Hohmann Transfer Calculator
Precise Delta-V and Orbital Mechanics Calculation Tool
Select the planet or star being orbited.
Distance from the center of the central body (e.g., LEO ~6778 km).
Distance from the center for the final orbit (e.g., GEO ~42164 km).
Δv_total = |Δv₁| + |Δv₂|
0.000 km/s
0.000 km/s
0.00 hours
Orbital Transfer Visualization
Figure: Blue (Initial), Green (Target), Red (Hohmann Transfer Ellipse)
| Parameter | Value | Unit |
|---|
Understanding the Hohmann Transfer Calculator
The Hohmann transfer calculator is an essential tool for aerospace engineers, physics students, and space enthusiasts. It computes the most fuel-efficient way to move a spacecraft from one circular orbit to another in the same plane. This maneuver, named after Walter Hohmann, who published the concept in 1925, uses an elliptical transfer orbit that touches both the starting and ending circular orbits.
By using our Hohmann transfer calculator, you can instantly determine the impulse required (Delta-V) and the time it takes to travel between planets or satellites. Whether you are planning a mission from Low Earth Orbit (LEO) to Geostationary Orbit (GEO) or an interplanetary journey, understanding the orbital mechanics behind this calculation is crucial for mission success.
Hohmann Transfer Calculator Formula and Mathematical Explanation
The calculation of a Hohmann transfer involves several steps based on Kepler’s laws and Newton’s law of universal gravitation. The process requires two separate engine burns (impulsive maneuvers).
The Core Formulas
1. Semi-major axis of the transfer orbit (atrans):
atrans = (r₁ + r₂) / 2
2. Orbital Velocities (v):
Velocity in circular orbit: v = √(μ / r)
3. Delta-V for the first burn (Δv₁):
Δv₁ = √(μ / r₁) * (√(2r₂ / (r₁ + r₂)) - 1)
4. Delta-V for the second burn (Δv₂):
Δv₂ = √(μ / r₂) * (1 - √(2r₁ / (r₁ + r₂)))
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| r₁ | Initial Orbit Radius | km | 6,500 – 50,000 |
| r₂ | Target Orbit Radius | km | 6,500 – 400,000 |
| μ | Gravitational Parameter | m³/s² | Body Dependent |
| Δv | Change in Velocity | km/s | 0.5 – 15.0 |
Practical Examples (Real-World Use Cases)
Example 1: LEO to GEO
A satellite moves from a 300 km altitude circular orbit (r₁ ≈ 6,678 km) to a Geostationary orbit (r₂ ≈ 42,164 km). Inputting these values into the Hohmann transfer calculator shows that the first burn requires ~2.42 km/s and the second burn ~1.47 km/s, totaling a Delta-V of 3.89 km/s. The transfer time is approximately 5.27 hours.
Example 2: Earth to Mars (Sun-centric)
When traveling from Earth’s orbit (r₁ ≈ 1.496 × 10⁸ km) to Mars’ orbit (r₂ ≈ 2.279 × 10⁸ km) around the Sun, the Hohmann transfer calculator helps calculate the “Launch Window” Delta-V. The total transfer Δv is roughly 5.6 km/s relative to the Sun, with a travel time of about 259 days.
How to Use This Hohmann Transfer Calculator
- Select Central Body: Choose Earth, Mars, Sun, or enter a custom gravitational parameter (μ).
- Enter Initial Radius: Input the radius of your starting orbit in kilometers. Note: This is from the center of the body, not the surface altitude.
- Enter Target Radius: Input the radius of your final circular destination orbit.
- Review Results: The calculator updates in real-time to show the total Delta-V, individual burn requirements, and the time of flight.
- Analyze the Chart: Use the SVG visualization to see the scale of your transfer maneuver.
Key Factors That Affect Hohmann Transfer Calculator Results
- Central Body Mass: The larger the μ (mass), the higher the velocities and Delta-V requirements.
- Radius Ratio: The efficiency of a Hohmann transfer is highest when the ratio r₂/r₁ is less than ~11.9. For higher ratios, a bi-elliptic transfer might be more efficient.
- Orbital Inclination: This Hohmann transfer calculator assumes orbits are in the same plane. Plane changes significantly increase fuel costs.
- Atmospheric Drag: For very low orbits (under 200 km on Earth), drag can decay the orbit during the transfer.
- Specific Impulse (Isp): While the calculator provides Delta-V, the actual fuel mass depends on your engine’s efficiency.
- Time Constraints: Hohmann transfers are the most fuel-efficient but often the slowest. Missions requiring speed may use hyperbolic trajectories.
Related Tools and Internal Resources
- Orbital Mechanics Calculator – Deep dive into orbital periods and velocities.
- Delta-V Calculator – Calculate total rocket performance using the Tsiolkovsky equation.
- Kepler’s Third Law Calculator – Relationship between distance and orbital period.
- Space Travel Time Calculator – Estimate journey durations across the solar system.
- Specific Impulse Calculator – Efficiency of different rocket propellants.
- Thrust-to-Weight Ratio Calculator – Determine if your craft can lift off a planet’s surface.
Frequently Asked Questions (FAQ)