How to Calculate Satellite Collision Avoidance Delta-v
Constellations in low Earth orbit now execute thousands of conjunction avoidance manoeuvres each month. Flight dynamics teams need a quick, transparent way to translate predicted manoeuvre counts into delta-v and propellant demand so they can schedule replans, allocate ground contacts, and defend service life claims. This guide walks through the rocket equation with collision-avoidance inputs and shows how to present budgets that regulators and insurers understand.
The workflow complements mission assurance analyses such as ground-station contact probability and space tug delta-v budgeting, creating a coherent library for space traffic management.
Definition and boundaries
Collision-avoidance delta-v is the propulsion expenditure required to execute planned dodges in response to predicted conjunctions over a defined period, usually a month. It excludes routine station-keeping and orbit-raising unless those burns are piggybacked on avoidance events. The budget typically includes a contingency margin to cover late-breaking screenings or manoeuvre dispersions.
Define whether the period is calendar or orbital (e.g., 30 days vs. number of revolutions) and whether post-manoeuvre return-to-plane burns are included. Use observed execution history to calibrate margins so budgets remain credible to program management and insurers.
Variables and units
Capture propulsion and operations parameters explicitly:
- m0 – Spacecraft wet mass at period start (kg).
- Δvevent – Delta-v per avoidance manoeuvre (m/s).
- n – Number of avoidance manoeuvres in the period (count).
- Isp – Thruster specific impulse (s).
- p – Fractional margin (dimensionless) applied to total delta-v.
- Δvtot – Total period delta-v (m/s).
- f – Propellant mass fraction consumed (dimensionless).
- mprop – Propellant mass used (kg).
Use the propulsion configuration actually used for avoidance—cold gas, monopropellant, or electric—because Isp changes dramatically. If the spacecraft mass is changing rapidly due to other activities, pick the start-of-month mass but rerun the calculation mid-month to refresh propellant forecasts.
Formulas
Combine kinematic estimates with the rocket equation:
Δvtot = Δvevent × n × (1 + p)
Propellant fraction f = 1 − exp(−Δvtot ÷ (g0 × Isp))
Propellant mass mprop = m0 × f
g0 = 9.80665 m/s²
These relationships assume small burns where mass change during the period is minimal. For large constellations using electric propulsion, Δvevent may be expressed as equivalent chemical delta-v after thrust-arc simulation; just keep Isp consistent with that representation.
Step-by-step workflow
1. Derive per-event delta-v
Use screening outputs to set Δvevent based on historical miss distances and covariance. Include both in-plane and out-of-plane components. If you plan pairs of burns (dodge and re-phase), set Δvevent accordingly or split them into separate events.
2. Forecast manoeuvre counts
Extrapolate n from recent months, adjusting for solar cycle drag, debris breakups, or altitude changes. Coordination agreements with other operators can also reduce n—document any such assumptions for transparency.
3. Set propulsion parameters and margin
Choose Isp from hot-fire or on-orbit telemetry. Set margin p based on operational philosophy; 10–20% is common when screening uncertainty is high. Align with risk tolerances declared in insurance policies.
4. Calculate total delta-v and propellant
Multiply Δvevent by n and (1 + p) to obtain Δvtot. Apply the rocket equation to compute f and mprop. Translate propellant mass into percentage of onboard reserves to communicate remaining service life.
5. Communicate and monitor
Share Δvtot and mprop with flight controllers and insurers. During the month, update n and re-run the calculation as screenings change. Pair these updates with communication plans similar to the disciplined reporting described in the laser interlink availability guide.
Validation and assurance
Validate Δvevent against executed manoeuvres by comparing commanded versus achieved delta-v from telemetry. Reconcile propellant estimates with tank pressure or mass gauging. When large discrepancies occur, adjust Isp or thruster efficiency factors before reforecasting.
Consider Monte Carlo simulations of conjunction rates to place confidence intervals on n. Even with uncertainty, the deterministic calculation provides a clear central estimate for budgeting and regulatory reporting.
Limits and caveats
The approach does not model attitude control propellant or momentum management that may accompany avoidance burns. Similarly, low-thrust electric manoeuvres may operate in thrust-arc mode where instantaneous Δv is not well-defined; in those cases, ensure Δvevent reflects the integrated effect over the burn arc. Finally, budgets assume engines ignite reliably—allocating additional margin for misfires may be warranted for aging fleets.
Keep classification and export controls in mind when sharing manoeuvre data; this article assumes unclassified, commercially operated constellations. Government systems may require additional handling.
Embed: Satellite collision avoidance delta-v calculator
Enter spacecraft mass, per-event delta-v, monthly manoeuvre count, and propulsion parameters to obtain total delta-v and propellant draw with margin.