gonegahgah wrote:[...]

One of the things it might be interesting giving some thought to is the stable areas of those gravitational valleys and dimensional volumes?

The most important area for stable orbits is closer into the valley's centre; but not too close.

Bring planets much closer together and I imagine the number of stable orbits drops dramatically.

Move further away and it takes very little effort to achieve escape velocity.

I mention volume for a specific reason.

Objects in a 4D universe would tend to be shorter than in our universe.

Why? Because their is just so much more sideways space to work with.

Conversely a 2Der would have to be so much taller to try to achieve a similar complexity to us.

Take a brain. Our cells are arranged in a 3 dimensional space allowing for many connections from all directions.

A 4Ders brain cells have a whole extra realm of dimension to start spinning connections off into so you can fit many more cells within a much smaller across length of space with greater complexity.

The same goes for atoms and chemisty which would probably be very bizarre to what we have. The extra space for movement allows a whole different more compact way of existance.

Now, if we take this and scale it in to our question here we tend to notice that the gravitational curve created by 4D space can find a region that is more like our 3D gravitational curve closer in.

If we use the mountain or valley example again we can see that there is a nice region within to play for stable orbits.

For 4D objects, if they scale down proportionally, we can find a region closer in that is not so steep and at the smaller scale matches that of ours.

So if you have boulders rolling around a 3D valley and have marbles rolling around a 4D valley I feel you will find an equivalency zone?

Steepness or not, if you reduce your size you can orbit closer to the ideal 4D region which becomes equally large in comparison due to your relative smaller size.

Does that sound feasible at all?

Again, the difference between 3D and 4D is not a matter of scale (quantity), but an inherent difference in behaviour (quality). The reason I chose a flat-top mountain vs. a pointed tip was to try to emphasize this difference. But, like all analogies, it's bound to fail if you stretch it too far. The important point here is that in 3D, the "mountain of stability", so to speak, has a certain kind of shape, and that in 4D, it's a fundamentally different kind of shape. It's like the difference between a circle and a triangle. They are fundamentally different kinds of shape, and changing the relative scales of things doesn't change the fact that one is circular and the other is triangular. You can make it a bigger or smaller triangle, but it will never become a circle, and vice versa. The difference between 3D orbits and 4D orbits is a fundamental difference that doesn't change with scale. No matter how you try to play with scaling things up or down, a 4D orbit is fundamentally unstable ("triangular") and can never be made to behave the same way as a 3D orbit ("circular").

That is, unless you postulate a different kind of physics that allows a 1/r^2 decay of the force of gravity over distance. Then you will have the same kind of orbits that 3D has, except with an extra dimension of space. But then, it would mean that physics in this "modified" 4D space must behave in a fundamentally different way, and it won't be analogous to 3D physics at all.

Or, alternatively, you can postulate a momentum that is proportional to r^3, which could possibly balance out the 1/r^3 decay of gravity, but then it would imply an even bigger change to the physics of how things move, probably making the result completely unrecognizable to us in the process.

Unfortunately, this is the way the math works. A 1/r^2 gravitational decay is fundamentally different from a 1/r^3 decay. It may look like a small difference in writing, but actually, mathematically speaking, they are as different as a triangle is to a circle. Their fundamental properties are mutually incompatible.