Hohmann transfer to Mars (3D)
About this app
Why you can only launch to Mars every 26 months: Earth and Mars on their real orbits, the transfer ellipse around the Sun and the 44° lead Mars needs at launch. Move the launch date, miss or hit Mars, Δv from vis-viva, a porkchop plot with the launch windows and the flight of Mariner 4 (1964).
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
The physics
A probe does not fly straight to Mars. It circles the Sun on an ellipse that touches Earth’s orbit on the inside and Mars’s orbit on the outside. This Hohmann transfer, described by Walter Hohmann in 1925, is the most economical two-burn path between two circular orbits. The half ellipse takes about 259 days. In that time Mars covers 136°, so it has to be 44° ahead at launch. This arrangement only returns after the synodic period of 780 days, roughly every 26 months.
What you see
Earth and Mars move on their orbits according to JPL orbital elements, and the transfer orbit is recomputed for every launch date. A sector shows the lead of Mars at launch, dashed the angle needed. A faint Mars marks where Mars is on the arrival day: if the date is wrong, the probe arrives at an empty spot. The numbers panel gives the flight time, the Δv at launch and at arrival from the vis-viva equation, and the value for a launch from Earth orbit. A porkchop plot shows the Δv for every pair of launch and arrival date.
Things to try
Move the launch date and watch the lead shrink until Mars is hit exactly. The strip above the slider shows the lowest Δv per launch day over eight years: the valleys are the launch windows. Switch to circular orbits for the textbook values of 259 days, 44.3° and 780 days, then back to the real, elliptical orbits, where every window turns out differently. With a free flight time the orbit always reaches Mars, and the Δv shows the price. Finally, fly Mariner 4: launch on 28 November 1964, flyby on 15 July 1965.
Frequently asked questions
- What is a Hohmann transfer?
- A Hohmann transfer is half an ellipse around the Sun that touches the departure planet’s orbit at its closest point to the Sun and the target planet’s orbit at its farthest point. One burn at launch raises the orbit, a second at the target matches the speed. Between two circular orbits it is the path with the lowest Δv using two burns.
- Why can you only fly to Mars every 26 months?
- On the Hohmann orbit the probe needs about 8.5 months. For Mars to be at the target then, it has to be about 44° ahead of Earth at launch. Because Earth overtakes Mars on the inner track, this arrangement only repeats after the synodic period of 780 days, a little over 2 years and 1 month.
- What does a porkchop plot show?
- A porkchop plot shows the fuel needed, measured as Δv or launch energy, over the launch date and the arrival date. The favourable combinations form closed contour lines whose shape resembles a pork chop. Mission planners read from it when a launch is possible.
- How accurate is the app?
- The planets follow JPL’s approximate orbits, valid from 1800 to 2050. All orbits lie in one plane; the 1.85° tilt of Mars’s orbit is left out. The orbits with a free flight time are solutions of Lambert’s problem. Δv ignores the planets’ gravity; only the row for a launch from a 200 km Earth orbit includes Earth’s pull.
Subject: Astronomy
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