How Long Does It Take to Get to Mars? The Orbital Math • The Science 360

Perseverance left Cape Canaveral on 30 July 2020 and touched down in Jezero Crater on 18 February 2021: 203 days. Over that time it travelled roughly 470 million kilometres around the Sun, while Mars, at its closest during the cruise in October 2020, was only about 62 million kilometres from Earth. That is not inefficiency. It is the cheapest way to get there, and the reasons it works out that way answer the question better than any average.

Quick answerUsually 6 to 8 months. The minimum-energy (Hohmann) transfer between idealised circular orbits takes 259 days. Real missions have taken from 131 days (Mariner 7, a flyby) to 333 days (Viking 2). Launch windows open every 26 months, and a crewed round trip would take about two and a half to three years.

Infographic: How long does it take to get to Mars? A to-scale diagram shows the Sun, Earth's and Mars's orbits and the half ellipse of a Hohmann transfer, with Mars 44.3 degrees ahead of Earth at launch. The minimum-energy trip takes 259 days, half an orbit with a semi-major axis of 1.262 AU, and launch windows come every 25.6 months. A bar chart of launch to arrival times shows the Mariner 7 flyby at 131 days, Perseverance at 203, the Hohmann ideal at 259 and Viking 2 at 333. Tiles: a Hohmann round trip takes 972 days; cutting the trip to 200 days costs only 120 m/s more burn; a constant 1 g drive would take 1.7 days. — Tap the image to view it full size. View the accessible, editable SVG.

Why don’t spacecraft fly straight to Mars?

Because a spacecraft leaving Earth is already doing 29.8 km/s around the Sun, the same as Earth. To fly "straight" at Mars you would first have to cancel most of that sideways motion, and then fight the Sun's gravity on the way out. Nobody has a rocket for that.

Instead, you add a little speed in the direction Earth is already moving. That stretches your solar orbit into an ellipse whose closest point to the Sun is at Earth's orbit and whose farthest point just touches Mars's orbit. You then coast for half an ellipse. This path, worked out by Walter Hohmann in 1925, is the minimum-energy route between two circular orbits, and it fixes the travel time with nothing but Kepler's third law.

How long is a Hohmann transfer to Mars?

Kepler's third law says that, for anything orbiting the Sun, the period in years squared equals the semi-major axis in astronomical units (AU) cubed: T² = a³. The transfer ellipse runs from Earth's orbit at 1 AU to Mars's mean orbit at 1.524 AU.

Step 1. Size of the transfer ellipse

a = \frac{1.000 + 1.524}{2} = \mathbf{1.262\ AU}

\begin{aligned}e &= \frac{1.524 - 1.000}{1.524 + 1.000} \\ &= 0.208\end{aligned}

Step 2. Full orbital period

T = a^{3/2} = 1.262^{1.5} = 1.418\ \text{years}

Step 3. You only fly half of it

\begin{aligned}t = \frac{T}{2} &= 0.709\ \text{years} \times 365.26\ \text{days} \\ &= \textbf{258.9 days}\end{aligned}

That is about 8.5 months.

To-scale diagram of the Sun with Earth's orbit at 1 AU and Mars's orbit at 1.524 AU. A transfer ellipse runs half way round from Earth at launch on the right to Mars at arrival on the left. Mars starts 44 degrees ahead of Earth; Earth ends up well ahead of Mars by arrival. — Figure 1. The Hohmann transfer to scale. At launch Mars must already be 44.3° ahead of Earth, so that it reaches the far end of the ellipse 259 days later at the same moment as the spacecraft. The dashed half shows the rest of the ellipse, which the spacecraft never flies.

Along the way you cover half the circumference of that ellipse, about 3.92 AU or 587 million kilometres, to reach a planet whose average distance is a fraction of that. The figure that matters is not distance but the energy needed to change orbits.

How much speed does it take?

The vis-viva equation gives the speed anywhere on an orbit: $v^2 = GM_{\mathrm{Sun}}\left(\frac{2}{r} - \frac{1}{a}\right)$ . Compare the transfer speeds at each end with the planets' own orbital speeds:

\begin{aligned}GM_{\mathrm{Sun}} &= 1.327\times10^{20}\ \mathrm{m^3/s^2} \\ 1\ \mathrm{AU} &= 1.496\times10^{11}\ \mathrm{m}\end{aligned}

Earth's orbital speed:

\sqrt{GM/r} = \mathbf{29.78\ km/s}

Transfer speed at 1 AU:

\begin{aligned}&\sqrt{GM\left(\frac{2}{1\ \mathrm{AU}} - \frac{1}{1.262\ \mathrm{AU}}\right)} \\ &= \mathbf{32.73\ km/s}\end{aligned}

Excess needed leaving Earth's influence:

v_\infty = 32.73 - 29.78 = \mathbf{2.94\ km/s}

Transfer speed at 1.524 AU: 21.48 km/s. Mars's orbital speed: 24.13 km/s. Mars catches up from behind at $v_\infty = \mathbf{2.65\ km/s}$ .

From a 300 km parking orbit, getting that 2.94 km/s of escape excess takes a burn of about 3.59 km/s. The spacecraft arrives with Mars overtaking it at 2.65 km/s, which a lander sheds by plunging into the atmosphere and an orbiter sheds with a braking burn or by skimming the upper air.

Why are Mars launch windows 26 months apart?

The phasing in Figure 1 is unforgiving. During the 259-day coast Mars moves 360° × 258.9 / 687.0 = 135.7° around the Sun. For it to meet the spacecraft at the 180° point, it must start 180 − 135.7 = 44.3° ahead of Earth. That relative geometry recurs once per synodic period, the time Earth takes to lap Mars:

\frac{1}{T_{\mathrm{syn}}} = \frac{1}{365.26} - \frac{1}{686.98}

T_{\mathrm{syn}} = \textbf{780 days} = \textbf{25.6 months}

That is the famous "every 26 months". It also explains a common misconception: you do not launch when Mars is closest. Closest approach (opposition) comes when Mars and Earth are lined up on the same side of the Sun. The launch geometry, with Mars 44° ahead, comes about three months earlier, and by the time you arrive Earth has pulled about 75° ahead of Mars. Figure 3 shows this on a real calendar, computed from the planets' actual elliptical orbits.

Two stacked timelines from 2020 to 2033. The top shows Earth to Mars distance swinging between about 0.4 and 2.6 AU, with closest approaches in late 2020, late 2022, early 2025, early 2027, spring 2029 and spring 2031. The bottom shows minimum departure excess speed, which dips to between 2.3 and 3.6 km/s at launch dates of July 2020, September 2022, October 2024, November 2026, December 2028 and January 2031, each a few months before closest approach. — Figure 3. Earth to Mars distance (top) and the best departure excess speed by launch date (bottom), from my own computation with JPL's mean orbital elements in a simplified flat solar system. The optimum launch dates (green) fall roughly two to five months before closest approach (orange). The model puts the 2020 optimum on 20 July; the real launches were on 19, 23 and 30 July.

Two more things fall out of that plot. First, not all windows are equal. Mars's orbit is noticeably eccentric ( $e = 0.093$ ), so it ranges from 1.38 to 1.67 AU from the Sun. Windows that deliver you to Mars near its perihelion are cheaper, which is why the minimum in Figure 3 drifts from 3.4 km/s in 2020 to 2.3 km/s in 2031, and the pattern repeats over roughly 15 to 17 years. Second, the Hohmann time itself shifts with that eccentricity: a transfer to Mars at its closest to the Sun takes 237 days, one to Mars at its farthest takes 281.

The 2026 window is open about now. In my simplified model its cheapest departure falls on 1 November 2026; real mission designs, which include Mars's 1.85° orbital tilt, shift that by weeks.

Why do most Mars missions take about 7 months, not 8.5?

Look at the record. Figure 4 lists launch-to-arrival times for twelve missions. Very few sit on the 259-day Hohmann line.

Horizontal bar chart of launch to arrival times: Mariner 7 131 days, Mariner 6 156, Perseverance 203, InSight 205, Mars Express 206, MRO 210, Pathfinder 212, Mariner 4 228, Curiosity 254, Viking 1 304, MAVEN 308, Viking 2 333. A dashed line marks the 259 day Hohmann time with a shaded band from 237 to 281 days. — Figure 4. Launch to arrival for twelve Mars missions, computed from launch dates in NASA's Mars chronology and the arrival dates (flyby, orbit insertion or landing) in each mission's records. The grey band is the range of Hohmann times allowed by Mars's eccentric orbit.

There are three reasons for the spread.

An exact half-orbit is a trap in three dimensions. Mars's orbit is tilted 1.85° to Earth's. For a transfer of exactly 180°, the start point, the end point and the Sun lie on a straight line, so they do not define a plane, and the trajectory has to make an expensive plane change. Mission designers therefore pick either a "Type I" path a bit shorter than 180° (Perseverance, MRO, InSight) or a "Type II" path a bit longer (Viking, MAVEN).

Faster is cheaper than it looks, thanks to the Oberth effect. I solved Lambert's problem (finding the orbit that connects two points in a given time) for every trip time, picking the best transfer angle each time. Figure 2 shows the result, and the table shows the burns that matter:

Line chart of excess speed against time of flight from 100 to 350 days. The total excess speed curve has a minimum of 5.6 km/s at 259 days and rises to 6.8 km/s at 200 days and 16.6 km/s at 100 days. Departure and arrival curves are shown separately. Purple tick marks at the bottom show real mission durations clustered between 203 and 228 days. — Figure 2. Minimum excess speed (v_∞) at departure, at arrival and combined, versus trip time, for transfers between circular, coplanar orbits. The bottom of the curve is broad, which is why so many missions settle between 200 and 230 days. My own calculation with a universal-variable Lambert solver.

Trip time	v_∞ at Earth	Burn from 300 km orbit	v_∞ at Mars	Burn into 250 km Mars orbit
259 days (Hohmann)	2.95 km/s	3.59 km/s	2.65 km/s	2.10 km/s
200 days	3.36 km/s	3.71 km/s	3.48 km/s	2.54 km/s
180 days	3.71 km/s	3.81 km/s	4.14 km/s	2.95 km/s
150 days	4.58 km/s	4.12 km/s	5.44 km/s	3.86 km/s
120 days	5.94 km/s	4.71 km/s	7.39 km/s	5.41 km/s

Cutting 59 days off the trip raises the departure burn by only 120 m/s, about 3%, because the burn happens deep in Earth's gravity well where each extra metre per second of burn buys much more than a metre per second of escape excess. Here is that calculation for the 200-day case:

At 300 km altitude: escape speed $v_{\mathrm{esc}} = 10.93\ \mathrm{km/s}$ , circular speed $v_c = 7.73\ \mathrm{km/s}$

\text{Burn} = \sqrt{v_\infty^2 + v_{\mathrm{esc}}^2} - v_c

Hohmann:

\begin{aligned}\sqrt{2.95^2 + 10.93^2} - 7.73 &= 11.32 - 7.73 \\ &= \mathbf{3.59\ km/s}\end{aligned}

200 days:

\begin{aligned}\sqrt{3.36^2 + 10.93^2} - 7.73 &= 11.43 - 7.73 \\ &= \mathbf{3.71\ km/s}\end{aligned}

For landers the arrival side costs nothing in fuel either, since the atmosphere does the braking. The real limit there is heating and parachute loads, which is why rover missions stay near 200 days rather than pushing to 150.

Flybys do not have to stop. Mariner 6 and 7 were flybys, so they could arrive at any speed. Mariner 7's 131 days is the fastest trip to Mars on the list, and no orbiter or lander has come close to it.

How long would a round trip to Mars take?

This is where Mars hurts. When you arrive, Earth is 75° ahead of Mars. To come home on a Hohmann orbit, Earth needs to be 75° behind Mars at departure. Earth gains on Mars at $360^\circ / 780\ \text{days} = 0.46^\circ$ per day, and it has to gain $360^\circ - 2 \times 75.2^\circ = 209.6^\circ$ .

\begin{aligned}\text{Wait on Mars} &= \frac{209.6^\circ}{0.4616^\circ/\text{day}} \\ &= \textbf{454 days}\end{aligned}

\begin{aligned}\text{Round trip} &= 259 + 454 + 259 \\ &= \textbf{972 days} \approx \textbf{2.7 years}\end{aligned}

NASA's long-stay ("conjunction class") reference missions look similar: transits of about six months each way and roughly 500 to 540 days at Mars. The alternative, a short-stay "opposition class" mission, spends only a few weeks at Mars but pays for it with a much longer, higher-energy return leg, often with a swing past Venus.

What is the fastest possible trip to Mars?

With chemical rockets you can buy speed, as the table shows, but the cost climbs quickly below about 150 days: you arrive so fast that capture or atmospheric entry becomes the problem. To do radically better you need an engine that keeps pushing for the whole trip.

For constant acceleration $a$ with a flip at the midpoint, ignoring the Sun's gravity and the planets' motion, the time to cover distance $d$ is $t = 2\sqrt{d/a}$ .

1 $g$ all the way (9.81 m/s²), closest approach of 2003 (55.8 million km)

\begin{aligned}t &= 2\sqrt{\frac{5.58\times10^{10}\ \mathrm{m}}{9.81\ \mathrm{m/s^2}}} = 2 \times 75{,}400\ \mathrm{s} \\ &= 150{,}800\ \mathrm{s} = \textbf{1.7 days}\end{aligned}

Peak speed at the midpoint:

a \times \frac{t}{2} = 9.81 \times 75{,}400 = 740\ \mathrm{km/s}

0.01 $g$ (0.098 m/s²), same distance: $t = \textbf{17 days}$

Log-log plot of trip time versus constant acceleration from 0.0001 to 10 metres per second squared, for distances of 55.8, 254 and 401 million kilometres. All three lines fall as one over the square root of acceleration, crossing the 259 day Hohmann time near 0.0005 to 0.003 metres per second squared and reaching about 2 to 5 days at 1 g. — Figure 5. Travel time with continuous thrust and a midpoint flip. Even 0.001 m/s² (a ten-thousandth of a g) sustained for months beats the Hohmann coast. Nothing that can sustain 1 g for days exists; this is the regime of The Expanse's fictional Epstein drive.

Ion engines already deliver continuous thrust, but at accelerations around 10⁻⁴ m/s² or less for a loaded spacecraft, where Figure 5 shows no advantage over coasting. The gap between that and 1 g is a factor of about 100,000.

How far away is Mars, and why “225 million km” is misleading

The closest approach in recorded history was 55.76 million km on 27 August 2003. The farthest is about 401 million km, when Mars is on the far side of the Sun. The "average distance" often quoted is 225 million km, but if you average the actual Earth to Mars distance over time using the orbits in Figure 3, you get about 1.70 AU, or 254 million km. The two planets spend more time on opposite sides of the Sun than near each other. Either way, distance is the wrong number for travel time. The right ones are 259 days, 44°, and 780 days.

Radio signals have it easier: at the speed of light the one-way delay ranges from 3.1 minutes at closest approach to 22.3 minutes at the farthest.

The short version: a minimum-energy trip to Mars is half an orbit of an ellipse with

a = 1.262\ \mathrm{AU}

, which takes 259 days. Real missions take 200 to 230 days because a slightly faster path costs only about 3% more launch energy and avoids a 3D geometry problem. Windows open every 26 months, and a crew would spend about 15 months on Mars waiting to come home.

FAQ

How long does it take to get to Mars?

Usually about 6 to 8 months. The minimum-energy Hohmann transfer between idealised circular orbits takes 259 days. Real missions have ranged from 131 days (the Mariner 7 flyby) to 333 days (Viking 2), and most recent landers and orbiters arrived after 203 to 212 days.

Why can we only launch to Mars every 26 months?

For a low-energy transfer, Mars must be about 44 degrees ahead of Earth at launch. Earth laps Mars once every synodic period of about 780 days, which is 25.6 months, so that alignment repeats roughly every 26 months.

How long would a round trip to Mars take?

With minimum-energy transfers both ways, about two and a half to three years: roughly 8 to 9 months out, about 15 months waiting on Mars for the planets to realign, and 8 to 9 months back. In the circular-orbit model that totals about 970 days.

What is the fastest possible trip to Mars?

With chemical rockets, trips of 4 to 5 months are possible at the cost of much higher speeds at both ends, roughly 10 km/s of combined excess speed for 150 days versus 5.6 km/s for the 259-day Hohmann path. A hypothetical engine sustaining 1 g of thrust could make it in 2 to 5 days.

Sources

NASA NSSDC, Chronology of Mars Exploration (launch dates for Mariner 4, 6, 7, Viking 1, 2, Pathfinder, Mars Express, MRO, MSL, MAVEN, InSight, Mars 2020): nssdc.gsfc.nasa.gov/planetary/chronology_mars.html
NASA NSSDC, Mars Fact Sheet (semi-major axis 1.524 AU, eccentricity 0.0934, inclination 1.85°, orbital period 687 days, synodic period 779.9 days): nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html
E. M. Standish, JPL Solar System Dynamics, "Approximate Positions of the Planets" (mean orbital elements used for Figure 3): ssd.jpl.nasa.gov/planets/approx_pos.html
NASA JPL / Universe Today, 2003 close approach of Mars at 55.76 million km: universetoday.com/articles/mars-is-close-and-getting-closer
British Astronomical Association, Data for the Great Perihelic Opposition, 2003: britastro.org (Mars section, 2003 opposition data)
Viking 2 orbit insertion on 7 August 1976, NASA Mars Exploration Program archive: mars.jpl.nasa.gov/missions/past/viking.html (archived)
NASA NTRS 20140013259, nuclear thermal propulsion study for Mars Design Reference Architecture 5.0 (about 6-month transits, roughly 540 days at Mars): ntrs.nasa.gov/citations/20140013259
Space.com, "How long does it take to get to Mars?" (typical figures as reported by NASA, light-time): space.com/24701-how-long-does-it-take-to-get-to-mars.html

Header image: NASA/JPL-Caltech/MSSS (image PIA22487), regraded for this article.

Why don’t spacecraft fly straight to Mars?

How long is a Hohmann transfer to Mars?

How much speed does it take?

Why are Mars launch windows 26 months apart?

Why do most Mars missions take about 7 months, not 8.5?

How long would a round trip to Mars take?

What is the fastest possible trip to Mars?

How far away is Mars, and why “225 million km” is misleading

FAQ

How long does it take to get to Mars?

Why can we only launch to Mars every 26 months?

How long would a round trip to Mars take?

What is the fastest possible trip to Mars?

Related on The Science 360

Sources