The mission closes. The thruster reaches 600 km in 7.1 days, the propellant covers the transfer, 5 years of operations and disposal with 2.14 kg to spare, and lowering to 509 km at the end of the mission meets the 5-year re-entry limit. GMAT re-flew 4 of 4 runs; every compared number agrees within tolerance or meets its requirement.
| Quantity | Value | How it was obtained |
|---|---|---|
| Insertion orbit | 510 km, 97.44° | Node at 10:30 local time on 15 Mar 2027 |
| Operational orbit | 600 km, 97.44° | Same plane as insertion |
| Delta-v | 49.3 m/s | orbit-averaged numerical integration |
| Time | 7.1 days | Thruster fires 64% of the time (sunlight only); drag at F10.7 = 127 |
| Propellant | 0.365 kg | 10.0 mN at 1100 s, 80.0 kg at insertion |
| Item | Propellant | Basis |
|---|---|---|
| Transfer | 0.365 kg | Spiral above |
| Drag make-up | 0.056 kg | 7.6 m/s over 5 years with a strong solar cycle (expected cycle: 4.3 m/s) |
| Disposal | 0.365 kg | Lowering to 509 km |
| Margin | 0.079 kg | 10% of the need |
| Needed | 0.865 kg | Loaded: 3.000 kg · 2.135 kg to spare |
Left at 600 km after 5 years of operations, the satellite would outlive the 5-year rule with a weak solar cycle. The plan lowers it to 509 km in 4.6 days (50 m/s, 0.36 kg), the highest orbit that still re-enters 4.5 years after the end of the mission with a weak cycle (0.5 years of margin on the limit).
| Solar activity | Left at 600 km | After lowering to 509 km |
|---|---|---|
| Expected solar cycle (f10.7 70-180) | 7.8 y | 2.3 y |
| Weak solar cycle (f10.7 65-120) | 28.1 y | 4.5 y |
| Strong solar cycle (f10.7 75-240) | 3.5 y | 1.5 y |
Years from the end of the mission to re-entry (150 km). The weak cycle is the design case for disposal; the strong cycle is the design case for drag make-up.
| Quantity | Fast model | GMAT | Diff. | Result |
|---|---|---|---|---|
| Transfer time Time to reach the operational mean altitude, thruster off in eclipse. |
7.13 days | 7.12 days | +0.2% tol. ±5% |
agrees |
| Transfer propellant Propellant used by the spiral. |
0.365 kg | 0.364 kg | +0.2% tol. ±5% |
agrees |
| Decay rate at the operational orbit Least-squares slope over 60 days, F10.7 = 126. Different atmosphere models (NRLMSISE-00 against MSISE-90). |
12.7 m/day | 10.6 m/day | +19.6% tol. ±30% |
agrees |
| Disposal descent propellant Lowering to 509 km. |
0.365 kg | 0.364 kg | +0.1% tol. ±5% |
agrees |
| Disposal descent time Drag helps the descent; solar inputs differ. |
4.55 days | 4.55 days | +0.1% tol. ±10% |
agrees |
| Re-entry after end of mission (Schatten nominal) Re-enters 2.61 years after the end of the mission (limit 5). The fast model's expected solar cycle is shown for reference; the solar inputs differ. |
2.29 years | 2.61 years | – | met |
| Re-entry after end of mission (Schatten −2σ) Re-enters 3.40 years after the end of the mission (limit 5). The fast model's weak solar cycle is shown for reference; the solar inputs differ. |
4.48 years | 3.40 years | – | met |
Re-fly the in-plane spiral from the insertion orbit to the operational altitude with a 4x4 gravity field, MSISE-90 drag and the Earth's shadow switching the thruster off. Script: transfer.script · GMAT run time 5 s.
Coast 60 days at the operational altitude with constant solar activity and compare the decay rate of the mean semi-major axis (least-squares fit) with the fast model's density table (NRLMSISE-00 against GMAT's MSISE-90). Script: drag.script · GMAT run time 5 s.
Starting at the end of the mission, lower the orbit to 509 km, then let drag bring the satellite down, with the Schatten nominal solar-cycle prediction. The run stops at 150 km or 8 years after the end of the mission. Script: disposal_nominal.script.
Starting at the end of the mission, lower the orbit to 509 km, then let drag bring the satellite down, with the Schatten −2σ (weak) solar-cycle prediction. The run stops at 150 km or 8 years after the end of the mission. Script: disposal_minus2sigma.script.
| Topic | Fast model | GMAT verification |
|---|---|---|
| Orbit | Near-circular, orbit-averaged; J2 nodal regression | Numerical integration (RK89), Brouwer-Lyddane mean elements |
| Gravity | Point mass + J2 | JGM-2 4×4 during burns, J2 during multi-year coasts |
| Thrust | Constant thrust and Isp, tangential, off in the cylindrical Earth shadow | ElectricThruster fed by a SolarPowerSystem with dual-cone shadow |
| Atmosphere | NRLMSISE-00 averaged along the orbit (inclination and local time) | MSISE-90 |
| Solar activity | expected solar cycle (F10.7 70-180): sinusoid with a 11-year period and its minimum in 2030; weak and strong bounds with the same timing | NASA Schatten predictions, nominal and −2σ (constant flux for the transfer and drag checks) |
| Plane changes | Edelbaum (analytic) | Not verified in this version |
| Not modelled | Solar radiation pressure, third bodies, attitude constraints on thrusting, thruster start-up transients, ground-station contacts, collision avoidance manoeuvres. | |
name: EO smallsat 80 kg, Hall thruster, 510 to 600 km insertion_epoch_utc: '2027-03-15T00:00:00' spacecraft: dry_mass_kg: 77.0 propellant_kg: 3.0 drag_area_m2: 0.8 drag_coefficient: 2.2 reflectivity_cr: 1.3 propulsion: kind: electric thrust_mN: 10.0 isp_s: 1100.0 input_power_W: 200.0 duty_cycle: 1.0 fires_in_eclipse: false power: available_for_propulsion_W: 250.0 insertion_orbit: altitude_km: 510.0 sun_synchronous: true ltan_hours: 10.5 operational_orbit: altitude_km: 600.0 sun_synchronous: false operations: duration_years: 5.0 maintain_altitude: true disposal: rule: fcc_5yr max_years_after_end_of_mission: 5.0 design_margin_years: 0.5 constraints: max_transfer_days: 30.0 propellant_margin_fraction: 0.1