Hohmann Transfer Calculator — Delta-v, Transfer Time & Propellant | Minimum-Energy Orbit Transfer

Hohmann transfer calculator

The Hohmann transfer calculator can help you find the transfer trajectory requiring the minimum amount of propellant (fuel and oxidizer) to go from one circular orbit to another. Our calculator can quickly find the characteristics of the Hohmann transfer, including delta-v. Do you have a rocket engine with you? Our calculator can also provide you with the required mass of propellant for a Hohmann transfer.

Are you hearing about Hohmann's transfer for the first time? Are the words “Hohmann transfer delta-v calculation” and “Hohmann transfer orbit” confusing, or are you curious and want to understand what all the fuss is about? If yes, the article below is a perfect place to understand all the concepts with Hohmann transfer examples. Please read on!

Before we start: a Hohmann transfer example

Before you start reading, we would like to give you a chance to ponder the Hohmann transfer and its application. Let us say you are the commander of a spaceship that needs to go from Earth to Mars. Your spacecraft uses chemical propulsion, and you want to know how much propellant (including both fuel and oxidizer) is needed for the travel.

What assumptions can you make about the nature of Earth's and Mars's orbits so that you can make use of the Hohmann transfer? Don't worry if you don't know the answer yet — you will know it by the end of the article (psst! the answer is given at the end).

How to use the Hohmann transfer calculator

To use our calculator, you need very few details:

• First, you should know your primary body characteristics: mass and radius. Use the unit switcher to change the mass unit to “Weights of Earth” if your primary body is Earth, or to “Weights of Sun” if it is the Sun (you then measure mass in multiples of Earth's or the Sun's mass).
• Next is your initial and final orbit's altitude measured from the surface of the primary body.

With these pieces of information, the Hohmann transfer calculator provides details about the transfer orbit (or transfer ellipse) properties and the delta-v (Δv). After the delta-v calculation, if you enter your rocket engine's specific impulse (I_sp) and initial mass, the calculator also applies the rocket equation to give you the amount of propellant needed for the transfer.

Both the American (imperial) and metric measurement systems are supported. If you add propellant cost, you can express the result not only in US dollars but in other world currencies, including the Russian ruble, euro, pound, yuan, yen, and rupee.

Preliminary definitions and concepts

Astrodynamics

Astrodynamics is the field of physics that deals with the motion of artificial objects under the influence of the gravitational field of one or more natural bodies. Astrodynamics is used in interplanetary trajectory design (e.g., Earth to Mars), constellation design of navigation, communication, and Earth-observation satellites, space tourism, and more.

Trajectory of an object

The path traversed by an object in space is called its trajectory. The motion of an object under the influence of a single primary body is called a two-body problem and is characterized by conic sections (Kepler orbits):

• Open trajectories — a hyperbola or a parabola.
• Closed trajectories — a circle or an ellipse. On a circle the velocity is always tangential; on an ellipse the velocity is tangential only at the perigee and apogee. These properties let the Hohmann transfer find the most fuel-efficient transfer.

Specific angular momentum

Specific angular momentum is the angular momentum divided by mass. Each orbit is characterized by a specific angular momentum that remains constant. For an elliptical orbit:

where μ = GM is the gravitational parameter (the product of the primary body's mass M and the gravitational constant G; for Earth μ ≈ 398,600 km³/s²), and r_a and r_p are the apogee and perigee radii of the ellipse. For a circular orbit r_a = r_p, so h = √(μr), and if the orbital velocity is known, h = r·v.

Orbit transfers

An orbit transfer changes a spacecraft from one orbit to another. The Hohmann transfer connects two circular orbits with a single transfer ellipse that is tangent to both. It requires exactly two engine burns — one to leave the initial orbit and enter the transfer ellipse, and one to circularize on the destination orbit — which makes it the most propellant-efficient two-impulse transfer between coplanar circular orbits.

Rocket equation and “delta-v”

Delta-v (Δv) is the measure of the “effort” needed to perform an orbital maneuver — the change in velocity the engine must provide. The Tsiolkovsky rocket equation relates delta-v to the propellant consumed:

where v_e is the exhaust velocity, I_sp is the specific impulse, g₀ = 9.80665 m/s², m₀ is the initial mass, and m_f is the final (dry) mass. The propellant mass is m_p = m₀(1 − e^−Δv/v_e).

Hohmann transfer & delta-v calculation

For two circular orbits of radii r₁ (initial) and r₂ (final) around a body with gravitational parameter μ, the transfer ellipse has a semi-major axis a = (r₁ + r₂)/2. Using the vis-viva equation, the two burns are:

The transfer time is half the orbital period of the transfer ellipse. Our calculator also reports the transfer orbit's eccentricity, periapsis, apoapsis, and specific angular momentum.

Traveling from Earth to Mars using the Hohmann transfer calculator

Going back to our opening example: to use a Hohmann transfer between Earth and Mars, we assume both planets travel on circular, coplanar orbits around the Sun. With the Sun as the primary body and the planets' orbital radii as the “orbits,” the calculator returns the delta-v needed to leave Earth's orbit, the delta-v to match Mars's orbit, the transfer time (about 8–9 months), and — with your engine's I_sp and spacecraft mass — the propellant required for the journey. That is the assumption the example asked you to find!