In what ways do Earth's motions change over time?

1 Answer

In several different ways and they combine in interesting ways. I've linked in a video that does a nice job of explaining the various orbital wobbles:

Explanation:

The Earth has a lot of wobbles and such in its orbit around the Sun. Three things that these wobbles affect are:

orbital eccentricity - or how close to a circle the Earth moves around the Sun

http://www.indiana.edu/~geol105/images/gaia_chapter_4/milankovitch.htm

axial obliquity - or how far the Earth tilts in its axis
http://www.indiana.edu/~geol105/images/gaia_chapter_4/milankovitch.htm
precession - which is the wobble that has the axis point in different directions

http://www.indiana.edu/~geol105/images/gaia_chapter_4/milankovitch.htm

This youtube video explains in detail how all this happens:

detailed video of Earth orbital wobbles

http://www.mnn.com/earth-matters/climate-weather/stories/everything-you-need-to-know-about-earths-orbit-and-climate-cha

You may want to read up on Milankovitch cycles.