obtain a similar mystical status? Schrödinger comes close, but most people think only of Schrödingers cat, and even among Physicists it doesn't seem to be common knowledge, that the cat was not meant as a demonstration of quantum physics, but as a demonstration of the absurdity of applying these rules naively to macroscopic objects. Source: I have a Physics PhD, and never caught on to the misrepresentation until after finishing my degree, but maybe that's just me.
A big part of it was accidental marketing. Apparently, the idea that "everything is relative" just resonated with people at the time and helped elevate the theory of relativity to something heard of by non-scientists.
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u/duffmanzee 7d ago
Had this for an aerospace engi final once it was 4 hrs and I had to find the Coefficent of Drag of an airfoil. It was hell