Coastor

Meet Coastor, a spacecraft who saves fuel by burning, coasting and burning again.

To move from one circular orbit to a bigger one, the most fuel-efficient simple route is a Hohmann transfer. The spacecraft fires its engine once to stretch its orbit into an ellipse that just touches the outer orbit. It then coasts halfway round that ellipse without using fuel, and fires again at the far side to round out into the new circle.

The coasting time is half the period of the transfer ellipse, t = π√(a³/GM), where a is the ellipse's semi-major axis. From Earth at 1 AU to Mars at about 1.52 AU, a ≈ 1.26 AU, and Kepler's third law gives a trip of about 0.71 years, roughly 259 days.

The planets must be lined up correctly before launch, so these windows to Mars open only about every 26 months.

Walter Hohmann described the idea in 1925, long before spaceflight. Many real Mars missions follow paths close to it.