The common method for a spacecraft to shift between two orbits is called a Hohmann Transfer, and that the guy who calculated it (in 1925) was inspired by a science fiction book written in 1897, which gave a generally correct explanation of the concept of orbit trajectory

Hohmann transfer orbit

Hohmann transfer orbit, labelled 2, from an orbit (1) to a higher orbit (3)

An example of a Hohmann transfer orbit between Earth and Mars, as used by the NASA InSight probe.

Hohman · Earth · Mars

In orbital mechanics, the Hohmann transfer orbit (/ˈhoʊmən/) is an elliptical orbit used to transfer between two circular orbits of different radii around a central body in the same plane. The Hohmann transfer often uses the lowest possible amount of propellant in traveling between these orbits, but bi-elliptic transfers can beat it in some cases.

The orbital maneuver to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the transfer orbit and a second to move off it. This maneuver was named after W… Continue Reading (11 minute read)