Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

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)


  • the acceptable time range would be for years in [ 1900, 2100 ]
  • 1 km error margin (or better)
share|improve this question
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) –  Jerry Schirmer Mar 7 '12 at 13:38
@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 –  ring0 Mar 7 '12 at 14:30
even the earth, moon and sun system is not solveable in analytic closed form: en.wikipedia.org/wiki/Three-body_problem –  Jerry Schirmer Mar 7 '12 at 21:48
add comment

1 Answer

up vote 4 down vote accepted

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.

share|improve this answer
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. –  ring0 Mar 7 '12 at 13:01
@ring0 I was only suggesting that you retrieve the reference from the code’s comments. I have now replaced my answer with this reference. –  F'x Mar 7 '12 at 13:06
@F\'x thanks, good idea. Btw, how did you find the ephemerids.htm page... it's not linked from the top page(?) –  ring0 Mar 7 '12 at 16:27
@ring0 Google :) –  F'x Mar 7 '12 at 17:01
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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