Walker Constellations¶

Generator for Walker constellation patterns (Delta and Star) using T:P:F notation.

For understanding Walker constellation geometry and usage examples, see Walker Constellations.

Walker Pattern¶

WalkerPattern ¶

WalkerPattern()

Walker constellation pattern type.

Defines whether the constellation uses a Delta (360°) or Star (180°) RAAN spread.

Attributes:

Name	Type	Description
`DELTA`	`Any`	Walker Delta pattern with 360° RAAN spread (global coverage). Used by GPS, Galileo, and similar navigation constellations.
`STAR`	`Any`	Walker Star pattern with 180° RAAN spread (polar coverage). Used by Iridium and similar communications constellations.

Example

import brahe as bh

delta = bh.WalkerPattern.DELTA  # 360° RAAN spread
star = bh.WalkerPattern.STAR    # 180° RAAN spread

Initialize instance.

DELTA `class-attribute` ¶

DELTA: Any = WalkerPattern.DELTA

Walker constellation pattern type.

Defines whether the constellation uses a Delta (360°) or Star (180°) RAAN spread.

Attributes:

Name	Type	Description
`DELTA`		Walker Delta pattern with 360° RAAN spread (global coverage). Used by GPS, Galileo, and similar navigation constellations.
`STAR`		Walker Star pattern with 180° RAAN spread (polar coverage). Used by Iridium and similar communications constellations.

Example

import brahe as bh

delta = bh.WalkerPattern.DELTA  # 360° RAAN spread
star = bh.WalkerPattern.STAR    # 180° RAAN spread

STAR `class-attribute` ¶

STAR: Any = WalkerPattern.STAR

Walker constellation pattern type.

Defines whether the constellation uses a Delta (360°) or Star (180°) RAAN spread.

Attributes:

Name	Type	Description
`DELTA`		Walker Delta pattern with 360° RAAN spread (global coverage). Used by GPS, Galileo, and similar navigation constellations.
`STAR`		Walker Star pattern with 180° RAAN spread (polar coverage). Used by Iridium and similar communications constellations.

Example

import brahe as bh

delta = bh.WalkerPattern.DELTA  # 360° RAAN spread
star = bh.WalkerPattern.STAR    # 180° RAAN spread

Walker Constellation Generator¶

WalkerConstellationGenerator ¶

WalkerConstellationGenerator(t: int, p: int, f: int, semi_major_axis: float, eccentricity: float, inclination: float, argument_of_perigee: float, reference_raan: float, reference_mean_anomaly: float, epoch: Epoch, angle_format: AngleFormat, pattern: WalkerPattern)

Generator for Walker constellation patterns using T:P:F notation.

Walker constellations place satellites in circular or near-circular orbits with: - T total satellites distributed across P planes - Each plane inclined at the same angle - Planes evenly spaced in RAAN (spread depends on pattern type) - Satellites within each plane evenly spaced in mean anomaly - Phase offset F controls inter-plane phasing

Two pattern types are supported via pattern: - WalkerPattern.DELTA: 360° RAAN spread (global coverage, e.g., GPS, Galileo) - WalkerPattern.STAR: 180° RAAN spread (polar coverage, e.g., Iridium)

All satellites in the constellation share the same semi-major axis, eccentricity, inclination, and argument of perigee. They differ only in RAAN and mean anomaly.

Parameters:

Name	Type	Description	Default
`t`	`int`	Total number of satellites (must be divisible by p)	required
`p`	`int`	Number of orbital planes	required
`f`	`int`	Phasing factor (0 to p-1)	required
`semi_major_axis`	`float`	Semi-major axis in meters	required
`eccentricity`	`float`	Eccentricity (dimensionless)	required
`inclination`	`float`	Inclination in degrees or radians (based on angle_format)	required
`argument_of_perigee`	`float`	Argument of perigee	required
`reference_raan`	`float`	RAAN for plane 0	required
`reference_mean_anomaly`	`float`	Mean anomaly for first satellite	required
`epoch`	`Epoch`	Reference epoch for ephemeris generation	required
`angle_format`	`AngleFormat`	Format for angular inputs	required
`pattern`	`WalkerPattern`	Pattern type (DELTA for 360° RAAN, STAR for 180° RAAN)	required

Raises:

Type	Description
`ValueError`	If p is zero, t is not divisible by p, or f >= p.

Example

import brahe as bh

epoch = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)
# Walker Delta constellation (GPS-like)
gen = bh.WalkerConstellationGenerator(
    t=24,                       # 24 total satellites
    p=3,                        # 3 orbital planes
    f=1,                        # phasing factor 1
    semi_major_axis=bh.R_EARTH + 20200e3,  # GPS altitude
    eccentricity=0.0,
    inclination=55.0,
    argument_of_perigee=0.0,
    reference_raan=0.0,
    reference_mean_anomaly=0.0,
    epoch=epoch,
    angle_format=bh.AngleFormat.DEGREES,
    pattern=bh.WalkerPattern.DELTA,  # 360° RAAN spread
)

# Generate Keplerian propagators
propagators = gen.as_keplerian_propagators(60.0)

Initialize instance.

eccentricity `property` ¶

eccentricity: Any

Eccentricity.

epoch `property` ¶

epoch: Any

Reference epoch.

num_planes `property` ¶

num_planes: Any

Number of orbital planes.

pattern `property` ¶

pattern: Any

Walker pattern (Delta or Star).

phasing `property` ¶

phasing: Any

Phasing factor.

satellites_per_plane `property` ¶

satellites_per_plane: Any

Number of satellites per plane (T/P).

semi_major_axis `property` ¶

semi_major_axis: ndarray

Semi-major axis in meters.

total_satellites `property` ¶

total_satellites: Any

Total number of satellites in the constellation.

as_keplerian_propagators `method descriptor` ¶

as_keplerian_propagators(step_size: float) -> list[KeplerianPropagator]

Generate Keplerian propagators for all satellites in the constellation.

Parameters:

Name	Type	Description	Default
`step_size`	`float`	Step size in seconds for propagation	required

Returns:

Type	Description
`list[KeplerianPropagator]`	list[KeplerianPropagator]: List of propagators, one per satellite

as_numerical_propagators `method descriptor` ¶

as_numerical_propagators(propagation_config: NumericalPropagationConfig, force_config: ForceModelConfig, params: ndarray = None) -> list[DNumericalOrbitPropagator]

Generate numerical orbit propagators for all satellites in the constellation.

Parameters:

Name	Type	Description	Default
`propagation_config`	`NumericalPropagationConfig`	Propagation configuration	required
`force_config`	`ForceModelConfig`	Force model configuration	required
`params`	`ndarray`	Parameter vector [mass, drag_area, Cd, srp_area, Cr]	`None`

Returns:

Type	Description
`list[DNumericalOrbitPropagator]`	list[DNumericalOrbitPropagator]: List of propagators, one per satellite

as_sgp_propagators `method descriptor` ¶

as_sgp_propagators(step_size: float, bstar: float, ndt2: float, nddt6: float) -> list[SGPPropagator]

Generate SGP propagators for all satellites in the constellation.

This method creates TLE data for each satellite using the provided drag and mean motion derivative parameters.

Parameters:

Name	Type	Description	Default
`step_size`	`float`	Step size in seconds for propagation	required
`bstar`	`float`	B* drag term (Earth radii^-1)	required
`ndt2`	`float`	First derivative of mean motion divided by 2 (rev/day²)	required
`nddt6`	`float`	Second derivative of mean motion divided by 6 (rev/day³)	required

Returns:

Type	Description
`list[SGPPropagator]`	list[SGPPropagator]: List of propagators, one per satellite

builder `staticmethod` ¶

builder(t: int, p: int, f: int, semi_major_axis: float, inclination: float, epoch: Epoch) -> WalkerConstellationGeneratorBuilder

Create a builder for constructing a Walker constellation generator.

The builder takes the six required inputs directly; optional inputs are provided through chained setter calls before calling build().

Parameters:

Name	Type	Description	Default
`t`	`int`	Total number of satellites (must be divisible by p)	required
`p`	`int`	Number of orbital planes	required
`f`	`int`	Phasing factor (0 to p-1)	required
`semi_major_axis`	`float`	Semi-major axis in meters	required
`inclination`	`float`	Inclination in degrees by default, or radians if `angle_format()` is set to `AngleFormat.RADIANS`	required
`epoch`	`Epoch`	Reference epoch for ephemeris generation	required

Returns:

Name	Type	Description
`WalkerConstellationGeneratorBuilder`	`WalkerConstellationGeneratorBuilder`	New builder instance, with
	`WalkerConstellationGeneratorBuilder`	`eccentricity`, `argument_of_perigee`, `reference_raan`, and
	`WalkerConstellationGeneratorBuilder`	`reference_mean_anomaly` defaulted to `0.0`, `angle_format` defaulted
	`WalkerConstellationGeneratorBuilder`	to `AngleFormat.DEGREES`, and `pattern` defaulted to `WalkerPattern.DELTA`.

Example

import brahe as bh

epoch = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)
gen = (
    bh.WalkerConstellationGenerator.builder(
        12, 3, 1, bh.R_EARTH + 780e3, 98.0, epoch
    )
    .eccentricity(0.001)
    .base_name("Constellation")
    .build()
)

satellite_elements `method descriptor` ¶

satellite_elements(plane_index: int, sat_index: int, angle_format: AngleFormat) -> ndarray

Get Keplerian elements for a specific satellite.

Parameters:

Name	Type	Description	Default
`plane_index`	`int`	Plane index (0 to P-1)	required
`sat_index`	`int`	Satellite index within plane (0 to T/P - 1)	required
`angle_format`	`AngleFormat`	Output angle format	required

Returns:

Type	Description
`ndarray`	np.ndarray: Keplerian elements [a, e, i, raan, argp, M]

with_base_name `method descriptor` ¶

with_base_name(name: str) -> WalkerConstellationGenerator

Set a base name for satellite naming.

When set, satellites will be named as "{base_name}-P{plane}-S{sat}" (e.g., "GPS-P0-S0", "GPS-P0-S1", "GPS-P1-S0", etc.)

Parameters:

Name	Type	Description	Default
`name`	`str`	Base name for the constellation satellites	required

Returns:

Name	Type	Description
`WalkerConstellationGenerator`	`WalkerConstellationGenerator`	Self with the base name set

Walker Constellation Generator Builder¶

WalkerConstellationGeneratorBuilder ¶

WalkerConstellationGeneratorBuilder()

Builder for WalkerConstellationGenerator.

Created by WalkerConstellationGenerator.builder(), which takes the six required inputs (t, p, f, semi_major_axis, inclination, epoch). Optional inputs are provided through chained setters and default to the same values as the flat constructor's optional parameters. build() validates the t/p/f invariants and constructs the generator, raising RuntimeError instead of panicking if they are violated.

Example

import brahe as bh

epoch = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)
gen = (
    bh.WalkerConstellationGenerator.builder(12, 3, 1, bh.R_EARTH + 780e3, 98.0, epoch)
    .eccentricity(0.001)
    .base_name("Constellation")
    .build()
)

Initialize instance.

angle_format `method descriptor` ¶

angle_format(angle_format: AngleFormat) -> WalkerConstellationGeneratorBuilder

Set the angle format for inclination, argument_of_perigee, reference_raan, and reference_mean_anomaly.

Defaults to AngleFormat.DEGREES if not called.

Parameters:

Name	Type	Description	Default
`angle_format`	`AngleFormat`	Format for angular inputs	required

Returns:

Name	Type	Description
`WalkerConstellationGeneratorBuilder`	`WalkerConstellationGeneratorBuilder`	The builder, for method chaining.

argument_of_perigee `method descriptor` ¶

argument_of_perigee(argument_of_perigee: float) -> WalkerConstellationGeneratorBuilder

Set the argument of perigee.

Defaults to 0.0 if not called.

Parameters:

Name	Type	Description	Default
`argument_of_perigee`	`float`	Argument of perigee. Units: (deg) by default, or (rad) based on `angle_format`	required

Returns:

Name	Type	Description
`WalkerConstellationGeneratorBuilder`	`WalkerConstellationGeneratorBuilder`	The builder, for method chaining.

base_name `method descriptor` ¶

base_name(name: str) -> WalkerConstellationGeneratorBuilder

Set a base name for satellite naming.

Applied to the generator after construction, via WalkerConstellationGenerator.with_base_name(). Unset by default.

Parameters:

Name	Type	Description	Default
`name`	`str`	Base name for the constellation satellites	required

Returns:

Name	Type	Description
`WalkerConstellationGeneratorBuilder`	`WalkerConstellationGeneratorBuilder`	The builder, for method chaining.

build `method descriptor` ¶

build() -> WalkerConstellationGenerator

Construct the generator from the accumulated configuration.

Validates the t/p/f invariants and constructs the generator. This consumes the builder. The builder is single-use: calling build() a second time raises RuntimeError.

Returns:

Name	Type	Description
`WalkerConstellationGenerator`	`WalkerConstellationGenerator`	Initialized generator.

Raises:

Type	Description
`RuntimeError`	If the builder was already consumed by a prior `build()` call, or if `p` is zero, `t` is not divisible by `p`, or `f` >= `p`.

eccentricity `method descriptor` ¶

eccentricity(eccentricity: float) -> WalkerConstellationGeneratorBuilder

Set the eccentricity.

Defaults to 0.0 if not called.

Parameters:

Name	Type	Description	Default
`eccentricity`	`float`	Eccentricity (dimensionless, typically near 0 for Walker)	required

Returns:

Name	Type	Description
`WalkerConstellationGeneratorBuilder`	`WalkerConstellationGeneratorBuilder`	The builder, for method chaining.

pattern `method descriptor` ¶

pattern(pattern: WalkerPattern) -> WalkerConstellationGeneratorBuilder

Set the Walker pattern type.

Defaults to WalkerPattern.DELTA if not called.

Parameters:

Name	Type	Description	Default
`pattern`	`WalkerPattern`	Pattern type (DELTA for 360° RAAN, STAR for 180° RAAN)	required

Returns:

Name	Type	Description
`WalkerConstellationGeneratorBuilder`	`WalkerConstellationGeneratorBuilder`	The builder, for method chaining.

reference_mean_anomaly `method descriptor` ¶

reference_mean_anomaly(reference_mean_anomaly: float) -> WalkerConstellationGeneratorBuilder

Set the reference mean anomaly for the first satellite.

Defaults to 0.0 if not called.

Parameters:

Name	Type	Description	Default
`reference_mean_anomaly`	`float`	Mean anomaly for first satellite. Units: (deg) by default, or (rad) based on `angle_format`	required

Returns:

Name	Type	Description
`WalkerConstellationGeneratorBuilder`	`WalkerConstellationGeneratorBuilder`	The builder, for method chaining.

reference_raan `method descriptor` ¶

reference_raan(reference_raan: float) -> WalkerConstellationGeneratorBuilder

Set the reference RAAN for plane 0.

Defaults to 0.0 if not called.

Parameters:

Name	Type	Description	Default
`reference_raan`	`float`	RAAN for plane 0. Units: (deg) by default, or (rad) based on `angle_format`	required

Returns:

Name	Type	Description
`WalkerConstellationGeneratorBuilder`	`WalkerConstellationGeneratorBuilder`	The builder, for method chaining.

Walker Constellations¶

Walker Pattern¶

WalkerPattern ¶

DELTA class-attribute ¶

STAR class-attribute ¶

Walker Constellation Generator¶

WalkerConstellationGenerator ¶

eccentricity property ¶

epoch property ¶

num_planes property ¶

pattern property ¶

phasing property ¶

satellites_per_plane property ¶

semi_major_axis property ¶

total_satellites property ¶

as_keplerian_propagators method descriptor ¶

as_numerical_propagators method descriptor ¶

as_sgp_propagators method descriptor ¶

builder staticmethod ¶

satellite_elements method descriptor ¶

with_base_name method descriptor ¶

Walker Constellation Generator Builder¶

WalkerConstellationGeneratorBuilder ¶

angle_format method descriptor ¶

argument_of_perigee method descriptor ¶

base_name method descriptor ¶

build method descriptor ¶

eccentricity method descriptor ¶

pattern method descriptor ¶

reference_mean_anomaly method descriptor ¶

reference_raan method descriptor ¶

See Also¶

DELTA `class-attribute` ¶

STAR `class-attribute` ¶

eccentricity `property` ¶

epoch `property` ¶

num_planes `property` ¶

pattern `property` ¶

phasing `property` ¶

satellites_per_plane `property` ¶

semi_major_axis `property` ¶

total_satellites `property` ¶

as_keplerian_propagators `method descriptor` ¶

as_numerical_propagators `method descriptor` ¶

as_sgp_propagators `method descriptor` ¶

builder `staticmethod` ¶

satellite_elements `method descriptor` ¶

with_base_name `method descriptor` ¶

angle_format `method descriptor` ¶

argument_of_perigee `method descriptor` ¶

base_name `method descriptor` ¶

build `method descriptor` ¶

eccentricity `method descriptor` ¶

pattern `method descriptor` ¶

reference_mean_anomaly `method descriptor` ¶

reference_raan `method descriptor` ¶