Ground Station Pass Planning

Ground Station Pass Planning (space-systems/mission-design/ground-station-pass-planning)

Use when you must build the daily ground station contact schedule of a low-Earth satellite from its orbit elements and the station masks. This leaf propagates the circular two-body sub-satellite point over the planning horizon, computes the elevation of the satellite above each ground station, detects the contiguous passes above the station elevation mask, aggregates the daily contact window schedule with its downlink gaps, and merges the contacts of several ground stations into one plan, in pure Python stdlib. It sits between the single-pass visibility geometry leaf (space-systems/orbit-mechanics/satellite- coverage), the frame-level data bookkeeping leaf (space-systems/subsystems/command-data-handling) and the RF link sizing leaf (space-systems/subsystems/communication-link-budget): this leaf owns the multi-pass contact schedule and the outage layer of a day, and it consumes the orbit state from the ground-track propagation leaves. Does NOT do: the single-pass visibility geometry and pass-duration estimates (satellite-coverage); downlink data budgeting and frame accounting (command-data-handling); RF link sizing (communication-link- budget); physical orbit state propagation under Earth oblateness and atmospheric braking effects (kepler-orbit-propagation and orbital- perturbations own the physical propagation; this leaf takes the orbit elements as inputs and uses a simple circular two-body ground track).

Domain quick reference

• Fixed-step planner defaults (module constants): spherical Earth radius RE_KM = 6371 km, gravitational parameter MU = 398600.4418 km^3/s^2, Earth rotation rate OMEGA_E = 7.2921159e-5 rad/s, planner step STEP_S = 30 s, downlink gap threshold GAP_THRESHOLD_S = 600 s.
• Orbital period of the circular orbit at altitude h: T = 2 pi sqrt(a^3 / mu) with a = RE_KM + h. At 550 km, T = 5730.13 s (95.5 min).
• Sub-satellite ground track: the circular-orbit inertial position at the argument of latitude u(t) = u0 + n t (n the mean motion) is rotated from the RAAN and inclination frame, then by the Earth rotation greenwich_0 + OMEGA_E t; longitude is wrapped to [-180, 180]. No oblateness terms: the track is the simple two-body footprint. Each orbit the Earth rotates under the track, so the footprint drifts west by about 23.9 deg per 95.5 min orbit at 550 km, which sets the pass cadence over a fixed station.
• Central angle lam between the station and the sub-satellite point: cos(lam) = sin(phi_s) sin(phi) + cos(phi_s) cos(phi) cos(delta_lon).
• Elevation of the satellite above the station: elevation = atan2(cos(lam) - RE_KM / r, sin(lam)) in degrees with r = RE_KM + altitude. The station zenith (lam = 0) reads 90 deg; the horizon is the central angle where cos(lam) = RE_KM / r, 22.9961 deg at 550 km. A 10 deg elevation mask maps to the 14.9676 deg central angle at 550 km, the satellite-coverage access convention used in the inverse identity checks.
• Pass detection: sample the elevation every 30 s over the horizon and accumulate contiguous samples at or above the mask into passes; pass duration = end_s - start_s + STEP_S for the inclusive sample run.
• Daily contact schedule: bundle the detected passes with the total contact seconds and list the inter-pass downlink gaps of at least GAP_THRESHOLD_S (600 s); a gap runs from the previous pass end plus one step to the next pass start.
• Maximum downlink gap: the longest interval with no contact, counting the horizon boundaries before the first pass and after the last pass (horizon minus last pass end minus one step); a satellite with no passes returns the whole horizon.
• Multi-station merge: run the pass detection for every station, sort all contacts by start, and merge any contact whose start is within STEP_S of the previous contact end; each merged contact keeps the station index of the station that opened it and the highest maximum elevation of the merged passes.

Workflow

1. Fix the orbit state and the planning horizon: the orbital altitude, inclination, RAAN, initial argument of latitude, Greenwich angle and horizon_h, with the module constants RE_KM, MU, OMEGA_E, STEP_S and GAP_THRESHOLD_S.
2. Ground-track propagation traverse: compute the orbital period with orbital_period_s, then step the sub-satellite point over the horizon with subsatellite_point (the circular two-body ground track rotated by the Earth rotation).
3. Elevation traverse: compute the elevation of the satellite above the station from the central angle with elevation_angle (90 deg at the zenith, 0 at the horizon central angle).
4. Pass-detection traverse: detect the contiguous passes above the station elevation mask with detect_passes over the 30 s planner step and read the per-pass start, end, duration and maximum elevation.
5. Downlink-gap-analysis traverse: aggregate the daily contact schedule with daily_contact_schedule (pass count, total contact seconds, gap list filtered by the gap threshold) and size the longest outage with max_downlink_gap, horizon boundaries included.
6. Multi-station-contact-plan traverse: merge the contacts of several ground stations into one plan with ground_station_contact_plan and read the merged contact list, the total contact seconds and the maximum downlink gap of the plan.
7. Guard traverse: confirm the deterministic checks, the coverage inverse identities and the ValueError rejections with the contract test scripts/test_ground_station_pass_planning.py.

Worked example

Circular LEO at 550 km, inclination 53 deg, RAAN 0, initial argument of latitude 0, Greenwich angle 0, 24 h horizon, 30 s step. Berlin station 52.52 N, 13.405 E with a 10 deg mask (module outputs):

• Orbital period: orbital_period_s(550.0) = 5730.13 s (95.5 min).
• Pass detection: detect_passes returns 5 passes above the mask, total contact 2280 s (38.0 min):
  • pass 1: start 6540 s, end 6900 s, duration 390 s, max elevation 23.350 deg;
  • pass 2: start 12450 s, end 12900 s, duration 480 s, max elevation 66.945 deg;
  • pass 3: start 18390 s, end 18870 s, duration 510 s, max elevation 82.905 deg;
  • pass 4: start 24360 s, end 24840 s, duration 510 s, max elevation 62.159 deg;
  • pass 5: start 30360 s, end 30720 s, duration 390 s, max elevation 20.611 deg.
• Daily contact schedule: daily_contact_schedule lists 4 inter-pass downlink gaps of 5520 s, 5460 s, 5460 s and 5490 s; max_downlink_gap = 55650 s (15.46 h), the trailing horizon interval after pass 5 ends at 30720 s.
• Multi-station plan: ground_station_contact_plan with Berlin and Madrid (40.42 N, 3.70 W), both masks 10 deg, returns 6 merged contacts, total 3540 s (59 min) and max gap 49680 s (13.8 h). The first merged contact starts 6270 s (opened by the Madrid station, index 1) and runs 660 s with max elevation 24.381 deg; Madrid's closing pass 36240 to 36690 s extends the day and shortens the trailing outage from 15.46 h to 13.8 h.

Verification

• Confirm orbital_period_s(550.0) = 5730.13 s within 0.1 s and equal to the closed form 2 pi sqrt(a^3 / mu).
• Confirm subsatellite_point at t = 0 with zero argument of latitude, RAAN and Greenwich angle sits at lat 0, lon 0, and that the zenith check elevation_angle(52.52, 13.405, 52.52, 13.405, 550) reads 89.99999 deg within 1e-3.
• Confirm the coverage inverse identity: a station at the 14.9676 deg central angle of the 10 deg mask observes elevation 10.000 deg within 1e-3, and the 22.9961 deg horizon central angle of the 550 km orbit observes elevation 0 deg within 1e-3.
• Confirm detect_passes on the worked example returns 5 passes with the listed starts and durations within 1 s and maximum elevations within 0.01 deg, and that every duration equals end minus start plus the 30 s step.
• Confirm daily_contact_schedule totals 2280.0 s within 1 s with the 4 listed gap durations within 1 s, and that the total equals the sum of the pass durations.
• Confirm max_downlink_gap = 55650.0 s within 1 s and that an empty pass list returns 86400.0 s (the whole 24 h horizon).
• Confirm ground_station_contact_plan (Berlin and Madrid) returns 6 contacts, 3540.0 s within 1 s and max gap 49680.0 s within 1 s, with the merged total never below either single-station total and never above the sum of the station totals.
• Confirm ValueError rejection of negative altitudes, inclinations outside [0, 180] deg, negative propagation times, negative elevation masks and non-positive horizons.
• Confirm determinism: identical inputs return identical schedules, the fixed-step propagation loop uses no RNG.
• Run the contract test offline: python3 scripts/test_ground_station_pass_planning.py (35 tests, deterministic).

Related leaves

• space-systems/orbit-mechanics/satellite-coverage: the single-pass visibility circle and pass-duration estimates that this leaf's elevation mask convention inverts; coverage geometry, not the daily schedule.
• space-systems/subsystems/command-data-handling: the downlink data budgeting and frame accounting that consumes the contact totals this leaf produces.
• space-systems/subsystems/communication-link-budget: the RF link sizing for the station antennas once the contact windows are fixed.
• space-systems/orbit-mechanics/ground-track-repeat: the repeat cycle that sets how the daily contact pattern of this leaf repeats.
• space-systems/orbit-mechanics/kepler-orbit-propagation: the physical state propagation whose elements this leaf takes as inputs for the simple circular two-body ground track.

Pitfalls

• Reading the maximum downlink gap from the gap list only: the maximum includes the horizon boundaries, so the Berlin day shows 55650 s, the trailing interval after the last pass, not the largest 5520 s inter-pass gap.
• Holding the Greenwich angle fixed over the horizon: the Earth rotates under the inertial track by about 23.9 deg per 95.5 min orbit at 550 km, and the west drift sets the pass cadence over a fixed station.
• Forgetting the inclusive sample run: a pass sampled at its start and end spans end - start + 30 s, so a 6540 to 6900 s pass lasts 390 s, not 360 s.
• Setting the mask at the horizon: a 0 deg mask reaches the 22.9961 deg horizon central angle while a 10 deg mask shrinks the day to the 14.9676 deg cone; masks above the highest pass of the day (about 82.9 deg for the worked example) return no passes.
• Treating the merged plan as a sum: overlapping station contacts merge into one, so the multi-station total never exceeds the sum of the station totals and can equal the better single station when one station dominates every window.
• Routing frame-level downlink data budgeting here: command-data- handling owns how many bits fit in the contact; this leaf owns when the contact happens and how long the outages last.
• Routing physical orbit propagation here: this leaf's ground track is the simple circular two-body footprint; oblateness and atmospheric effects on the orbit state belong to the propagation leaves.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_ground_station_pass_planning.py

The 35 tests cover the worked example anchors (period 5730.13 s within 0.1, 5 Berlin passes with starts, durations and maximum elevations within the spec bounds, daily total 2280 s, gaps 5520/5460/5460/5490 s, maximum downlink gap 55650 s, empty-horizon 86400 s, merged Berlin and Madrid plan with 6 contacts, 3540 s and 49680 s), the sub-satellite point epoch and drift checks, the zenith 90 deg identity, the coverage inverse identities at the 14.9676 deg and 22.9961 deg central angles, the duration identity, the merged-total bounds identity, run determinism, and ValueError rejection of negative altitudes, out-of- range inclinations, negative times, negative elevation masks and non-positive horizons.

Compliance

• Standards referenced, not reproduced: ECSS space mission design standards (ecss.nl) frame the ground station contact scheduling context; the pass geometry, two-body ground track and elevation relations above are common astrodynamics, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.