Formula & Calculator
Hohmann Transfer Total Delta-V
Sum of the two impulsive burns required to complete a Hohmann transfer between two circular orbits.
Interpretation
Hohmann transfer total Δv: Δv_total = Δv1 + Δv2, sum of the two impulsive burns. Example: Δv1=2.94 km/s, Δv2=1.91 km/s → total=4.85 km/s.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Δv_total | Total delta-v | m/s |
| Δv1 | First burn delta-v | m/s |
| Δv2 | Second burn delta-v | m/s |
What it means
The total Δv for a Hohmann transfer is the sum of the first burn (to enter the transfer ellipse) and the second burn (to circularise at the target orbit). This is the minimum Δv for a two‑impulse transfer between coplanar circular orbits. The total Δv is used to calculate the propellant required and to compare with other transfer options. Understanding this total is essential for mission planning and for spacecraft design.
Worked example
Hohmann Transfer Total Δv – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Δv₁ | 2430 |
| Δv₂ | 1470 |
| Parameter | Value |
|---|---|
| Δv₁ | 2400 |
| Δv₂ | 1500 |
Common mistakes
- Hohmann transfer total delta‑V: Δv_total = Δv₁ + Δv₂.
- Δv₁: First burn (from initial to transfer orbit).
- Δv₂: Second burn (from transfer to final orbit).
- Assumes coplanar, circular orbits.
- Minimum Δv for two‑impulse transfer between circular orbits.
Applications
Hohmann transfer total delta‑V, Δv_total = Δv₁ + Δv₂, is the sum of the two impulses required for the transfer. It determines the fuel requirement for moving between coplanar circular orbits. Engineers use this in mission planning to compute propellant mass and to design spacecraft propulsion systems. By optimising the total Δv (e.g., using bi‑elliptic transfer for large radius ratios), aerospace engineers can reduce fuel consumption and enable more ambitious missions.
- Orbital transfer optimisation for Earth‑to‑GEO or interplanetary
- Propellant mass budgeting and tank sizing
- Selection of launch windows and transfer durations
- Design of multi‑stage upper stages for deep space
- Mission feasibility and cost analysis
Frequently Asked Questions
It is the sum of the two impulsive burns required to complete a Hohmann transfer between two circular orbits.
Δv1 = first burn (perigee) to enter the transfer ellipse
Δv2 = second burn (apogee) to circularise into the target orbit
It determines the propellant required for the transfer. Minimising it is the goal of trajectory design.
- Only accounting for the first burn and forgetting the required circularisation burn at the destination orbit.
- Using the wrong sign for the burns (they are always positive).
- Assuming the burns are instantaneous (impulsive) when they may have finite duration.
From LEO (r1 = 6,678 km) to GEO (r2 = 42,164 km). Compute Δv1 ≈ 2425 m/s and Δv2 ≈ 1470 m/s (typical values). Total Δv = 2425+1470 = 3895 m/s.
It increases with the radius ratio, but the Hohmann transfer is optimal for circular orbits.
For very large radius ratios (r2/r1 > 11.94), a bi‑elliptic transfer can require less Δv than a Hohmann transfer.
Using the formulas: Δv1 = √(μ/r1)·(√(2r2/(r1+r2)) − 1) and Δv2 = √(μ/r2)·(1 − √(2r1/(r1+r2))).
For a Hohmann transfer to Mars (r1≈1 AU, r2≈1.52 AU), total Δv ≈ 3.6 km/s (approximate).
By using a planet’s gravity to change the spacecraft’s velocity without expending propellant, reducing the required Δv.