SSO Coverage by Latitude Band¶
Computes 30-day coverage statistics for a 550 km sun-synchronous orbit (LTAN 10:30, descending node) carrying a 10° half-angle nadir sensor.
Results are reported per 5° latitude band:
Number of sample points in the band
Cumulative coverage fraction (% of points seen ≥ once)
Mean revisit time (hours)
Maximum revisit time (hours)
Object API — uses Spacecraft.sunsync, Sensor, AoI.from_region, and Coverage.
[1]:
import time
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as mcolors
from missiontools import Spacecraft, Sensor, AoI, Coverage
1. Spacecraft and Sensor¶
A nadir-pointing 10° half-angle sensor is body-mounted along the spacecraft nadir axis (body-z = nadir, body-vector [0, 0, 1] in the sensor convention).
[2]:
EPOCH = np.datetime64('2025-01-01T00:00:00', 'us')
sc = Spacecraft.sunsync(
altitude_km = 550.0,
node_solar_time = '10:30',
node_type = 'descending',
epoch = EPOCH,
)
sensor = Sensor(half_angle_deg=10.0, body_vector=[0, 0, 1])
sc.add_sensor(sensor)
period_s = 2 * np.pi * np.sqrt(sc.a**3 / sc.central_body_mu)
swath_km = 2 * (sc.a - sc.central_body_radius) * np.tan(np.radians(10.0)) / 1e3
print(f"Semi-major axis : {sc.a / 1e3:.1f} km")
print(f"Inclination : {np.degrees(sc.i):.3f}°")
print(f"Orbital period : {period_s / 60:.1f} min")
print(f"Propagator : {sc.propagator_type}")
print(f"FOV half-angle : {np.degrees(sensor.half_angle_rad):.0f}°")
print(f"Ground swath : ~{swath_km:.0f} km")
Semi-major axis : 6928.1 km
Inclination : 97.593°
Orbital period : 95.6 min
Propagator : j2
FOV half-angle : 10°
Ground swath : ~194 km
2. Per-Band Coverage Analysis¶
For each 5° latitude band we create an AoI.from_region, attach a fresh Coverage object, and compute coverage fraction and revisit time.
Note — 36 bands × 30 days takes a few minutes.
[3]:
T_START = EPOCH
T_END = EPOCH + np.timedelta64(30 * 86_400, 's')
MAX_STEP = np.timedelta64(20, 's')
POINT_DENSITY = 200_000 # km²/point (~450 km resolution)
LAT_EDGES = np.arange(-90, 91, 5) # 37 edges → 36 bands
def band_label(lo_deg, hi_deg):
lo_s = f"{abs(lo_deg):.0f}°{'S' if lo_deg < 0 else 'N'}"
hi_s = f"{abs(hi_deg):.0f}°{'S' if hi_deg <= 0 else 'N'}"
return f"{lo_s} – {hi_s}"
rows = [] # (label, n_pts, cov_pct, mean_rev_h, max_rev_h)
t0 = time.perf_counter()
for lo_deg, hi_deg in zip(LAT_EDGES[:-1], LAT_EDGES[1:]):
aoi = AoI.from_region(
lat_min_deg = float(lo_deg),
lat_max_deg = float(hi_deg),
point_density = POINT_DENSITY,
)
n = len(aoi)
cov = Coverage(aoi, [sensor])
cf = cov.coverage_fraction(T_START, T_END, max_step=MAX_STEP)
rt = cov.revisit_time(T_START, T_END, max_step=MAX_STEP)
cov_pct = cf['final_cumulative'] * 100.0
mean_rev_h = rt['global_mean'] / 3600.0 if not np.isnan(rt['global_mean']) else float('nan')
max_rev_h = rt['global_max'] / 3600.0 if not np.isnan(rt['global_max']) else float('nan')
rows.append((band_label(lo_deg, hi_deg), n, cov_pct, mean_rev_h, max_rev_h))
elapsed = time.perf_counter() - t0
print(f"Done in {elapsed:.1f} s")
Done in 151.3 s
3. Coverage Table¶
[4]:
print(f" {'Band':>13} {'Pts':>5} {'Coverage':>10} {'Mean Rev':>10} {'Max Rev':>10}")
print(f" {'─'*13} {'─'*5} {'─'*10} {'─'*10} {'─'*10}")
for label, n, cov_pct, mean_rev_h, max_rev_h in rows:
mean_s = f"{mean_rev_h:8.2f} h" if not np.isnan(mean_rev_h) else " — "
max_s = f"{max_rev_h:8.2f} h" if not np.isnan(max_rev_h) else " — "
print(f" {label:>13} {n:>5} {cov_pct:>9.1f}% {mean_s} {max_s}")
Band Pts Coverage Mean Rev Max Rev
───────────── ───── ────────── ────────── ──────────
90°S – 85°S 9 0.0% — —
85°S – 80°S 28 75.0% 15.49 h 113.24 h
80°S – 75°S 48 100.0% 24.58 h 588.37 h
75°S – 70°S 65 100.0% 38.04 h 533.89 h
70°S – 65°S 84 100.0% 29.01 h 629.53 h
65°S – 60°S 100 100.0% 55.47 h 515.14 h
60°S – 55°S 118 100.0% 52.80 h 583.17 h
55°S – 50°S 132 98.5% 36.87 h 702.71 h
50°S – 45°S 148 95.9% 22.69 h 705.03 h
45°S – 40°S 160 100.0% 49.80 h 705.04 h
40°S – 35°S 173 100.0% 71.24 h 609.43 h
35°S – 30°S 184 100.0% 83.34 h 513.82 h
30°S – 25°S 194 100.0% 89.96 h 464.93 h
25°S – 20°S 201 100.0% 91.86 h 536.63 h
20°S – 15°S 208 100.0% 81.06 h 608.33 h
15°S – 10°S 213 100.0% 68.57 h 680.03 h
10°S – 5°S 216 98.6% 38.60 h 703.92 h
5°S – 0°S 218 90.8% 18.79 h 59.74 h
0°N – 5°N 218 90.8% 18.74 h 59.74 h
5°N – 10°N 216 97.7% 38.58 h 703.92 h
10°N – 15°N 213 100.0% 63.73 h 680.02 h
15°N – 20°N 208 100.0% 84.18 h 608.33 h
20°N – 25°N 201 100.0% 90.64 h 536.63 h
25°N – 30°N 194 100.0% 94.49 h 464.93 h
30°N – 35°N 184 100.0% 87.71 h 513.82 h
35°N – 40°N 173 100.0% 69.86 h 609.42 h
40°N – 45°N 160 100.0% 53.66 h 681.12 h
45°N – 50°N 148 95.3% 17.60 h 58.58 h
50°N – 55°N 132 97.7% 36.29 h 702.71 h
55°N – 60°N 118 100.0% 54.78 h 583.18 h
60°N – 65°N 100 100.0% 53.87 h 515.14 h
65°N – 70°N 84 100.0% 34.27 h 658.59 h
70°N – 75°N 65 100.0% 37.55 h 533.89 h
75°N – 80°N 48 100.0% 24.46 h 580.18 h
80°N – 85°N 28 75.0% 15.33 h 170.54 h
85°N – 90°N 9 0.0% — —
4. Visualisation¶
[5]:
labels = [r[0] for r in rows]
lat_mids = [(lo + hi) / 2 for lo, hi in zip(LAT_EDGES[:-1], LAT_EDGES[1:])]
cov_pcts = np.array([r[2] for r in rows])
mean_revs = np.array([r[3] for r in rows])
max_revs = np.array([r[4] for r in rows])
# Colour bars by coverage fraction
norm = mcolors.Normalize(vmin=0, vmax=100)
cmap = plt.cm.RdYlGn
colours = [cmap(norm(v)) for v in cov_pcts]
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 10), sharey=True)
# --- Coverage fraction ---
ax1.barh(lat_mids, cov_pcts, height=4.5, color=colours, edgecolor='white', linewidth=0.4)
ax1.axvline(100, color='tab:green', linestyle='--', linewidth=1.0, alpha=0.7, label='100% coverage')
ax1.set_xlabel('Cumulative coverage fraction (%)')
ax1.set_ylabel('Latitude (°)')
ax1.set_title('30-day coverage fraction')
ax1.set_xlim(0, 105)
ax1.set_yticks(lat_mids[::2])
ax1.set_yticklabels([f"{int(l):+d}°" for l in lat_mids[::2]])
ax1.grid(True, axis='x', alpha=0.3)
ax1.legend(fontsize=9)
# Add value labels
for lat, v in zip(lat_mids, cov_pcts):
if v > 0:
ax1.text(min(v + 1, 103), lat, f"{v:.0f}%", va='center', fontsize=7)
# --- Mean revisit time ---
valid = ~np.isnan(mean_revs)
ax2.barh(np.array(lat_mids)[valid], mean_revs[valid], height=4.5,
color='tab:blue', alpha=0.7, edgecolor='white', linewidth=0.4)
ax2.set_xlabel('Mean revisit time (hours)')
ax2.set_title('30-day mean revisit time')
ax2.grid(True, axis='x', alpha=0.3)
# Inclination limit annotation
ax2.axhline(np.degrees(sc.i) - 90, color='grey', linestyle=':', linewidth=1.0,
label=f'Inclination limit ({np.degrees(sc.i):.1f}°)')
ax2.axhline(-(np.degrees(sc.i) - 90), color='grey', linestyle=':', linewidth=1.0)
ax2.legend(fontsize=9)
fig.suptitle(
f'550 km SSO | LTAN 10:30 | 10° half-angle nadir sensor | 30-day window',
fontsize=11, y=1.01
)
plt.tight_layout()
plt.show()
