Simulators

Four small simulators for the sums in the lessons. Move a slider and the answer changes at once. Each one uses the same formula its lesson explains, so you can check your own working against it. Everything runs in your browser; nothing is saved or sent.

Jump on Mars

How high could you jump, and how long would you hang in the air? The speed you leave the ground with depends on your legs, not on the planet, so the same take-off speed is used on each world. Height \(h = v^2 / 2g\), time in the air \(t = 2v/g\). See Jumping on Mars and the Mars jump, worked out.

Launch window

Ships to Mars leave when Mars is about 44° ahead of Earth in its orbit, so that a 259-day half-ellipse arrives just as Mars gets there. Pick a date to see where the planets are and when the next window opens. The planets move on circles here, so the real windows can differ by a few weeks. See Hohmann transfer and Launch windows.

The rocket equation

How much speed can a rocket gain from its fuel? \(\Delta v = v_e \ln(m_0/m_1)\), where \(v_e\) is the exhaust speed, \(m_0\) the full mass and \(m_1\) the empty mass. Compare the answer with what each step of a trip to Mars needs. See Tsiolkovsky's rocket equation.

A parachute in thin air

How fast does a lander fall under its parachute? At terminal speed the drag balances the weight: \(v = \sqrt{2mg / (\rho C_d A)}\). Mars has 38% of Earth's gravity but air only about 1.6% as dense. See Parachutes and terminal speed.

The numbers: \(g\) = 9.81 m/s² on Earth, 3.71 on Mars, 1.62 on the Moon; air at the ground 1.225 kg/m³ on Earth and about 0.020 on Mars (NASA Mars fact sheet).