Orbital lifetime calculator
Decay of a circular orbit under atmospheric drag with the density model of the PocketQube review. Change the spacecraft, the altitude or the solar activity, or add a drag sail, and check the five- and 25-year limits.
- Low: 5.8 years
- Moderate: 20.4 months
- High: 9 months
Show the data as a table
| Time (years) | Low: 5.8 years | Moderate: 20.4 months | High: 9 months |
|---|---|---|---|
| 0 | 500 | 500 | 500 |
| 1 | 492 | 454 | — |
| 2 | 482 | — | — |
| 3 | 469 | — | — |
| 4 | 450 | — | — |
| 5 | 418 | — | — |
| 6 | — | — | — |
- Drag force at the start
- 0.136 µN
- Δv per year to hold altitude
- 17.2 m/s
- Initial decay rate
- 2.65 km/month
First-order model: constant solar activity, single scale height, no lift or attitude changes. Real decay follows the solar cycle, so quote lifetimes as ranges; compliance analyses need empirical models such as NRLMSISE-00 and solar-cycle forecasts.
DETERMINISTIC PHYSICS & DATA METHODOLOGY
How This Calculator Works
Source modules: lib/physics/decay.ts, lib/physics/atmosphere.ts
Integrates circular low-Earth-orbit semi-major axis decay under free-molecular aerodynamic drag using a second-order Runge–Kutta (midpoint) scheme coupled to the solar-flux-driven Kennewell (ASWS) single-scale-height thermosphere.
Governing Equations & Physical Model
da/dt = −√(μ·a) · ρ(h) · (C_D · A / m)Derived from specific orbital energy ε = −μ/(2a) and drag dissipation −a_D·v, integrated with step limits Δt ≤ 1 day and |Δh| ≤ 100 m down to 180 km.
ρ(h) = 6×10⁻¹⁰ · exp(−(h − 175) / H), H = T / (27 − 0.012·(h − 200))Exospheric temperature T = 900 + 2.5·(F10.7 − 70) + 1.5·Ap [K] couples 10.7 cm solar radio flux and planetary geomagnetic index Ap.
A_proj = A_tot / 4, B = C_D · (A_proj + A_sail / 2) / mRandomly tumbling convex body presents one quarter of its external area; a flat tumbling drag sail adds half of its one-sided area.
Inputs, Parameters & Units
| Parameter | Unit | Physical definition |
|---|---|---|
| m | kg | Spacecraft wet mass at deployment (0.25 kg nominal 1P limit; 2.0 kg CDS Rev. 14.1 1U limit). |
| A_proj, A_sail | cm², m² | Mean tumbling body cross-section (37.5 cm² for a 50 mm 1P cube) and optional drag-sail area. |
| C_D | — | Free-molecular drag coefficient (default 2.2). |
| h₀, F10.7, Ap | km, sfu, — | Initial circular altitude, 10.7 cm solar flux (70 low, 140 moderate, 210 high), and geomagnetic Ap index. |
Assumptions & Validity Limits
- The Kennewell (ASWS 1999) polynomial is calibrated over 180–500 km; runs initialized above 500 km are upward extrapolations and are explicitly flagged.
- Re-entry is declared at h = 180 km, below which remaining orbital life is a few days.
- Constant F10.7/Ap scenarios bound solar-cycle sensitivity; formal licensing debris filings require NRLMSISE-00 or JB2008 with time-varying solar forecasts.
Worked Default Reference Case
For A_proj = 37.5 cm² and C_D = 2.2, ballistic parameter B = 0.033 m²/kg yields 1.7 years under moderate solar activity, spanning 0.72 to 5.84 years across high and low solar flux.
- Ballistic parameter B
- 0.033 m²/kg
- Lifetime (moderate F10.7 = 140)
- 1.7 years
- Solar high / low range
- 0.72 – 5.84 years
- 5-year ceiling (moderate)
- 559 km