Existing MATLAB projects to describe the lunar spin

When I search for MATLAB examples concerning Earth and Moon, I only see those describing Earth orbiting about the Sun, or Moon orbiting around Earth, but nowehere did I ever see examples dealing with Earth or Moon rotating about their polar axis.

I would enjoy a complete 3D-graphic simulation of Earth's and Moon's motions showing Moon synchronous orbiting around Earth and rotating about its polar axis, and showing also what happens when you specify in the MATLAB context that the Moon doesn't rotate.

Does such an example exist?

Nota bene: I'm no mathematician at all.

Answer 1

[John D'Errico]

The moon DOES rotate, very much so. It just rotates in a very specific manner, to match its rotation around the earth. So we think of it as not rotating. But if you looked at the system from above, you would see the rotation. The same thing has happened with Mercury, rotating around the sun, tidally locked in a 3:2 resonance. (I did not know about the 3:2 resonance until I looked it up, so I learn something new every day.) It makes 3 rotations for every 2 trips around the sun. The moon is tidally locked into a 1:1 resonance round the earth. That means nobody ever sees the back side of the moon - quite important so the aliens can hide there in the movies. ;-)

Is there a simulation in MATLAB? I don't know, but I doubt it. Most of the simulations of this sort you see in MATLAB were written by students, who are usually tasked with showing the orbital motions of the planets around the sun. Essentially, purely gravitational interactions between bodies in orbit, but those bodies were modeled as point masses. A simulation that also involves planetary rotation will be a step upwards in complexity. Not at all impossible, but odds are students will have stopped before that point is reached.

Anyway, any explicit simulation that shows these bodies all rotating as they really do will be terribly difficult to visualize. This because of the relative size of those bodies compared to the distances between them. So if you can actually visualize the earth revolving around the sun, then the moon certainly looks like a point of reflected light, but no more than that. The same would apply to the earth. In turn that means such a simulation would probably be terribly dissapointing. So the simulation would need to seriously zoom into the planets to make things viewable as they were rotating. Again, probably more work than it is worth. Sorry, but it probably helps to explain why this is something that while of moderate interest to you just does not happen.

If you did decide it was of serious interest to you, then go ahead and write it. Post it on the File Exchange. I am sure it would receive interest if well done.

[Bindidon]

Thanks for your reply.

I'm aware of the lunar spin: I read a 130 pages long treatise written in 1750 by a German mathy astronomer (Tobias Mayer).

" Anyway, any explicit simulation that shows these bodies all rotating as they really do will be terribly difficult to visualize. This because of the relative size of those bodies compared to the distances between them. "

I intuitively thought that differential equations describing motions of celestial bodies (including their spin) would be independent of the observer's abstract position, like when looking at the bodies using a telescope and zooming them 'nearer'.

Maybe this was a desperately naive approach.

*

The reason for me asking is that many contrarian people doubt on blogs about the lunar spin in exactly the same way as they doubt about several other matters, like GHE, time dilation, viruses etc etc.

They doubt about lunar spin because Moon shows us the same of itself all the time : exactly that has been since millenaries the reason to be convinced of its spin :-)

[John D'Errico]

Please learn to use comments, instead of a new answer to make a reply.

As I said, typically the equations solved to show the orbits of planets presume the planets are represented by point masses. This is entirely adequate for most such simulations. Yes, you could solve the problem at a deeper level, where rotation of the bodies themselves are simulated. But as I said, that adds a new layer of complexity.

And then the code to zoom in on such a simulation adds more complexity. Or changing the moon to show rotation or not would add another level of complexity.

Would it be interesting? Yes. I suppose so. Has it been done by someone using MATLAB at the level you want to see? I doubt it. A search might turn something up. But we see dozens of questions asked about planetary simulations on this site, and they are never getting to the level you want. This is why I say not to get your hopes up. You can always add infinite levels of compexity, to the point where you have oceanic tides being simulated, plate tectonics, etc. Every model has a point where the modelor has decided to give up the quest for perfection. But the models we see all too often here have stopped well before the point you want.

As for many people who might in theory be interested, my guess is the people who think the earth is flat, etc., will not believe a model made in MATLAB anyway. Don't forget about those aliens hiding on the dark side of the moon either. :)