Orbital Decay

Orbital Decay and Deorbit Lifetime (space-systems/orbit-mechanics/orbital-decay)

Use when the task is the drag decay of a circular low Earth orbit spacecraft: the ballistic coefficient, the altitude decay rate and the decay per orbit and per day, the deorbit lifetime, and the 25-year disposal compliance of the mission.

Domain quick reference

• Atmospheric drag is the dominant non-conservative perturbation below roughly 600 km: it removes orbital energy and the orbit shrinks continuously until reentry. The decay is fastest at low altitude because density rises exponentially as the orbit descends.
• Ballistic coefficient B = m / (Cd * A) in kg/m^2, with m the mass, A the projected drag area, and Cd the drag coefficient (typically 2.0 to 2.5 for satellites in the free-molecule to continuum transition regime). High B decays slowly, low B decays fast.
• Single-layer exponential atmosphere model: rho(h) = rho_ref * exp(-(h - h_ref) / H), with default rho_ref = 2.789e-10 kg/m^3 at h_ref = 200 km and scale height H = 60 km. These are representative thermospheric values for first-order sizing; the logic accepts refined densities (MSIS or standard atmosphere tables) as parameters. Real density varies by an order of magnitude over the solar cycle, so treat any single-point answer as a snapshot.
• Decay rate from orbital energy balance, dE/dt = -F_drag * v: dh/dt = -rho * Cd * A / m * sqrt(mu * a), negative (altitude decreases). Per orbit: dh/dt * T; per day: dh/dt * 86400.
• Deorbit lifetime, closed form of the exponential-atmosphere decay equation with sqrt(mu * a) held constant: t = (H / |dh/dt_0|) * (1 - exp(-(h0 - hf) / H)). As the target altitude hf approaches 0, the factor approaches 1 and the lifetime approaches H / |dh/dt_0|, the classic scale-height estimate.
• Worked anchor: a 300 kg satellite with 1.5 m^2 drag area and Cd 2.2 at 500 km circular has B = 90.91 kg/m^2, decays at 1.0818e-3 m/s (93.47 m per day, 6.13 m per orbit), and deorbits to 200 km in about 1.746 years. The same bus at 400 km decays at 5.6858e-3 m/s (491.25 m per day) because density is 5.3 times higher there, and deorbits in about 0.32 years.
• Disposal rule: post-mission disposal guidance for LEO commonly requires a deorbit lifetime of 25 years or less from end of mission. If the computed lifetime exceeds the limit, drag augmentation (a deployed drag sail or a higher-drag attitude) lowers the ballistic coefficient and shortens the lifetime; the lifetime scales linearly with B, so doubling the drag area halves the lifetime.

Workflow

1. Collect the bus inputs: mass (kg), projected drag area (m^2), drag coefficient (2.0 to 2.5), the initial circular altitude (km), and the target altitude (km, commonly 0 or the reentry interface).
2. Compute the ballistic coefficient with ballistic_coefficient(mass, area, cd) and the density at altitude with atmospheric_density.
3. Compute the instantaneous decay with decay_rate, then convert to the mission-facing numbers with decay_per_orbit and decay_per_day.
4. Compute the deorbit lifetime with lifetime_seconds or lifetime_years down to the target altitude.
5. Run the disposal check with disposal_compliant(lifetime_years) against the 25-year limit; if not compliant, raise the drag area (drag augmentation) and re-run until the lifetime meets the limit.
6. Sanity-check the model regime: below 600 km the exponential model is a sizing tool, not a precise ephemeris; for a committed deorbit plan, redo the estimate with a higher-fidelity atmosphere and solar activity model.

Pitfalls

• Routing J2 questions here: secular J2 effects (RAAN drift, argument of perigee drift, nodal period change) belong to the orbital-perturbations leaf; drag is dissipative and shrinks the orbit, J2 is conservative and rotates it.
• Routing maneuver questions here: propulsive delta-v budgets, the rocket equation, and transfer burns belong to hohmann-transfer, lambert-transfer, or the propulsion domain pack; this leaf sizes passive decay, not engine burns.
• Routing airfoil aerodynamics here: wing drag polars, cd0, and induced drag belong to the aerodynamics domain; the drag coefficient here multiplies a spacecraft reference area against the tenuous upper atmosphere, a different regime entirely.
• Routing standard atmosphere questions here: temperature, pressure, and density profiles for aircraft belong to the cross-cutting isa-atmosphere leaf; the exponential model here is a thermospheric density approximation for drag decay, not an ISA profile.
• Treating the decay rate as constant: density rises as the orbit drops, so the decay accelerates; the closed-form lifetime accounts for this with the (1 - exp(...)) factor, do not multiply the initial rate by time directly.
• Ignoring the drag area: the decay scales linearly with Cd * A / m, so a deployed drag sail changes the lifetime by an order of magnitude; always state the area assumption.
• Using the wrong density parameters: rho_ref and H must match the altitude band of the orbit; the 60 km single scale height is a sizing assumption and differs from the scale height of a precise standard atmosphere at any one altitude.
• Sign errors: decay_rate, decay_per_orbit, and decay_per_day are negative (altitude decreases); the lifetime uses the magnitude of the initial rate.
• Forgetting the target altitude: lifetime to the reentry interface is shorter than lifetime to a higher parking altitude; quote the target with the answer.
• Trusting a single snapshot: solar activity moves density by roughly an order of magnitude over the 11-year cycle; give a range or state the activity assumption.

Behavior contract (gate 3)

The ballistic coefficient, exponential atmosphere density, decay rate, decay per orbit and per day, deorbit lifetime, and 25-year disposal logic are exercised by the gate 3 contract test: scripts/test_orbital_decay.py against scripts/orbital_decay_logic.py (stdlib unittest, offline). Run: python3 scripts/test_orbital_decay.py

Compliance

• Standards referenced, not reproduced: the ECSS space engineering series (systems engineering ECSS-E-ST-10C, space environment ECSS-E-ST-10-04C) frames space environment and disposal engineering for European projects; the exponential-atmosphere decay model and the 25-year disposal guideline are common astrodynamics practice, summary-only per standards-map.yaml (ecss is a free ESA download).
• compliance: STANDARDS-REF, gated: false.