Hohmann Transfer
Calculate Hohmann transfer delta-v, transfer orbit parameters, orbital velocities, and time of flight between two circular orbits. Free online orbital mechanics calculator with interactive charts for astrophysics students and aerospace engineers.
About This Calculator
The Hohmann Transfer Calculator computes the orbital parameters, delta-v requirements, and transfer time for moving a spacecraft between two circular orbits using the most fuel-efficient two-burn transfer method. Named after German engineer Walter Hohmann (1880–1945), this maneuver is fundamental to astrodynamics and is used for satellite orbit raising, interplanetary missions, and spacecraft rendezvous.
The calculator uses the vis-viva equation v² = μ(2/r − 1/a) and Kepler's laws to determine all transfer parameters. Given the altitudes of the initial and target orbits above a selected primary body (Earth, Sun, Moon, Mars, Jupiter, or Saturn), it computes the transfer orbit semi-major axis a = (r₁ + r₂)/2, eccentricity e = |r₂ − r₁|/(r₁ + r₂), and the required delta-v at each burn: Δv₁ at periapsis to enter the transfer ellipse, and Δv₂ at apoapsis to circularize into the target orbit. The total delta-v is the sum of both burns. The transfer time (time of flight) is half the orbital period of the transfer ellipse: T = π√(a³/μ). If you provide your spacecraft's specific impulse and initial mass, the calculator also estimates the propellant mass required using the Tsiolkovsky rocket equation.
For example, a Hohmann transfer from low Earth orbit (400 km altitude) to geostationary orbit (35,786 km) around Earth requires the first burn to add about 2.45 km/s at LEO and the second burn to add about 1.46 km/s at GEO, totaling approximately 3.91 km/s of delta-v. The transfer takes roughly 5.25 hours (0.22 days). An interplanetary transfer from Earth to Mars around the Sun requires about 2.94 km/s at Earth's orbit and 2.65 km/s at Mars's orbit, totaling 5.59 km/s with a transfer time of approximately 259 days (8.5 months).
Applications
Aerospace Engineering: Design orbital maneuvers for satellite deployment, station-keeping, and interplanetary trajectories. Hohmann transfers provide the minimum delta-v (and thus minimum propellant) for transferring between two circular orbits, making them essential for mission planning and propellant budget calculations.
Physics Education: Understand orbital mechanics through the vis-viva equation, conservation of angular momentum, and Kepler's third law. The calculator demonstrates how a single impulse at one point in an orbit changes the entire trajectory and how orbital energy relates to semi-major axis.
Space Enthusiasts: Plan realistic space missions by computing delta-v budgets and transfer windows. Real-world applications include geostationary satellite insertion, Mars transfer trajectories, and lunar mission planning. The optional propellant calculation shows how much fuel is needed based on engine efficiency.
Frequently Asked Questions
What is a Hohmann transfer orbit?
A Hohmann transfer is an elliptical orbit used to move a spacecraft from one circular orbit to another using two engine burns. It is the most fuel-efficient two-burn orbital transfer method. The transfer orbit is an ellipse whose periapsis touches the initial orbit and apoapsis touches the target orbit.
How do you calculate delta-v for a Hohmann transfer?
Delta-v for a Hohmann transfer is calculated using the vis-viva equation: Δv₁ = √(μ(2/r₁ - 1/a)) - √(μ/r₁) for the first burn at periapsis, and Δv₂ = √(μ/r₂) - √(μ(2/r₂ - 1/a)) for the second burn at apoapsis, where μ is the gravitational parameter, r₁ and r₂ are orbit radii, and a is the transfer orbit semi-major axis.
What is the formula for Hohmann transfer time?
The transfer time (time of flight) for a Hohmann transfer is half the orbital period of the transfer ellipse: T = π × √(a³/μ), where a is the semi-major axis of the transfer orbit and μ is the gravitational parameter of the primary body. This equals the time to travel from periapsis to apoapsis along the transfer ellipse.
When is a Hohmann transfer used?
Hohmann transfers are used for satellite orbit raising (e.g., LEO to GEO), interplanetary missions (e.g., Earth to Mars), and spacecraft rendezvous. The maneuver requires both orbits to be coplanar and circular (or nearly circular). Real-world applications include geostationary satellite insertion and Mars transfer orbits.
What is the difference between periapsis and apoapsis?
Periapsis is the point on an orbit closest to the central body, where the spacecraft moves fastest. Apoapsis is the point farthest from the central body, where the spacecraft moves slowest. In a Hohmann transfer, the first burn occurs at periapsis (on the initial orbit) and the second at apoapsis (on the target orbit).
How much delta-v is needed for Earth to Mars Hohmann transfer?
A Hohmann transfer from Earth orbit to Mars orbit (around the Sun) requires approximately 2.9 km/s for the first burn at Earth's orbit and 2.6 km/s for the second burn at Mars's orbit, giving a total delta-v of about 5.5 km/s. The transfer takes approximately 8.5 months.
What is the ideal rocket equation for propellant mass?
The Tsiolkovsky rocket equation gives propellant mass as mₚ = m₀ × (1 - exp(-Δv / (Isp × g₀))), where m₀ is initial mass, Δv is the required velocity change, Isp is specific impulse, and g₀ = 9.80665 m/s² is standard gravity. This equation is used to calculate how much propellant is needed for the Hohmann transfer burns.
Can a Hohmann transfer be used to go from a higher to a lower orbit?
Yes, a Hohmann transfer works in both directions. When going from a higher to a lower orbit, the first burn is retrograde (slowing down) at apoapsis to lower the opposite side of the orbit, and the second burn is also retrograde at periapsis to circularize. The magnitude of delta-v required is the same as going from lower to higher orbit.