Martian Alpha Blog

Porkchop Plots Explained: Mars Launch Windows

Why Mars launches cluster every 26 months, how a porkchop plot shows the cheapest dates, and a worked example from NASA numbers (259 days, 44 degrees).

By Martian Alpha Research5 min read

A porkchop plot is a chart of departure date against arrival date, with contour lines showing how much launch energy each pair of dates needs. For Mars, the cheapest region repeats about every 26 months, because that is how often Earth and Mars return to the same relative positions. NASA's Mars Fact Sheet gives that repeat interval, the synodic period, as 779.94 days, or about 25.6 months. In the simplest minimum-energy trip, a spacecraft coasts for about 259 days and must leave when Mars is about 44 degrees ahead of Earth.

Why there is a "window" at all#

A spacecraft doesn't fly straight at Mars. It leaves Earth already moving around the Sun at Earth's speed, fires its rocket to change that solar orbit, and then coasts. NASA's basics of spaceflight guide describes the cheapest version, a Hohmann transfer: an ellipse whose closest point to the Sun is at Earth's orbit and whose farthest point is at Mars' orbit. The guide compares aiming at Mars to throwing a dart at a moving target, so you have to lead it, and adds that the opportunity for a minimum-energy transfer to Mars occurs about every 25 months. Venus opportunities come about every 19 months.

NASA JPL's education lesson Let's Go to Mars! Calculating Launch Windows says the launch window, depending on the target, can be a few minutes or as much as a few weeks long. Launch too early or too late and the spacecraft reaches Mars' orbit when the planet isn't there.

Worked example: the 44-degree rule#

The JPL lesson walks through a simplified calculation, assuming circular, coplanar orbits and constant speeds (it states plainly that none of these is exactly true). Here are its steps:

  1. Earth is 1 AU from the Sun and Mars about 1.52 AU, so the transfer ellipse's semi-major axis is about 1.26 AU.
  2. Kepler's third law gives a full transfer-orbit period of about 1.41 years, roughly 517 days. The trip is half an orbit: about 259 days.
  3. Mars goes around the Sun in about 687 days, so it moves about 0.524 degrees a day. In 259 days it moves about 136 degrees.
  4. The spacecraft arrives where Mars will be 180 degrees around from the launch point. Subtract Mars' 136 degrees of motion and Mars must start about 44 degrees ahead of Earth at launch.

That lead angle repeats once per synodic period. NASA's fact sheet lists Mars' sidereal orbit as 686.98 days and Earth's as 365.256 days; combining them (1 / (1/365.256 − 1/686.98)) gives about 779.9 days, matching the 779.94 days on the sheet.

How much energy is that?#

Launch energy is often quoted as C3, the square of the speed the spacecraft still has after escaping Earth, in km²/s². Using the same circular approximation and the fact sheet's orbital speeds, our own arithmetic gives:

  • Earth's orbital speed: 29.78 km/s.
  • Speed needed at the start of the transfer ellipse: about 29.78 × √(2 × 1.524 / 2.524) ≈ 32.7 km/s.
  • Speed gained relative to Earth: about 2.9 km/s, so C3 is about 8.6 km²/s².

That's a textbook minimum, not a mission design. Real trajectories adjust for the planets' elliptical, slightly tilted orbits.

What a porkchop plot adds#

The textbook example gives one pair of dates. A porkchop plot computes the trajectory for every pair on a grid of departure and arrival dates and draws contours of equal launch energy. NASA's Mars Science Laboratory launch-arrival space study uses this kind of plot: for each Earth launch date and Mars arrival date it records the departure energy, the direction of the launch asymptote and the arrival speed. The contours form closed, chop-shaped regions, and the cheapest trajectories sit near the centre of each one.

How to read one:

  • Horizontal axis: departure date. Vertical axis: arrival date. A point is one specific trajectory.
  • Contours: constant C3. Each loop joins dates with the same launch energy. The innermost loop is the lowest-energy region, the bullseye, and the loops get larger and costlier moving outward.
  • Diagonal lines: constant flight time. Slide along one to see what a faster trip costs.
  • Arrival speed matters too. A cheap departure can mean a fast arrival, which makes capture or entry harder. Mission designers plot arrival speed as well and trade the two off.
  • The width of the low-energy region shows how much room there is. A broad bullseye leaves more flexibility in the departure date than a narrow one.

Why rocket size shows up in the chart#

Launch energy converts into a requirement on the launch vehicle. A lower C3 lets a given rocket send a heavier spacecraft; a higher one cuts the mass it can send. Our rocket equation guide shows the arithmetic behind that, and comparing launch vehicles lists the vehicles. For orbit basics, see LEO vs GEO.

Try it on Martian Alpha#

Martian Alpha's Interplanetary Launch-Window Calculator draws porkchop plots for Earth to Mars, Venus and Jupiter, solved from published planetary orbits, and lists upcoming windows. It's part of the Space Enthusiast plan ($5 a month); see the plans page. It's a learning tool, not a mission-design tool, and it doesn't replace the NASA references above. Related free pages: the 3D solar system, the deep-space mission tracker and the engineering toolkit for delta-v and Hohmann calculators.

FAQ#

How often can you launch to Mars?#

About every 26 months. NASA's Mars Fact Sheet lists the synodic period as 779.94 days, and NASA's spaceflight basics guide gives about 25 months for minimum-energy opportunities.

How long does a trip to Mars take?#

On the simplified minimum-energy path in the JPL lesson, about 259 days. Real missions vary their trajectories, which can make the trip shorter or longer.

What does C3 mean?#

Characteristic energy: the square of the speed a spacecraft has left after escaping Earth's gravity, in km²/s². A lower C3 means the launch vehicle needs to do less.

Why is it called a porkchop plot?#

Because the closed contours of equal launch energy, drawn on a departure-date against arrival-date graph, look like a pork chop.

Is a launch window the same as a launch opportunity?#

Roughly: the opportunity is the stretch of months when a transfer is efficient, and the window is the period within it, which can be minutes to weeks depending on the mission, when a launch can actually succeed.

Sources#

This article is for information only and is not financial advice. Do your own research before making any investment.