3D graphics are not available here, so a top-down 2D view is shown. The physics is exactly the same.
Important moments are announced, and the mission log lists every event with its time.
Locked during the flight. Press Reset to change it.
Now: Auto. Auto slows down for burns and important moments.
Engine errors make course corrections necessary, as in real flights.
The white line marks what the mission needs (including about 1.5–2 km/s lost to gravity and drag on the way up). More thrust burns the propellant faster; more mass lowers every stage’s mass ratio.
Changes take effect after Reset.
⚠️ A teaching model, not mission software. Planets move on circular orbits in one plane, the rocket is fictional (with realistic numbers) and the air is simplified. The motion itself is honest Newtonian physics solved numerically. What the model simplifies.
Throw a ball sideways and it curves down to the ground. Throw it faster and it lands farther away. Isaac Newton imagined a cannon on a high mountain: fire fast enough and the ball falls around the curved Earth without ever reaching the ground. That is an orbit. A rocket’s job is to climb above the air and then go sideways fast enough to keep missing the Earth.
On the pad, two forces fight: thrust pushing up and weight ($W = mg$) pulling down. The rocket lifts off only when thrust is bigger than weight, and Newton’s second law gives the acceleration: $a = (T - W - D)/m$. As it burns propellant the mass drops, so the acceleration grows. In orbit at 200 km, gravity is still 94% as strong as on the ground; the spacecraft just moves sideways at about $v = \sqrt{GM/r} \approx 7.8$ km/s. Getting that speed is hard: the rocket equation $\Delta v = v_e \ln(m_0/m_f)$ says most of a rocket must be propellant, which is why rockets drop empty stages.
To go higher you do not point at the target; you speed up along your orbit. That adds orbital energy $\varepsilon = v^2/2 - GM/r$ and stretches the circle into an ellipse whose far point rises (vis-viva: $v^2 = GM(2/r - 1/a)$). For the Moon, a 3.1 km/s burn makes the far point reach the Moon’s distance, timed so the Moon is there when the spacecraft arrives. For Mars, the burn must beat escape speed and leave about 2.9 km/s pointing along Earth’s motion around the Sun: the spacecraft then coasts on half of a Hohmann ellipse from 1 AU to 1.52 AU. Near the target its gravity takes over (its sphere of influence) and the path relative to it is a hyperbola: brake at the closest point to be captured, or let it swing you onto a new path (a flyby). The computer finds the path by adding up gravity from every body in tiny time steps (Runge–Kutta integration), not by drawing ready-made curves.
1. Physics mode: set thrust to 65% and launch. Thrust is less than weight, so the rocket sits on the pad burning fuel until it is light enough to lift off (about 43 s); by then too much propellant is gone and it falls back. 2. Add 6 t of cargo and fly to the Moon: the departure burn runs out of propellant and the spacecraft is stranded (the rocket equation at work). 3. Fly to Mars with the window offset at +30°: the departure burn has to be bigger and the spacecraft cannot brake at Mars. 4. Fly the Moon free return and watch the figure-8 path bring the spacecraft home without a single extra burn.
The simulator does not follow pre-drawn curves. In small time steps (a tenth of a second at launch, hours between the planets) it adds up all the forces on the spacecraft, works out its acceleration, and steps its position and velocity forward. These are the equations it uses.
Thrust $\vec T$ points along the rocket; the propellant flow $\dot m$ is constant for each stage. On the first stage, thrust rises from 7,607 kN at sea level to 8,227 kN in vacuum because the outside air pressure on the nozzle disappears. Drag $D = \tfrac12 \rho v^2 C_D A$ uses an exponential atmosphere $\rho = \rho_0 e^{-h/H}$ with $\rho_0 = 1.225$ kg/m³ and $H = 8.5$ km. The quantity $q = \tfrac12\rho v^2$ is the dynamic pressure; its peak is max-Q.
$I_{sp}$ is the specific impulse in seconds ($g_0 = 9.80665$ m/s²). Stage 1 uses kerosene engines ($I_{sp}$ about 288 s at sea level, 311 s in vacuum), Stage 2 a vacuum engine (348 s) and the departure stage hydrogen (450 s). Dropping each empty stage raises the mass ratio $m_0/m_f$ of the next one.
The Moon mission includes the Earth and the Moon; the Mars mission includes the Sun, Earth and Mars. For a circular orbit $v_c = \sqrt{GM/r}$; escape speed is $v_{esc} = \sqrt{2GM/r}$; the period is $T = 2\pi\sqrt{r^3/GM}$.
Negative energy means a closed ellipse with semi-major axis $a$; zero or positive means escape. The departure and braking burns are cut off when $\varepsilon$ reaches the planned value.
Earth to Mars: $\Delta v_1 = 2.94$ km/s (relative to Earth, far away: $v_\infty$), $t = 259$ days. Mars moves 136° in that time, so it must be 44° ahead of Earth at departure. Leaving from a 200 km orbit, the burn must give $v_p = \sqrt{v_\infty^2 + 2GM_E/r_p} \approx 11.4$ km/s, a $\Delta v$ of about 3.6 km/s.
Each $\mathbf k$ is the rate of change (velocity, acceleration, mass flow) evaluated at the start, twice in the middle and at the end of the step. The step $\Delta t$ is 1% of the local orbital time scale $\sqrt{r^3/GM}$ (at most 0.5 s while an engine burns, 0.1 s in the lower atmosphere). In a test of 20 orbits around a lone Earth, the energy changed by less than 1 part in a billion.
The two missions are separate: a Mars mission does not stop at the Moon. Stopping there would mean braking into lunar orbit and then speeding up again, which costs much more Δv than flying straight from Earth orbit to Mars.
| Earth → Moon | Earth → Mars | |
|---|---|---|
| Distance | about 384,400 km (average) | 55 to 400 million km, depending on where the planets are |
| Trip time | about 3 days | about 7 to 9 months (Hohmann: 259 days) |
| Departure burn from a 200 km orbit | about 3.1 km/s (trans-lunar injection) | about 3.6 km/s (trans-Mars injection) |
| Braking to stay | about 0.85 km/s into a 100 km lunar orbit | about 0.9 km/s into a long elliptical orbit (about 2 km/s for a low circular one) |
| When can you go? | Almost any time; the Moon comes round every 27.3 days | Only in launch windows, about every 26 months |
| Radio delay (one way) | about 1.3 seconds | about 3 to 22 minutes |
| Surface gravity | 1.62 m/s² (about 1/6 of Earth’s) | 3.71 m/s² (about 3/8 of Earth’s) |
| Main force on the coast | Earth’s gravity, then the Moon’s | The Sun’s gravity for most of the trip |
Sources: NASA Planetary and Lunar Fact Sheets (NSSDCA); NASA Mars Exploration Program. Trip times and Δv are typical values; real missions vary.
Ten questions are picked from a bank of 20. Each answer is explained.
This is a teaching simulator. It shows the real physics of rocket flight and orbits, but it must not be used to plan or check a real mission. Its simplifications:
About 3 days. The crewed lunar flights of 1968 to 1972 took about three days to reach the Moon. In this simulator the coast from the trans-lunar injection burn to the lunar orbit insertion burn takes about 3.4 days.
Key takeaway: about 3 days of coasting after the departure burn.About 7 to 9 months. A Hohmann transfer, the slowest but most fuel-efficient simple path, takes about 259 days. Real missions often use a little more energy to arrive sooner: the Perseverance rover took 203 days in 2020 to 2021.
Key takeaway: 259 days on a Hohmann transfer; real missions take about 7 to 9 months.Because everything is moving. The spacecraft starts in orbit moving sideways at 7.8 km/s, and the Moon and Mars move along their own orbits. Gravity bends every path into a curve, so mission planners aim where the target will be when the spacecraft arrives and let gravity do most of the work. Speeding up along the orbit is far cheaper than fighting gravity in a straight line.
Key takeaway: aim for where the target will be and let gravity curve the path.About 7.8 km/s sideways at 200 km altitude. Because the rocket also has to climb and push through the air, it loses about 1.5 to 2 km/s to gravity and drag on the way up, so a rocket needs about 9.4 km/s of delta-v in total, even with the free 0.47 km/s that Earth’s spin gives a rocket launched east from the equator.
Key takeaway: about 7.8 km/s, which costs about 9.4 km/s of delta-v.A launch window is the period when the planets are in the right places for an efficient trip. For a Hohmann transfer, Mars must be about 44 degrees ahead of Earth when the spacecraft leaves. Earth goes round the Sun faster than Mars and catches up with it again only every 780 days, about 26 months, so the windows repeat on that cycle. Try the window offset slider in Physics mode to see the cost of launching at the wrong time.
Key takeaway: the right planet positions repeat only every 26 months.It is half of an ellipse that just touches both orbits: for an outward trip it touches the starting orbit at its closest point to the Sun or planet and the target orbit at its farthest point. One burn puts the spacecraft on the ellipse and a second burn at the other end matches the new orbit. Between two circular orbits in the same plane it is the two-burn transfer that needs the least delta-v, but it is slow.
Key takeaway: half an ellipse between two orbits, with a burn at each end.Orbit needs sideways speed, not just height. A few seconds after liftoff the rocket tips over by a few degrees and then lets gravity bend its path more and more horizontal: a gravity turn. Following the direction of motion keeps the air from pushing sideways on the rocket, which matters most near max-Q.
Key takeaway: orbit is about going sideways fast; the gravity turn does it gently.Delta-v = v_e ln(m0/mf): the speed a rocket can gain depends on its exhaust speed and on the ratio of its full to empty mass. Because of the logarithm, each extra km/s needs a much bigger mass ratio. That is why most of a rocket is propellant, why rockets use stages, and why a few extra tonnes of cargo can make a mission impossible.
Key takeaway: delta-v depends on exhaust speed and the full-to-empty mass ratio.Real Mars missions do not stop at the Moon on the way. Stopping would mean braking into lunar orbit and speeding up again, which costs extra delta-v. Leaving straight from a low Earth orbit is cheaper, so the simulator treats the Moon and Mars as two different journeys.
Key takeaway: a stop at the Moon would cost extra fuel.The physics is real: Newtonian gravity from every body, thrust, mass loss and drag, solved with a fourth-order Runge-Kutta method. The main numbers come out close to real values, such as about 3.1 km/s for trans-lunar injection, 3 days to the Moon and 259 days to Mars. But the planets move on circles in one plane, the launch site is on the equator and the rocket is fictional, so it is a learning tool, not mission-planning software.
Key takeaway: real physics with simplified planets and a fictional rocket.