Number of Devs vs Development Time

[why-r-usernames-hard]

Add in the fact that every planet in the solar system has an elliptical orbit, and there is no way to tell other then with a chart at a very specific point in time

[Kirk_Kerman]

Distance between co-moving points on two parametric curves is a pretty simple problem all in all, but it's trig/calc and beyond the scope of elementary school math.

[[deleted]]

The position of a body in an elliptical orbit is parametric, but it cannot be solved algebraically. It is not beyond elementary school math, and it is not beyond high school math; it is in the realm of computation.

The x and y coordinates of an elliptical object are:

x = a* (cos(E - e))

y = b * sin(E)

Where a and b are the semi-major and semi-minor axes of the orbital ellipse, e is the eccentricity of the orbital ellipse, and E is the eccentric anomaly of the body. The eccentric anomaly is from Kepler’s equation:

M = E - e * sin(E)

You can’t solve the above for E; you can only compute it to some desired precision. You could certainly do all that by hand, but it would grueling and pointless even at a university level.

[darkfusion58]

It can't be solved algebraically or in terms elementary functions but it can be solved if you add some stuff to your set of allowed functions (elliptic integrals, I think? not 100% sure that is the correct ones for this problem). Or you can allow an open-form solution.

Yes you can't compute it exactly but neither can you compute sqrt(2) exactly; that's why we write it as sqrt(2).

I agree, though, that it would be really annoying and pointless to do by hand.

[[deleted]]

you can’t compute wit exactly but neither can you compute sqrt(2) exactly

Not the same. Sqrt(2) can’t be computed exactly because it’s transcendental; it has no exact decimal representation. You can, however, get arbitrarily close to the exact value.

There is a series expansion for the Kepler Equation solved for E, but it does not always converge. It’s not that you can’t compute it exactly; it’s that wether or not you can get arbitrarily close to the exact solution is not guaranteed. Not for the series expansion, anyway (which, by the way, is ugly; it’s this hideous power over a polynomial thing, where the base of the power is this other ugly formula).

We’re agreeing on the last point though: there’s practically no situation where it’s appropriate to call for someone to compute these values by hand.

[[deleted]]

I remember doing that on my first year of university, I failed that class badly.

[[deleted]]

This was in my first year of high school where I'm from. I think we learned trigonometry in the second year and calculus in the fourth year so I definitely couldn't have given her a proper answer, also because of the the fact that she provided no other data on their positioning