Question

Does the earth have a height? If so, what is it?

Answer 1

For the solar system, there is an invariable plane and the Earth's orbital plane is inclined to this plane by about `1^o`. So the height/depth about this plane is utmost `sin 1^o` AU., nearly.

Explanation:

As a matter of convenience, Earth's orbital plane ecliptic is used as the reference for all computations, for orbiters in the solar system.

Yet, for the system as a whole, there appears to be a mean-position-plane about which the thin disc of the orbital space of the solar system has evolved. It is natural that this is not the ecliptic.

The range for the normal distance of the Earth's center from the invariable plane is `+- (aphelion) sin (alpha), alpha` = inclination of the ecliptic to the invariable plane. This is approximately `+-sin 1^o` AU