Hohmann Transfer Calculator Formula

Hohmann Transfer Equations:

\[ \Delta v = \sqrt{\frac{\mu}{r_1}} \left( \sqrt{\frac{2r_2}{r_1 + r_2}} - 1 \right) + \sqrt{\frac{\mu}{r_2}} \left( 1 - \sqrt{\frac{2r_1}{r_1 + r_2}} \right) \]

Initial Orbital Radius (r₁):

Target Orbital Radius (r₂):

Standard Gravitational Parameter (μ):

km³/s²

Or select a planet:

Total Δv Required:

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1. What is a Hohmann Transfer?

A Hohmann transfer is an orbital maneuver that moves a spacecraft between two circular orbits in the same plane using two engine impulses. It's the most fuel-efficient method for such transfers.

2. How Does the Calculator Work?

The calculator uses the Hohmann transfer equations:

\[ \Delta v_1 = \sqrt{\frac{\mu}{r_1}} \left( \sqrt{\frac{2r_2}{r_1 + r_2}} - 1 \right) \] \[ \Delta v_2 = \sqrt{\frac{\mu}{r_2}} \left( 1 - \sqrt{\frac{2r_1}{r_1 + r_2}} \right) \] \[ \Delta v_{total} = \Delta v_1 + \Delta v_2 \]

Where:

\( \Delta v \) — Velocity change required (km/s)
\( \mu \) — Standard gravitational parameter (km³/s²)
\( r_1 \) — Initial orbital radius (km)
\( r_2 \) — Target orbital radius (km)

Explanation: The first burn places the spacecraft into the transfer orbit, and the second burn circularizes the orbit at the new altitude.

3. Importance of Hohmann Transfers

Details: Hohmann transfers are fundamental to orbital mechanics and are used for satellite deployments, interplanetary missions, and space station rendezvous.

4. Using the Calculator

Tips: Enter orbital radii in kilometers. For Earth, μ = 398600 km³/s². Select a planet to automatically fill μ, or enter a custom value.

5. Frequently Asked Questions (FAQ)

Q1: Why is the Hohmann transfer most efficient?
A: It uses exactly two burns (minimum possible) and follows an elliptical orbit that's tangent to both circular orbits.

Q2: What are the limitations of Hohmann transfers?
A: They only work for coplanar circular orbits and require more time than higher-energy transfers.

Q3: How does transfer time vary with orbit size?
A: Transfer time is half the period of the elliptical transfer orbit: \( t = \pi \sqrt{\frac{(r_1 + r_2)^3}{8\mu}} \)

Q4: Can this be used for interplanetary transfers?
A: Yes, but with the Sun as the central body (μ = 1.327×10¹¹ km³/s²) and planetary orbits as r₁ and r₂.

Q5: How does altitude affect Δv requirements?
A: Higher orbits require less Δv to reach even higher orbits, but more Δv to return to lower orbits.