Question

Do the planets orbit the sun on a 2-D plane?

Answer 1

No, the planets do not orbit the Sun in a 2D plane.

Explanation:

Each planet orbits the sun in a slightly different plane. This is called inclination. The orbit of the Earth, the plane of the ecliptic, is defined to be the 0° plane. Hence, by definition, the inclination of the Earth's orbit is 0°.

The orbital inclination of the planets relative to the ecliptic are:
Mercury `7.01^@`;
Venus `3.39^@`;
Earth `0^@`;
Mars `1.85^@`;
Jupiter `1.31^@`;
Saturn `2.49^@`;
Uranus `0.77^@`;
Neptune `1.77^@`;