How did gravity build astronomical objects that rotate?

[Paulibus]

Can gravity form non-axial rotations such that any stars, planets and moons do not rotate in planar orbits but orbit in any orbital direction they wish?

. There's a bit of confusion here. In an empty model universe the orbits for two masses attracted to each other by gravity are always "planar" and "axial; relative motion then lies in a plane defined by two lines: one joining the two masses and the other along their relative velocity as seen by any observer (assuming the two lines to not be collinear). You might say that a lump traveling in any direction "it wishes" orbits a central attracting mass it encounters in a plane determined by what this "wish" was when they first met and began perceptibly to gravitate, but this is a bit wooly, don't you think?

Random axial rotation would be a logical conclusion. Have you examples to the contrary? Shear only affects the process of collapse.

Random axial rotation would be logical only if one took a large enough average over many independently-formed systems. Logical in the case of planetary systems formed by gravitational collapse in different parts of a galaxy, yes. But not in planet formation in say, our solar system. Henry Ford was wrong: history is not bunk, and planetary formation initiated by gravitational shear in a single rotating disc is a process with a shared history.

Don't most of our planets rotate (roughly -- ignore their seasons) in the same sense (clockwise or anticlockwise) if viewed from a distance, along the ecliptic axis? With their moons? I'll check. If so, that's your example. Just remember, shear and gravity go together, like a horse and carriage.

 

[Paulibus]

I came across http://www.sjsu.edu/faculty/watkins/solarspin.htm that could provide an example?

One of the most remarkable features of our solar system is that nearly all of the revolutions and rotations are in the same direction. From a point high above the north pole of the solar system the planets are revolving about the sun and rotating about their axes in a counterclockwise direction. This holds true also for the asteroids. If the planets and asteroids were formed from merely random accretions the would be an even mixture of the directions of revolution and rotation. The sun itself also rotates in a counterclockwise direction. The satellites of the planets also generally revolve and rotate in a counterclockwise direction. Of the thirty something satellites only six do not do so; they are said to have retrograde motion. Of the six exceptions five are outer satellites likely to be captured asteroids.

The Exceptions
Venus and possibly Uranus are the exceptions to the counterclockwise rotations of the planets. Venus travels around the sun once every 225 Earth days but it rotates clockwise once every 243 days. This pecular combination gives it a day with respect to the sun of 117 Earth days. Uranus is tilted on its side about 90° so its direction of rotation is ambiguous. Its angle of inclination is usually given as 98° which would mean that its direction of rotation is not retrograde. If its direction of rotation is presumed retrograde then its angle of inclination would be 82°.