Half an ellipse around the Sun, plus two impulsive Δv’s
The transfer semi-major axis is a_t = (r1 + r2) / 2, and the time of flight is the half-period π √(a_t³ / μ_sun). Vis-viva on that ellipse, compared with each circular speed √(μ / r), gives the two heliocentric impulses. For Earth to Mars the flight is about 259 days, with roughly 2.94 km/s at Earth’s orbit and 2.65 km/s at Mars’s, totaling about 5.59 km/s — and the next geometrically similar window is one synodic period later, about 780 days. Those Δv figures are changes of heliocentric velocity. Leaving low Earth orbit, or capturing into a Mars orbit, still has to deal with each planet’s gravity well (a patched conic or an Oberth burn this page does not compute).
The single-body Hohmann transfer calculator is the same geometry around one primary you name (Earth, or a μ you type). The synodic period page is the wait-time identity on its own, including tabulated planetary periods that differ slightly from the Keplerian periods implied by these mean radii. For a mission Δv budget you can add atmospheric or capture legs on the delta-v budget tool.
Sources
- Hohmann, “Die Erreichbarkeit der Himmelskörper,” 1925; standard Hohmann transfer.
- Vallado, Fundamentals of Astrodynamics and Applications; Prussing and Conway, Orbital Mechanics.
- IAU solar gravitational parameter and astronomical unit.
Frequently asked questions
Why is this not the Δv I would need to leave LEO?
These impulses are heliocentric. Climbing out of low Earth orbit, or braking at Mars, requires additional Δv that depends on the parking and capture orbits. A patched-conic or an Oberth burn is a different (and usually larger) number.
How is this different from the Hohmann transfer calculator?
That page is a coplanar transfer around a single body (Earth by default, or a μ you type). This one is a heliocentric planet-to-planet leg, with solar μ, AU radii, and a synodic wait.
Are planetary orbits really circular and coplanar?
No. Mars has a noticeable eccentricity, and a real trajectory is optimized around a launch window, not a pure Hohmann. This is the textbook first estimate.