🚀 Hohmann Transfer Calculator
Calculate the most fuel-efficient transfer orbit between two circular orbits
Example: 6,871,000 m = 500 km altitude (LEO)
Example: 42,164,000 m = 35,786 km altitude (GEO)
How to Use This Calculator
Enter Initial Orbit Radius
Input the radius of your starting circular orbit (r₁) in meters. This is the distance from Earth's center to the spacecraft. For example, a 500 km altitude orbit has radius 6,871,000 m.
Enter Final Orbit Radius
Input the radius of your target circular orbit (r₂) in meters. This must be greater than the initial radius. For example, geostationary orbit has radius 42,164,000 m.
Calculate Transfer Parameters
Click "Calculate" to get the total delta-v required, the two burns needed, and the transfer time. The Hohmann transfer is the most fuel-efficient way to move between circular orbits.
Formula
Semi-Major Axis: a = (r₁ + r₂) / 2
First Burn: Δv₁ = √(GM/r₁) × (√(2r₂/(r₁+r₂)) - 1)
Second Burn: Δv₂ = √(GM/r₂) × (1 - √(2r₁/(r₁+r₂)))
Transfer Time: t = π√(a³/GM)
Where:
- r₁ = Initial orbit radius (m)
- r₂ = Final orbit radius (m)
- a = Semi-major axis of transfer ellipse (m)
- G = Gravitational constant = 6.67430 × 10⁻¹¹ m³kg⁻¹s⁻²
- M = Central body mass (kg)
- Δv₁, Δv₂ = Velocity changes at each burn (m/s)
Example: LEO to GEO Transfer
Transfer from 500 km altitude to geostationary orbit:
- r₁ = 6,871,000 m (500 km altitude)
- r₂ = 42,164,000 m (35,786 km altitude)
- a = (6,871,000 + 42,164,000) / 2 = 24,517,500 m
First burn: Δv₁ ≈ 2.5 km/s
Second burn: Δv₂ ≈ 1.5 km/s
Total: Δv ≈ 4.0 km/s
Transfer time: ~5.3 hours
About the Hohmann Transfer Calculator
The Hohmann Transfer Calculator determines the most fuel-efficient way to transfer between two circular orbits. Named after German engineer Walter Hohmann who published the concept in 1925, this transfer method uses an elliptical transfer orbit that is tangent to both the initial and final circular orbits. It's the standard method used for most orbital transfers in space missions.
When to Use This Calculator
- Satellite Deployment: Plan transfers from low Earth orbit to geostationary orbit
- Space Mission Planning: Calculate fuel requirements for orbital maneuvers
- Spacecraft Design: Determine propulsion system requirements
- Educational Purposes: Learn about orbital mechanics and transfer orbits
- Mission Analysis: Compare different transfer strategies
Why Use Our Calculator?
- ✅ Hohmann Transfer: Accurate implementation of the optimal transfer method
- ✅ Complete Parameters: Calculates both burns, total delta-v, and transfer time
- ✅ Educational Tool: Understand orbital transfer mechanics
- ✅ Mission Planning: Essential for space mission design
- ✅ Free to Use: No registration required
- ✅ Mobile Friendly: Works on all devices
Understanding Hohmann Transfers
A Hohmann transfer consists of two impulsive burns:
- First Burn: At the perigee (lowest point) of the transfer ellipse, accelerate to enter the transfer orbit
- Coast Phase: Travel along the elliptical transfer orbit for half an orbit (180°)
- Second Burn: At the apogee (highest point) of the transfer ellipse, accelerate again to circularize the final orbit
- Efficiency: This method minimizes total delta-v compared to other transfer strategies
Real-World Applications
- Geostationary Satellite Deployment: Most communications satellites use Hohmann transfers from LEO to GEO
- Lunar Missions: Apollo missions used Hohmann-like transfers to reach the Moon
- Mars Missions: Interplanetary transfers use similar principles
- Space Station Rendezvous: Spacecraft use Hohmann transfers to reach the ISS
- Satellite Constellation Deployment: Moving satellites to their operational orbits
Transfer Time
The transfer time is exactly half the period of the transfer ellipse:
- Formula: t = π√(a³/GM), where a is the semi-major axis
- LEO to GEO: Approximately 5.3 hours
- Longer Transfers: Larger altitude differences require longer transfer times
- Timing: The spacecraft must arrive at the target orbit at the right time
Tips for Using This Calculator
- Remember that r₁ must be less than r₂ for the standard Hohmann transfer
- The transfer time is half an orbital period, so plan accordingly
- Real missions may require additional delta-v for inclination changes or plane changes
- For very large altitude differences, bi-elliptic transfers may be more efficient
- Atmospheric drag in low orbits can affect the initial burn timing and efficiency
Frequently Asked Questions
What is a Hohmann transfer?
A Hohmann transfer is the most fuel-efficient method to move a spacecraft between two circular orbits. It uses an elliptical transfer orbit that is tangent to both the initial and final orbits, requiring two burns: one to enter the transfer orbit and one to circularize at the destination.
Why is the Hohmann transfer optimal?
The Hohmann transfer minimizes the total delta-v (change in velocity) required. It uses the minimum energy transfer orbit, which is an ellipse with the perigee at the lower orbit and apogee at the higher orbit. Any other transfer would require more fuel.
How long does a Hohmann transfer take?
The transfer time is exactly half the period of the transfer ellipse. For a transfer from low Earth orbit (500 km) to geostationary orbit (35,786 km), this takes approximately 5.3 hours. The time increases with larger altitude differences.
Can I use this for interplanetary transfers?
The Hohmann transfer concept applies to interplanetary travel, but the calculations are more complex because you're transferring between orbits around different bodies (e.g., Earth to Mars). The principle is the same: use the minimum energy transfer orbit.
What if I need to change orbital inclination?
Changing orbital inclination requires additional delta-v. You can either combine the plane change with one of the Hohmann transfer burns (more efficient) or do it as a separate maneuver. The calculator assumes coplanar orbits (same inclination).
Are there alternatives to Hohmann transfers?
Yes, for very large altitude differences (r₂/r₁ > 11.9), a bi-elliptic transfer can be more efficient. There are also fast transfers that use more fuel but take less time. However, for most practical applications, Hohmann transfers are optimal.