What does the angle between plane of earth's orbit and ecliptic vary between?

Question

What does the angle between the plane of the earth's orbit and the ecliptic (now about 23.5 degrees) vary between, and over what time scale?

Answer 1

By definition, it is zero; the ecliptic is the plane of earth's orbit (or rather, the inverse: the path the Sun seems to follow along the sky).

But you're probably looking for variations in the axial tilt of the Earth. There's a lot of formulas in the article, and on the (astronomically speaking) short timescale of a few million years, it oscillates between 22 and 24.5 degrees with a period of about 41,000 years. See the graph below, the red dot is the year 2000:

_{(picture by Tfr000 on Wikipedia, data from Laskar (1986))}