Rotate, zoom and inspect a simplified model of the Sun, Earth and Mars, and the curved Hohmann transfer path a spacecraft would follow between them.
Calculated model. This 3D model is not a demo, it is a working model built from my own calculations. The orbit, the flight path and the telemetry all come from the Hohmann orbital transfer and the mathematics set out further down the page.
Loading 3D scene…
Day 0 of 259
0% complete
Telemetry
Phase
Launch & parking orbit
Velocity
0.0 km/s
Fuel100%
Drag to rotate · Scroll to zoom · Pinch on mobile
Mission playbackReady for launch
Energy Exchange
Trading speed for height
As the spacecraft curves around Earth and swings outward, it trades kinetic energy for gravitational potential energy, reaching a little further with every ellipse.
Loading 3D scene…
Energy
Kinetic · KE0%
Potential · GPE0%
Distance1.00× rp
Drag to rotate · Scroll to zoom
The Mathematics
The maths behind the transfer
The models above aren't just for show. Every position, speed and fuel reading comes from the standard formulas a mission planner uses to design an Earth-to-Mars Hohmann transfer. Here is the same maths, worked through with real numbers.
μ = 1.327 × 10¹¹ km³/s²
Sun's gravity (GM)
r₁ = 1.496 × 10⁸ km
Earth orbit radius
r₂ = 2.279 × 10⁸ km
Mars orbit radius
a = 1.888 × 10⁸ km
Transfer semi-major axis
01 · Transfer ellipse
Sizing the transfer
a = (r1 + r2) / 2
The craft coasts along half an ellipse that just touches Earth's orbit at one end and Mars's at the other. Its semi-major axis a is simply the average of the two orbit radii.
→ a ≈ 1.888 × 10⁸ km (≈ 1.26 AU)
02 · Orbital speeds
The vis-viva equation
v = √( μ · (2/r − 1/a) )
Vis-viva gives the speed at any distance r on an orbit of semi-major axis a. A circular orbit (a = r) reduces it to v = √(μ/r).
Earth v₁ ≈ 29.8 km/s · Mars v₂ ≈ 24.1 km/s transfer vₚ ≈ 32.7 km/s (at Earth) transfer vₐ ≈ 21.5 km/s (at Mars)
03 · Delta-v budget
Two burns, one budget
Δv = Δv1 + Δv2
Delta-v is the speed change each engine burn must supply. The first speeds the craft up to enter the transfer at Earth; the second matches Mars's slower orbital speed on arrival.
The trip is half of the transfer ellipse's orbital period, so the travel time depends only on a and the Sun's gravity.
t ≈ 2.24 × 10⁷ s ≈ 259 days ≈ 8.5 months
05 · Why fuel matters
Turning Δv into propellant
Δv = ve · ln( m0 / mf )
The Tsiolkovsky rocket equation links the delta-v budget to how much propellant is needed. Because the relationship is exponential, a bigger Δv demands disproportionately more fuel, which is why the gauge on the first model falls with each burn.
with vₑ ≈ 4.4 km/s → m₀ / m_f = e^(Δv/vₑ) ≈ 3.6 · so ≈ 72% of the launch mass is propellant