2
$\begingroup$

I had no luck trying to find a function that determines the distance between Earth and Moon versus time.

(Moon ground level to Earth sea level)

Accuracy:

  • the acceptable time range would be for years in [ 1900, 2100 ]
  • 1 km error margin (or better)
$\endgroup$
3
  • 3
    $\begingroup$ You're not going to get a closed-form analytical solution for this. The three body problem is known to be chaotic, so as soon as you factor in the gravitation of bodies other than the Earth and the Moon, there is no analytic function that describes the paths of the two bodies. The best you're going to do is empirical or numerical data, depending on your purpose. (or you can just solve the Kepler problem, and ignore anything but the Earth's and Moon's gravitation, and treat them like point masses) $\endgroup$ Mar 7, 2012 at 13:38
  • $\begingroup$ @Jerry The closed form would certainly be too complex for what I need, while the Sun may also be factored in? (the other influences like other planets, comets, asteroids collision... seem hard to integrate) Considering the acceptable error margin above, the numerical application (ie the formulas having a number of constants in it) will be enough. I'm planning on purchasing the book from J.Meeus. Thanks $\endgroup$
    – Déjà vu
    Mar 7, 2012 at 14:30
  • 1
    $\begingroup$ even the earth, moon and sun system is not solveable in analytic closed form: en.wikipedia.org/wiki/Three-body_problem $\endgroup$ Mar 7, 2012 at 21:48

1 Answer 1

5
$\begingroup$

You can check Meeus 'Astronomical Algorithms' (1st Ed), Chapter 51. It is implemented for example in the (Javascript) source code of this page for example.

$\endgroup$
4
  • $\begingroup$ Thanks but I'd prefer to rely on some formulas - that people here can look at - than to reverse engineer a JS code, which implementation may not be accurate. $\endgroup$
    – Déjà vu
    Mar 7, 2012 at 13:01
  • 1
    $\begingroup$ @ring0 I was only suggesting that you retrieve the reference from the code’s comments. I have now replaced my answer with this reference. $\endgroup$
    – F'x
    Mar 7, 2012 at 13:06
  • $\begingroup$ @F\'x thanks, good idea. Btw, how did you find the ephemerids.htm page... it's not linked from the top page(?) $\endgroup$
    – Déjà vu
    Mar 7, 2012 at 16:27
  • 1
    $\begingroup$ @ring0 Google :) $\endgroup$
    – F'x
    Mar 7, 2012 at 17:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.