Hohmann Transfer Calculator Tool

Hohmann Transfer Equation:

\[ \Delta v_{total} = \Delta v_1 + \Delta v_2 \]

Total Δv:

Δv1 (First Burn):

Δv2 (Second Burn):

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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 is the most fuel-efficient method for such transfers.

2. How Does the Calculator Work?

The calculator uses the Hohmann transfer equations:

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

Where:

\( r_1 \) — Initial circular orbit radius (km)
\( r_2 \) — Final circular orbit radius (km)
\( \mu \) — Standard gravitational parameter (km³/s²)
\( \Delta v \) — Velocity change required (m/s)

Explanation: The first burn transfers the spacecraft to an elliptical transfer orbit, and the second burn circularizes the orbit at the new altitude.

3. Importance of Hohmann Transfers

Details: Hohmann transfers are fundamental to space mission planning, used for satellite deployments, interplanetary trajectories, and space station rendezvous.

4. Using the Calculator

Tips: Enter both orbit radii in kilometers. For Earth orbits, the default μ value of 398600 km³/s² is appropriate. For other bodies, use their specific μ values.

5. Frequently Asked Questions (FAQ)

Q1: When is a Hohmann transfer not optimal?
A: For very large orbit changes (radius ratio > 11.94), bi-elliptic transfers may be more efficient.

Q2: How does plane change affect Δv requirements?
A: This calculator assumes coplanar orbits. Plane changes require additional Δv not accounted for here.

Q3: What are typical Δv values for Earth orbits?
A: LEO to GEO transfer typically requires about 4 km/s total Δv.

Q4: How accurate is this calculator?
A: It provides theoretical minimum Δv. Real missions require additional margins for perturbations and control.

Q5: Can this be used for interplanetary transfers?
A: The basic principle applies, but interplanetary transfers typically use patched conic approximations.