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Constellations

The Constellation class provides factory methods for designing satellite constellations using several well-known algorithms.

Walker Delta

A Walker Delta constellation distributes satellites evenly across orbital planes with a RAAN spread of 360 degrees.

import lox_space as lox

epoch = lox.Time("2025-01-01T00:00:00.000 TAI")

constellation = lox.Constellation.walker_delta(
    "iridium",
    epoch,
    lox.Origin("Earth"),
    nsats=66,
    nplanes=6,
    semi_major_axis=7159 * lox.km,
    inclination=53 * lox.deg,
    phasing=1,
)

print(len(constellation))  # 66
print(constellation.name)  # "iridium"

Walker Star

Same as Walker Delta but with a RAAN spread of 180 degrees.

constellation = lox.Constellation.walker_star(
    "polar",
    epoch,
    lox.Origin("Earth"),
    nsats=8,
    nplanes=4,
    semi_major_axis=7000 * lox.km,
    inclination=90 * lox.deg,
)

Street-of-Coverage

Optimizes satellite placement for continuous coverage using the method of Huang, Colombo, and Bernelli-Zazzera (2021).

constellation = lox.Constellation.street_of_coverage(
    "coverage",
    epoch,
    lox.Origin("Earth"),
    nsats=24,
    nplanes=4,
    semi_major_axis=7159 * lox.km,
    inclination=53 * lox.deg,
    coverage_fold=1,
)

Flower

Flower constellations produce repeating ground tracks. The orbital shape can be computed from a perigee altitude (the mean radius, gravitational parameter, and rotation rate are derived from the origin automatically) or provided directly as semi-major axis and eccentricity.

constellation = lox.Constellation.flower(
    "flower14",
    epoch,
    lox.Origin("Earth"),
    n_petals=14,
    n_days=1,
    nsats=28,
    phasing_numerator=1,
    phasing_denominator=28,
    inclination=53 * lox.deg,
    perigee_altitude=780 * lox.km,
)

Using with Scenarios

Constellations can be added to a Scenario for visibility analysis:

scenario = lox.Scenario(t0, t1).with_constellation(constellation)

Each satellite is converted to a Spacecraft using the propagator specified at constellation creation time (default: "vallado", also available: "j2").

Constellation

A named collection of satellites produced by a constellation design algorithm.

Use the classmethods to create constellations of different types.

Methods:

  • flower –

    Create a Flower constellation (repeating ground tracks).

  • street_of_coverage –

    Create a Street-of-Coverage constellation.

  • walker_delta –

    Create a Walker Delta constellation (RAAN spread = 360 deg).

  • walker_star –

    Create a Walker Star constellation (RAAN spread = 180 deg).

Attributes:

name property 

name: str

Return the constellation name.

satellites property 

satellites: list[ConstellationSatellite]

Return the list of satellites.

flower classmethod 

flower(
    name: str,
    time: Time,
    origin: Origin,
    *,
    n_petals: int,
    n_days: int,
    nsats: int,
    phasing_numerator: int,
    phasing_denominator: int,
    inclination: Angle,
    perigee_altitude: Distance | None = None,
    semi_major_axis: Distance | None = None,
    eccentricity: float | None = None,
    argument_of_periapsis: Angle | None = None,
    propagator: str = "vallado"
) -> Constellation

Create a Flower constellation (repeating ground tracks).

street_of_coverage classmethod 

street_of_coverage(
    name: str,
    time: Time,
    origin: Origin,
    *,
    nsats: int,
    nplanes: int,
    semi_major_axis: Distance,
    inclination: Angle,
    eccentricity: float = 0.0,
    coverage_fold: int = 1,
    argument_of_periapsis: Angle | None = None,
    propagator: str = "vallado"
) -> Constellation

Create a Street-of-Coverage constellation.

walker_delta classmethod 

walker_delta(
    name: str,
    time: Time,
    origin: Origin,
    *,
    nsats: int,
    nplanes: int,
    semi_major_axis: Distance,
    inclination: Angle,
    eccentricity: float = 0.0,
    phasing: int = 0,
    argument_of_periapsis: Angle | None = None,
    propagator: str = "vallado"
) -> Constellation

Create a Walker Delta constellation (RAAN spread = 360 deg).

walker_star classmethod 

walker_star(
    name: str,
    time: Time,
    origin: Origin,
    *,
    nsats: int,
    nplanes: int,
    semi_major_axis: Distance,
    inclination: Angle,
    eccentricity: float = 0.0,
    phasing: int = 0,
    argument_of_periapsis: Angle | None = None,
    propagator: str = "vallado"
) -> Constellation

Create a Walker Star constellation (RAAN spread = 180 deg).

ConstellationSatellite

A single satellite in a constellation.

Attributes:

  • index_in_plane (int) –

    Return the index within the plane (0-based).

  • plane (int) –

    Return the orbital plane index (0-based).

index_in_plane property 

index_in_plane: int

Return the index within the plane (0-based).

plane property 

plane: int

Return the orbital plane index (0-based).