What Is the Hohmann Transfer Orbit Delta-V & Time of Flight Calculator?
A Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii around the same central body.
How Does the Hohmann Transfer Orbit Delta-V & Time of Flight Calculator Work?
Calculates required tangential velocity increments using the vis-viva equation at both orbital boundaries.
Hohmann Transfer Orbit Delta-V & Time of Flight Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
a_{ ext{tx}} = rac{r_1 + r_2}{2}, quad Delta v_1 = sqrt{ rac{mu}{r_1}}left(sqrt{ rac{2 r_2}{r_1 + r_2}} - 1
ight), quad ext{TOF} = pi sqrt{ rac{a_{ ext{tx}}^3}{mu}}
Vis-viva equation applied at transfer ellipse apsides and Keplerian orbital half-period.
How to Use the Hohmann Transfer Orbit Delta-V & Time of Flight Calculator
- Enter initial and target circular orbit radii from the center of the body, and the gravitational parameter mu.
Step-by-Step Example Calculation
LEO to Geostationary Orbit (GEO) Transfer
Input Values:
initialOrbitRadiusKm:6678
finalOrbitRadiusKm:42164
standardGravParamKm3S2:398600.44
Worked Steps: Requires departure burn Δv₁ = 2.425 km/s, arrival burn Δv₂ = 1.464 km/s, total Δv = 3.889 km/s, TOF = 5.28 hours.
Understanding Your Result
Gives departure burn Δv1, circularization burn Δv2, total mission velocity increment, and transfer duration.
Factors That Affect the Result
- Orbit plane inclination differences require combined plane-change burns which increase delta-v.
When Should You Use This Calculator?
- Mission design for satellite orbit raising, lunar translunar injection, and interplanetary trajectory planning.
Assumptions & Limitations
- Assumes instantaneous impulsive burns, coplanar circular orbits, and two-body Keplerian physics.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact Keplerian solution for two-body orbital mechanics.