Hohmann Transfer Calculator for Dummies

Hohmann Transfer Equation:

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

Standard Gravitational Parameter (μ):

m³/s²

Initial Orbital Radius (r₁):

meters

Final Orbital Radius (r₂):

meters

Total Δv Required:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a Hohmann Transfer?

A Hohmann transfer is the most fuel-efficient method for transferring between two circular orbits in the same plane. It consists of two engine burns: one to leave the initial orbit, and another to enter the final orbit.

2. How Does the Calculator Work?

The calculator uses the Hohmann transfer equation:

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

Where:

\( \Delta v \) — Total velocity change required (m/s)
\( \mu \) — Standard gravitational parameter (G × M) of the central body (m³/s²)
\( r_1 \) — Initial orbital radius (m)
\( r_2 \) — Final orbital radius (m)

Explanation: The equation calculates the two velocity changes needed - one at periapsis to enter the transfer orbit, and one at apoapsis to circularize the final orbit.

3. Importance of Δv Calculation

Details: Accurate Δv calculation is crucial for mission planning, fuel requirements, and spacecraft design. It determines the feasibility of orbital maneuvers.

4. Using the Calculator

Tips: Enter μ (for Earth: 3.986×10¹⁴ m³/s²), initial and final orbital radii. All values must be positive and r₁ ≠ r₂.

5. Frequently Asked Questions (FAQ)

Q1: What's the most common use of Hohmann transfers?
A: Transferring spacecraft from low Earth orbit to geostationary orbit, or between planetary orbits.

Q2: Why is it called "Hohmann transfer"?
A: Named after German scientist Walter Hohmann who described it in his 1925 book "Die Erreichbarkeit der Himmelskörper".

Q3: What are the limitations of Hohmann transfers?
A: Only optimal for circular, coplanar orbits. For other cases, bi-elliptic transfers or other methods may be more efficient.

Q4: How does transfer time factor in?
A: Transfer time is half the period of the elliptical transfer orbit: \( t = \pi \sqrt{(r_1 + r_2)^3 / (8 \mu)} \).

Q5: Can this be used for interplanetary transfers?
A: Yes, but with the Sun as the central body (μ = 1.327×10²⁰ m³/s²) and planetary orbits as r₁ and r₂.