Delta-v budget
Delta-V Maneuver Budget
Every orbital maneuver costs velocity, and velocity costs propellant. Budget the burn before you build the tank.
// Two-body impulsive astrodynamics. Hohmann / plane-change / combined / circularize / deorbit, with a per-burn breakdown. Tsiolkovsky rocket equation for propellant mass. Keplerian trade-study accuracy — flight design needs finite-burn losses + numerical propagation.
This is a Hohmann transfer calculator and general impulsive-maneuver budgeter: it computes the burns for a Hohmann transfer, a pure plane change, a combined transfer-plus-plane-change, a circularization, and a deorbit burn from the vis-viva equation — two-body Keplerian astrodynamics with Earth's gravitational parameter μ = 398,600.4418 km³/s² (Space Mission Analysis and Design (SMAD) ch. 6–7; Vallado 2013, ch. 6) — then converts the total delta-v to propellant mass with the Tsiolkovsky rocket equation. It is an engineering trade-study tool: fast first-order numbers for sizing and comparison; flight design adds finite-burn losses and numerical propagation.
How this model works & what it omits
A spacecraft changes orbit by changing velocity. The size of that velocity change — the delta-v (Δv) — is the single number that sizes a propulsion system: it sets how much propellant you carry, which sets the wet mass, which sets the launch cost. Get the delta-v budget wrong early and the whole mass budget unravels. This tool budgets five canonical maneuvers, each a distinct two-body impulsive problem.
Hohmann transfer — the minimum-energy coplanar path between two circular orbits: a burn to enter an elliptical transfer orbit, a half-orbit coast, then a second burn to circularize at the target altitude. Plane change — a pure inclination rotation at fixed altitude, costing Δv = 2·v·sin(θ/2); it is brutally expensive at orbital speed, which is why launch directly into the right inclination whenever possible. Combined — a Hohmann transfer with the plane change folded into the second burn at apogee, where orbital speed is lowest and rotating the plane is cheapest; the apogee burn becomes the vector sum (law of cosines) of the circularization and rotation. Circularize — a single burn at apogee turning an elliptical orbit circular. Deorbit — a single retrograde burn lowering perigee into the atmosphere (typically 50–80 km) so atmospheric drag does the rest.
Orbital speeds come from the vis-viva equation v = √(μ·(2/r − 1/a)), with Earth's gravitational parameter μ = 398,600.4418 km³/s². Once the total delta-v is known, the Tsiolkovsky rocket equation m_p = m₀·(1 − e^(−Δv/v_e)) converts it to propellant mass, where the exhaust velocity v_e = I_sp·g₀ is set by the propulsion type — cold gas ~70 s, monopropellant ~220 s, bipropellant ~320 s, electric 1,000–3,000 s. Higher specific impulse means more delta-v per kilogram of propellant; the exponential makes high-Δv missions punishingly propellant-hungry on low-I_sp systems.
What this tool does not capture: finite-burn (gravity) losses from non-impulsive thrust, low-thrust spiral transfers (an electric-propulsion mission does not fly a Hohmann), J2 and third-body perturbations, plane-change savings from bi-elliptic transfers, launch-window and phasing constraints, and propulsion-system dry-mass scaling. It is an engineering trade-study tool — fast first-order numbers for sizing and comparison, not a flight-design propagator.
// pick a maneuver, then dial orbit geometry and propulsion.
Maneuver
// two-body impulsive astrodynamics.
Orbit geometry
// only the fields the chosen maneuver uses are active.
Propulsion
// Tsiolkovsky rocket equation: m_p = m0 (1 − e^(−Δv/ve)).
ve ≈ 2.157 km/s
Delta-v budget
// Hohmann transfer (altitude change) · 2 burns
216.7 m/s
Total delta-v
19.11 kg
Propellant mass
9.6%
Propellant fraction
180.9 kg
Final (dry) mass
48.3 min
Transfer time
// per-burn breakdown
50% of total budget
50% of total budget
// shareable URL encodes every input. no backend.
// delta-v by burn
// ai-generated breakdown of what these numbers mean — with diagrams.
Common questions
How much delta-v does a Hohmann transfer take?
For this Hohmann transfer calculator's 400 → 800 km preset: a ~109 m/s perigee burn to enter the transfer ellipse, a ~48-minute coast, then a ~108 m/s apogee burn to circularize — about 217 m/s total. That is the useful intuition for low Earth orbit (LEO): raising a circular orbit a few hundred kilometres costs a couple of hundred metres per second. Load the preset and drag the target altitude to see how the two burns scale.
Why is a plane change so expensive?
Because it rotates the whole velocity vector at orbital speed: Δv = 2·v·sin(θ/2). At 420 km, v ≈ 7.66 km/s, so rotating the plane a single degree costs ~134 m/s — more than half the price of the entire 400 → 800 km altitude raise. The International Space Station (ISS)-inclination preset rotates 51.6° in place: ≈ 6.7 km/s, which the rocket equation turns into ~88% of the 200 kg spacecraft's mass as bipropellant. The practical rules: launch into the right inclination, and if you must rotate, fold the change into the apogee burn where speed is lowest (the combined maneuver).
How do I convert delta-v to propellant mass?
With the Tsiolkovsky rocket equation: m_p = m₀·(1 − e^(−Δv/v_e)), where the exhaust velocity v_e = I_sp·g₀ is set by the propulsion type — specific impulse (Isp) of ~70 s for cold gas, ~220 s for monopropellant, ~320 s for bipropellant, 1,000–3,000 s for electric. The exponential makes high-Δv missions punishingly propellant-hungry on low-Isp systems. To turn that propellant mass into tank, thruster, and burn-time sizing, hand the total to the CubeSat propulsion calculator.
How much delta-v does it take to deorbit from 500 km?
The controlled-deorbit preset drops perigee from a 500 km circular orbit to 60 km with a single retrograde burn of ≈ 127 m/s — atmospheric drag does the rest. On the preset's 150 kg spacecraft at 220 s Isp, that is roughly 8.6 kg of propellant. To check whether natural decay alone already meets the Federal Communications Commission (FCC) 5-year rule — and to size the disposal burn against each regime's limit — use the Deorbit & Lifetime Compliance checker.
Is a Hohmann transfer always the cheapest way to change orbits?
It is the minimum-energy two-impulse transfer between coplanar circular orbits — the right default for a chemical-propulsion trade study. Two caveats from the omissions list above: for very large radius ratios a bi-elliptic (three-burn) transfer can undercut it, and a low-thrust electric mission does not fly a Hohmann at all — it spirals out continuously, accumulating more total delta-v over a much longer transfer. Both need tools beyond this one's impulsive two-body model.
References
- // Wertz, J. R., Everett, D. F., Puschell, J. J. (2011). Space Mission Engineering: The New SMAD, ch. 6–7 (Orbit & Constellation Design, Δv budgets).
- // Vallado, D. A. (2013). Fundamentals of Astrodynamics and Applications, 4th ed., ch. 6 (Orbital Maneuvering).
- // Hohmann, W. (1925). Die Erreichbarkeit der Himmelskörper. Oldenbourg, Munich.
- // Tsiolkovsky, K. E. (1903). Exploration of Outer Space by Means of Rocket Devices.
- // Curtis, H. D. (2014). Orbital Mechanics for Engineering Students, 3rd ed., ch. 6 (Orbital Maneuvers).
