Date-

Trip day-

Speed (Sun)-

From Earth-

To Mars-

Signal, one way-

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How long does it take to fly to Mars?

Blender 5.2 modelsThree.js r160Lambert solverapproximate public figuresgeneric spacecraft

The cheapest trip (a Hohmann transfer) takes about 259 days but is only possible in a window that opens every 26 months. Pick a launch date and a departure burn from low Earth orbit, watch the ship coast around the Sun, and see whether it meets Mars. Then explore how a faster trip costs far more fuel.

Presets

1. Launch date and departure burn

Launch date

Departure burn from 300 km orbit (delta-v)

Direction: toward / away from the Sun (0 = along Earth's motion)

Direction: out of the orbital plane

Aim target: time of flight for the Lambert solver

2. Arrival at Mars (target plane, to scale)

Scale

Arrival plan

3. Porkchop plot: cost of every launch / arrival pair

Show

Tap or click the plot to launch on that date with that arrival date. Dashed lines: constant trip time. Star: cheapest pair in view. Cross: your current choice.

4. Launch windows, next 11 years

Best launch	Arrive	Days	dv km/s	C3

Computed with the Lambert solver on the orbit model below. Tap a row to load it.

5. Faster trip = more fuel

Engine

Ship mass without outbound fuel (crew, habitat, cargo, return fuel)

6. Radio delay and radiation (order of magnitude)

Time on the surface before returning

Dose rates are public measurements: about 1.8 mSv/day in deep space inside a spacecraft (Curiosity RAD during its 2011-12 cruise) and about 0.6 mSv/day on the Martian surface. Solar-cycle, shielding and solar storms change this a lot; treat it as an order of magnitude.

7. Orbit model

Planets move on

Lambert reference arc planet orbits labels

Playback

Planets and the ship are drawn much larger than life so you can see them; orbits and distances are to scale.

Independent numerical checks (live)

The science

Hohmann transfer. The lowest-energy route between two circular orbits is half an ellipse touching both. With Earth at 1 AU and Mars at 1.524 AU the ellipse has a = 1.262 AU, so the trip takes half its period.

a_t = (r1 + r2) / 2 = 1.262 AU t_H = pi * sqrt(a_t^3 / mu_sun) = 259 days v_inf = v_E * (sqrt(2 r2 / (r1 + r2)) - 1) = 2.94 km/s (speed relative to Earth) dv = sqrt(v_inf^2 + 2 mu_E / r) - sqrt(mu_E / r) = 3.6 km/s from a 300 km orbit C3 = v_inf^2 = 8.7 km^2/s^2

Launch windows. Mars must be ahead of Earth by 180 deg - 360 deg x t_H / T_Mars = about 44 deg when you leave, so that it arrives at the meeting point at the same time. Earth gains one lap on Mars every synodic period 1 / (1/T_E - 1/T_M) = 780 days, so windows repeat about every 26 months. Real orbits are elliptical and tilted, so each window has a different best cost (the table above shows it).

Lambert's problem. Given the Earth position at launch, the Mars position at arrival and the flight time, the Sun-only orbit connecting them is found with the universal-variable method (single revolution, prograde). The porkchop plot solves it on a grid of about 8,000 launch/arrival pairs. C3 is the square of the speed relative to Earth when the ship leaves Earth's gravity.

Your own burn. The sim turns your delta-v into v_inf with v_inf^2 = (v_c + dv)^2 - 2 v_c^2 (v_c = 7.73 km/s at 300 km), adds it to Earth's velocity, and integrates r'' = -mu r / |r|^3 with fourth-order Runge-Kutta. The distance to Mars is then searched for its closest approach. A pass within Mars' sphere of influence (577,000 km) counts as an encounter; the periapsis follows from b = r_p sqrt(1 + 2 mu_M / (r_p v_inf^2)).

Fuel. The rocket equation dv = g0 Isp ln(m0/mf) means propellant grows exponentially with delta-v. A fast trip raises both departure and arrival speed, so the initial mass in orbit grows quickly as the flight time falls below about 200 days. Low-thrust electric propulsion is not modelled (it needs long spirals, not impulsive burns).

Radio delay and radiation. One-way delay = distance / c, from about 3 minutes (closest) to 22 minutes (far side of the Sun). Dose = measured dose rate x days; it is an estimate, not a mission plan.

Simplifications (honest list). Impulsive burns; the ship feels only the Sun (planet gravity is used for the departure and arrival formulas, not integrated); the encounter is judged without bending by Mars' gravity; Earth's own departure geometry is assumed to allow any direction; planets from Keplerian elements valid for 1800-2050 (position error of the order of 10^4 km), no gravity assists, no mid-course corrections, a generic spacecraft with no brand or real mission data. Public approximate figures only - not a flight-design tool.

Independent checks. The table compares closed-form results (Hohmann time and velocity, synodic period, lead angle, rocket equation) with the Lambert solver, the integrator and a phase-angle scan.