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I'm hoping to make a small mechanical demo (~10cm tall) that models an orbit that is similar to the Earth-Moon orbit - that is, only one side of the Moon faces Earth. I'm trying to keep it simple, so here's my idea so far:

enter image description here

where the blue and yellow represent Earth and Moon, respectively. These are meant to represent a different planet and its moon though.

The orbit of the Planet (blue) and its Moon (yellow) has the following differences:

  • Planet is eccentric
  • Only one face of the Planet and see its Moon, i.e. the horizontal bar on each disc should remain parallel. The bars are for explanatory purposes only.
  • Planet's rotation axis may shift (vertically along the green bar), but the Moon's orbital axis is fixed, i.e. Moon should be always in contact with the outer ring housing

My question is: how should the two discs be connected in order to to have the above properties? I've thought about using springs, but I think it'd be quite flimsy though.

I know about orreries, but typically they don't self-adjust orbits though. Also, I was hoping for a simpler mechanism given that there doesn't need to be empty space between the two discs. I'm only hoping to model the motion on just one plane.

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  • $\begingroup$ Have you calculated or looked up the percent eccentricities involved? Unless you deliberately want to exaggerate the amount for demo purposes, you might want to ignore it. $\endgroup$ – Carl Witthoft Feb 7 '16 at 14:09
  • $\begingroup$ Yes, I'm trying to demonstrate a substantial amount of eccentricity in my model. $\endgroup$ – John M. Feb 9 '16 at 6:50
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I started these as comments but they're way too long for comments. Basically, please clarify what you want.

  1. The orbit of the Planet (blue) and its Moon (yellow) has the following differences: Planet is eccentric." Why would the eccentricity of the planet's orbit affect its moon? You don't have a sun in that model, so really I don't understand what the planet's orbit has to do with any of this.

  2. "Only one face of the Planet [can] see its Moon." This isn't how our moon works. With our moon, only one side of it can see the planet. The way you have it described, it would be like if only the Western hemisphere could see the moon, and nobody in the Eastern hemisphere would have ever seen it. Also, the way you describe the motion (the bars are always parallel) is like both scenarios put together - the moon can only be seen from one hemisphere and that moon only has one face that can be observed.

  3. "Planet's rotation axis may shift" Here's where you really lost me. Maybe it's because your drawing isn't labeled (!), but you state you are, "only hoping to model the motion on just one plane." As I mention above, there is no sun, so I'm assuming the spinning disc that is your planet it spinning on its axis. If it is shown as spinning on its axis, then you can't move the planet to adjust the tilt of that axis and keep it planar. It looks like you might mean to do this by shifting the point of rotation, but all that would do is cause the entire planet to rotate eccentrically.

Please clarify your question by:

  1. Labeling your drawing
  2. Add several drawings showing "snapshots" of the motion you would like to demonstrate.

Also bear in mind that, to show rotation in a plane, the axis of rotation has to be orthogonal to the plane. As soon as you change the angle of the axis of rotation you cannot have a planar display. You could have a projection, but I'm not sure that you could depict a 2D projection of an off-axis sphere rotating with a "simple" setup.

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