How will gravity behave in a fourth spatial dimension? If we were somehow able to see or experience the fourth spatial dimension, how would gravity act on us in there? Does the direction of the pull change? Will it have any effect on light or anything else?
 A: I'm not sure I can give a good answer, but the 4th dimension gets pretty weird and a few things would happen.
First, the direction of pull wouldn't change, it would be towards the massive object.   There would be more directions to travel (up/down, back/forward, left/right and 4th-one way/4th-the other), but the pull would still be directly towards the object and any orbit would still be elliptical around the object.
The strength of gravitational pull would weaken by the cube of the distance, not the square of the distance, so gravitation would weaken over distance quite a bit faster.
There's a cool video that touches on what solar systems and galaxies would look like in 4D (the 4D part starts about 2 minutes in).   https://www.youtube.com/watch?v=tmNXKqeUtJM
Also, in 4d, density could grow much faster cause there's more space, matter could pack more tightly (and I don't want to guess how the electron shells would be affected).   But a cubic KM of water is 1 billion cubic meters, a bit over 1 billion tons.    a quadric (not sure that's the right word), or a KM to the 4th, in 4 dimensions would be a trillion meters to the 4th, a thousand times as many.   In theory, gravity would be much stronger close to a large object, but it would grow weaker faster. - this is, of-course, a pretty rough answer, as the 4th dimension doesn't exist in that sense, so it's only theoretical.   
