About the Hohmann Transfer Simulator
This simulation plans a two-burn Hohmann transfer between two circular, coplanar Earth orbits, the most fuel-efficient way to move between them. The spacecraft begins on the initial orbit, fires a prograde burn to enter an elliptical transfer orbit, coasts half a revolution, then fires a second burn to circularise at the target altitude. Every velocity is derived from the vis-viva equation, v = √(GM·(2/r − 1/a)), with GM = 3.986 × 10¹⁴ m³/s².
The two sliders set the initial and target orbit altitudes above Earth (200 km to 35 800 km), and the canvas labels the resulting mission, such as LEO → GEO. Launch Transfer animates the trajectory while the panel reports each orbit's velocity and period, the two delta-v burns, the total delta-v and the transfer time. Hohmann transfers underpin real missions, from raising satellites into geostationary orbit to interplanetary departure planning.
Frequently Asked Questions
What is a Hohmann transfer?
A Hohmann transfer is a manoeuvre that moves a spacecraft between two circular coplanar orbits using a single elliptical transfer orbit and two engine burns. The transfer ellipse touches the lower orbit at its periapsis and the higher orbit at its apoapsis. For most altitude changes it requires the least delta-v of any two-impulse transfer, which is why it is the standard reference for orbit-raising.
Why does it use exactly two burns?
The first burn raises the apoapsis from the initial orbit up to the target altitude, placing the craft on the transfer ellipse. After coasting halfway around, the second burn at apoapsis adds the velocity needed to circularise into the target orbit. With only two carefully timed impulses, the transfer reaches the new orbit without wasting propellant on continuous thrust.
What is the vis-viva equation used here?
The vis-viva equation, v = √(GM·(2/r − 1/a)), gives the orbital speed at any radius r for an orbit of semi-major axis a, where GM is Earth's gravitational parameter, 3.986 × 10¹⁴ m³/s². The simulation uses it to find the circular speeds of both orbits and the periapsis and apoapsis speeds on the transfer ellipse, from which each burn's delta-v is the difference between two such speeds.
What do the two sliders control?
The first slider sets the initial orbit altitude and the second sets the target altitude, each measured above Earth's surface and ranging from 200 km to 35 800 km. As you move them the mission badge updates (for example LEO → GEO), and the readouts for velocity, period, delta-v and transfer time recompute immediately, even before you press Launch Transfer.
How is the transfer time calculated?
The transfer takes exactly half the period of the elliptical transfer orbit, since the craft travels from periapsis to apoapsis. The simulation computes it as t = π·√(a³/GM), where a is the semi-major axis of the transfer ellipse, equal to half the sum of the two orbit radii. For a LEO-to-GEO transfer this works out to roughly five hours.
What does delta-v mean and why does it matter?
Delta-v is the change in velocity a burn imparts, measured in metres per second. It is the currency of spaceflight: the total delta-v budget determines how much propellant a mission needs, via the Tsiolkovsky rocket equation. The simulator reports Δv₁, Δv₂ and their sum so you can compare how expensive different orbit changes are.
Is the physics in this simulation accurate?
The velocity, period and delta-v figures use exact two-body Keplerian formulae with Earth's real gravitational parameter, so the numbers match textbook astrodynamics for idealised circular orbits. The model assumes coplanar orbits, instantaneous impulsive burns and no atmospheric drag or third-body effects, which is the standard simplification for first-order mission planning.
Does it work for lowering an orbit as well as raising one?
Yes. If the target altitude is below the initial one, the transfer runs in reverse: the first burn is a retrograde impulse that lowers the periapsis, and the second circularises at the lower orbit. The simulation detects the direction, reverses the animation accordingly and still reports the correct delta-v for the descending case.
Why is a Hohmann transfer considered the most efficient?
For transfers between coplanar circular orbits whose radii are not too dissimilar, the two-impulse Hohmann ellipse uses less total delta-v than any other two-burn path. For very large radius ratios a bi-elliptic transfer with three burns can beat it, but for typical satellite manoeuvres the Hohmann transfer remains the efficient benchmark.
What real missions use Hohmann transfers?
Communications satellites routinely use a Hohmann-style transfer to climb from a low parking orbit to geostationary orbit, the LEO → GEO case shown here. The same principle, scaled up around the Sun, plans efficient launch windows for journeys to Mars and other planets, where timing the departure to meet the target is essential.