Hohmann Transfer Orbit Calculator

About the Hohmann Transfer Orbit Calculator

The Hohmann transfer orbit is the most fuel-efficient two-impulse maneuver for moving a spacecraft between two coplanar circular orbits. Developed by Walter Hohmann in 1925, this elliptical transfer orbit touches the inner orbit at its periapsis and the outer orbit at its apoapsis, requiring exactly two engine burns.

This calculator computes both delta-v values (departure and arrival burns), the total Δv budget, the transfer time, and — using the Tsiolkovsky rocket equation — the propellant mass required for any given payload. It supports five preset central bodies (Earth, Mars, Moon, Sun, Jupiter) and allows custom gravitational parameters.

Whether you are a student solving orbital mechanics problems, an aerospace engineer planning mission trajectories, or a space enthusiast exploring mission scenarios, it gives the fundamental parameters needed to evaluate a Hohmann transfer. The engine comparison table shows propellant requirements across chemical and electric propulsion systems and helps you compare burns, transfer time, and propellant cost across mission profiles.

When This Page Helps

Orbital mechanics involves large numbers, gravitational parameters, and the exponential nature of the rocket equation — all of which make mental arithmetic impossible. This calculator handles the vis-viva equation, transfer orbit geometry, and Tsiolkovsky mass ratio in one step, letting you compare mission scenarios rapidly and evaluate different propulsion technologies.

How to Use the Inputs

1. Enter the inner and outer orbit radii in kilometers (measured from the center of the central body, not altitude).
2. Select the central body or use a custom gravitational parameter (μ = GM).
3. Enter the payload mass in kg and the engine specific impulse (Isp) in seconds.
4. Read the total Δv, individual burn magnitudes, transfer time, and propellant mass.
5. Compare propellant requirements across different engine types in the reference table.
6. Use preset buttons for common mission scenarios like LEO to GEO or Earth to Mars.

Example Calculation

Tips & Best Practices

• Remember orbit radius = altitude + body radius. LEO at 400 km altitude around Earth has radius 6771 km.
• The Hohmann transfer is energy-optimal for two-impulse maneuvers, but bi-elliptic transfers can be more efficient when the orbit ratio exceeds ~11.94.
• Transfer time increases sharply with orbit radius ratio — the Earth-to-Mars transfer takes about 8.5 months.
• Higher Isp engines need exponentially less propellant but typically provide lower thrust, making transfers slower.
• For real mission planning, also account for plane changes, launch windows, gravity assists, and atmospheric drag.
• The delta-v budget is the single most important number in mission design — it determines everything from propellant mass to launcher selection.

The Vis-Viva Equation

The vis-viva equation v = √(μ(2/r − 1/a)) is the key tool for computing velocities anywhere in an orbit. It relates the orbital speed at any distance r to the semi-major axis a and the gravitational parameter μ = GM. For circular orbits, r = a, giving v = √(μ/r). The Hohmann transfer calculation applies vis-viva at both the periapsis (inner orbit intersection) and apoapsis (outer orbit intersection) to find the transfer orbit velocities.

The Rocket Equation and Mass Budget

The Tsiolkovsky rocket equation Δv = Isp × g₀ × ln(m₀/m_f) shows that propellant mass grows exponentially with Δv. Doubling the Δv roughly squares the mass ratio. This exponential relationship is why high-Isp propulsion (ion engines, nuclear thermal) is so attractive for deep-space missions, even though these engines produce very low thrust and require longer transfer times.

Beyond Hohmann: Advanced Transfers

While the Hohmann transfer is the foundation of orbital mechanics education, real mission designs often use more complex trajectories. Low-thrust spiral transfers use continuous electric propulsion. Gravity assists from planets provide essentially free Δv. Lagrange point orbits enable station-keeping with minimal fuel. Understanding the Hohmann transfer provides the baseline against which all these advanced techniques are compared.

Frequently Asked Questions

• What is a Hohmann transfer orbit?

  It is an elliptical orbit that is tangent to both the initial and final circular orbits. The spacecraft fires its engine twice: once to enter the transfer ellipse and once to circularize at the target orbit. It is the most fuel-efficient two-burn maneuver between coplanar circular orbits.

• What is delta-v (Δv)?

  Delta-v is the total change in velocity a spacecraft needs. It is the fundamental currency of orbital mechanics — every maneuver costs some Δv, and the total Δv budget determines how much propellant is needed via the Tsiolkovsky rocket equation.

• Why is the orbit radius, not altitude, used?

  Orbital mechanics equations use distance from the center of the gravitating body. For Earth, add 6371 km (mean radius) to the orbital altitude to get the orbit radius.

• What is specific impulse (Isp)?

  Isp measures engine efficiency — the thrust produced per unit of propellant consumed per second. Higher Isp means less propellant for the same Δv. Chemical rockets have Isp 250-450 s, while ion engines can reach 3000-5000 s.

• How long does a Hohmann transfer take?

  The transfer time is half the orbital period of the transfer ellipse: t = π√(a³/μ). For LEO to GEO, this is about 5.3 hours. For Earth to Mars, it is about 259 days.

• Is the Hohmann transfer always the best option?

  No. For very large orbit ratio changes (> ~12:1), a bi-elliptic transfer can use less total Δv. For time-critical missions, higher-energy transfers are faster. And gravity assists can provide "free" Δv by using planetary flybys.