When a Longer Space Route Is Faster notebook

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When a Longer Space Route Is Faster

An explicit satellite chain shows when faster propagation compensates for the climb to orbit, with Earth-clearance checks for every space link.

Synthetic overhead-satellite chord-chain propagation arithmetic with Earth-clearance checks; no contemporary constellation model, moving-orbit routing graph, or network measurement.

The code uses Python 3 and the standard library. Saved output is from the checked CPU run.

import math

earth_km = 6371.0
light_km_s = 299792.458
fiber_index = 1.468

def compare(distance_km, altitude_km):
    radius = earth_km + altitude_km
    angle = distance_km / earth_km
    visibility_angle = 2.0 * math.acos(earth_km / radius)
    max_angle = min(math.radians(10.0), 0.99 * visibility_angle)
    hops = max(1, math.ceil(angle / max_angle))
    step = angle / hops
    clearance = radius * math.cos(step / 2.0) - earth_km
    assert clearance > 0.0
    orbital_distance = hops * 2.0 * radius * math.sin(step / 2.0)
    space_distance = 2.0 * altitude_km + orbital_distance
    space_ms = 1000.0 * space_distance / light_km_s
    fiber_ms = 1000.0 * distance_km * fiber_index / light_km_s
    assert orbital_distance <= radius * angle + 1e-9
    return hops, space_ms, fiber_ms

for altitude in [550.0, 1150.0]:
    denominator = fiber_index - (earth_km + altitude) / earth_km
    crossover = 2.0 * altitude / denominator
    print(f"altitude={altitude:.0f}km arc_crossover={crossover:.1f}km")
    for distance in [1000.0, 3000.0, 6000.0]:
        hops, space, fiber = compare(distance, altitude)
        print(f"  ground={distance:.0f}km hops={hops} "
              f"space={space:.3f}ms fiber={fiber:.3f}ms")
print("Earth-clearance and chord-length checks: passed")

altitude=550km arc_crossover=2882.1km
  ground=1000km hops=1 space=7.289ms fiber=4.897ms
  ground=3000km hops=3 space=14.529ms fiber=14.690ms
  ground=6000km hops=6 space=25.389ms fiber=29.380ms
altitude=1150km arc_crossover=8000.2km
  ground=1000km hops=1 space=11.606ms fiber=4.897ms
  ground=3000km hops=3 space=19.473ms fiber=14.690ms
  ground=6000km hops=6 space=31.274ms fiber=29.380ms
Earth-clearance and chord-length checks: passed

Sources

Delay is Not an Option — accepted primary manuscript: https://discovery.ucl.ac.uk/id/eprint/10062262/7/Handley_hotnets.pdf
Delay is Not an Option: Low Latency Routing in Space: https://discovery.ucl.ac.uk/id/eprint/10062262/

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