It's used like a proper noun place name, except not capitalised, so you would say “I'm going to space” or “Space is very big” in the same way you would say “I'm going to London” or “New York is very big.”. ...

Is space a proper noun?

The word ''space'' is a common noun. It is non-specific and, thus, should not be capitalized.

Is Earth and space capitalized?

We usually lowercase sun, moon, and earth, but, following The Chicago Manual of Style, when the does not precede the name of the planet, when earth is not part of an idiomatic expression, or when other planets are mentioned, we capitalize earth: ... The space shuttle will return to Earth next year.