Hohmann Transfer Calculator

Calculate fuel-efficient orbital transfer trajectories using Hohmann transfer orbit mechanics

Orbital Transfer Parameters

Primary Body Characteristics

km

Orbit Parameters

km

Altitude from surface of primary body

km

Altitude from surface of primary body

Rocket Engine Parameters (Optional)

s
kg

Hohmann Transfer Results

Transfer Orbit Properties

17,69,00,000 km
Semi-major Axis
0.1685
Eccentricity
4,77,67,54,392 km²/s
Specific Angular Momentum

Delta-V Requirements

2.432 km/s
Δv at Departure
2.233 km/s
Δv at Arrival
4.665 km/s
Total Δv

Transfer Time (Time of Flight)

7.7
Months
234.8
Days
5635.3
Hours
2,02,87,165
Seconds

Propellant Requirements

1,39,106.7 kg
Required Propellant Mass (69.6% of initial mass)

Calculation Method: Hohmann transfer orbit using two-body problem assumptions

Assumptions: Circular initial and final orbits, coplanar orbits, impulsive thrust

Orbital Velocities (km/s)

Initial Orbit: 30.041
Final Orbit: 25.343
Transfer at Perigee: 32.473
Transfer at Apogee: 23.110

Example: Earth to Mars Transfer

Mission Parameters

Primary Body: Sun (M = 1.989×10³⁰ kg, R = 696,340 km)

Earth Orbit: 146.4 million km altitude from Sun's surface

Mars Orbit: 206.0 million km altitude from Sun's surface

Spacecraft: 200,000 kg initial mass, Isp = 400s

Results

Total Δv Required: ~2.94 km/s

Transfer Time: ~8.6 months

Propellant Mass: ~139,105 kg (69.6% of initial mass)

Transfer Orbit: Elliptical with eccentricity ~0.205

Hohmann Transfer Steps

1

First Burn

Apply Δv₁ at initial orbit

Increases velocity to enter transfer ellipse

2

Coast Phase

Travel along transfer orbit

Half orbit duration (transfer time)

3

Second Burn

Apply Δv₂ at final orbit

Circularizes orbit at destination

Key Formulas

Transfer Orbit Semi-major Axis

a = (r₁ + r₂) / 2

Orbital Velocity

v = √(μ/r)

Transfer Time

t = π√(a³/μ)

Rocket Equation

mp = m₀(1 - e^(-Δv/Isp·g₀))

Transfer Tips

Hohmann transfer is most fuel-efficient for circular orbits

Requires precise timing for planetary transfers

Transfer time increases with orbital distance ratio

Only valid for coplanar circular orbits

Understanding Hohmann Transfer Orbits

What is a Hohmann Transfer?

A Hohmann transfer is an orbital maneuver that transfers a spacecraft between two circular orbits using the minimum possible delta-v (change in velocity). It consists of two engine burns and a coasting phase along an elliptical transfer orbit.

Why Use Hohmann Transfers?

  • Minimum fuel consumption for orbit changes
  • Well-understood and reliable maneuver
  • Foundation for interplanetary mission planning
  • Optimal for satellite orbit raising/lowering

Physics and Limitations

Assumptions

  • • Circular initial and final orbits
  • • Coplanar orbits (same orbital plane)
  • • Impulsive thrust (instantaneous burns)
  • • Two-body problem (no perturbations)

Real-World Considerations

  • • Planetary orbital eccentricity
  • • Gravitational perturbations
  • • Launch windows and timing
  • • Finite burn time effects

Note: Real missions often use modified Hohmann transfers or bi-elliptic transfers for better efficiency or mission constraints.