Lunar Frames¶

Transformations between Lunar-Centered Inertial (LCI), Lunar-Fixed Principal Axis (LFPA), Lunar-Fixed Mean-Earth/polar-axis (LFME), and Earth-Centered Inertial (ECI).

Note

For conceptual explanations and examples, see Lunar Reference Frames in the Learn section.

LCI ↔ LFPA¶

rotation_lci_to_lfpa `builtin` ¶

rotation_lci_to_lfpa(epc: Epoch) -> ndarray

Computes the rotation matrix from Lunar-Centered Inertial (LCI) to Lunar-Fixed Principal Axis (LFPA), using the DE440 lunar principal-axis binary PCK (moon_pa_de440).

Auto-loads the moon_pa_de440 PCK (downloading it to ~/.cache/brahe/naif if needed).

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation matrix	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: 3x3 rotation matrix transforming LCI -> LFPA

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
r = bh.rotation_lci_to_lfpa(epc)

rotation_lfpa_to_lci `builtin` ¶

rotation_lfpa_to_lci(epc: Epoch) -> ndarray

Computes the rotation matrix from Lunar-Fixed Principal Axis (LFPA) to Lunar-Centered Inertial (LCI). Inverse of rotation_lci_to_lfpa.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation matrix	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: 3x3 rotation matrix transforming LFPA -> LCI

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
r = bh.rotation_lfpa_to_lci(epc)

position_lci_to_lfpa `builtin` ¶

position_lci_to_lfpa(epc: Epoch, x_lci: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-inertial (LCI) position into the equivalent Cartesian Lunar-Fixed Principal Axis (LFPA) position.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lci`	`ndarray or list`	Cartesian LCI position (m), shape `(3,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LFPA position (m), shape `(3,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lfpa = bh.position_lci_to_lfpa(epc, [bh.R_MOON + 100e3, 0.0, 0.0])

position_lfpa_to_lci `builtin` ¶

position_lfpa_to_lci(epc: Epoch, x_lfpa: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-Fixed Principal Axis (LFPA) position into the equivalent Cartesian Lunar-inertial (LCI) position.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lfpa`	`ndarray or list`	Cartesian LFPA position (m), shape `(3,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LCI position (m), shape `(3,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lci = bh.position_lfpa_to_lci(epc, [bh.R_MOON, 0.0, 0.0])

state_lci_to_lfpa `builtin` ¶

state_lci_to_lfpa(epc: Epoch, x_lci: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-inertial (LCI) state (position and velocity) into the equivalent Cartesian Lunar-Fixed Principal Axis (LFPA) state.

The velocity transformation accounts for the transport term induced by the Moon's rotation.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lci`	`ndarray or list`	Cartesian LCI state `[position (m), velocity (m/s)]`, shape `(6,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LFPA state `[position (m), velocity (m/s)]`, shape `(6,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lci = [bh.R_MOON + 100e3, 0.0, 0.0, 0.0, 1.6e3, 0.0]
x_lfpa = bh.state_lci_to_lfpa(epc, x_lci)

state_lfpa_to_lci `builtin` ¶

state_lfpa_to_lci(epc: Epoch, x_lfpa: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-Fixed Principal Axis (LFPA) state (position and velocity) into the equivalent Cartesian Lunar-inertial (LCI) state. Inverse of state_lci_to_lfpa.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lfpa`	`ndarray or list`	Cartesian LFPA state `[position (m), velocity (m/s)]`, shape `(6,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LCI state `[position (m), velocity (m/s)]`, shape `(6,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lci = [bh.R_MOON + 100e3, 0.0, 0.0, 0.0, 1.6e3, 0.0]
x_lfpa = bh.state_lci_to_lfpa(epc, x_lci)
x_lci2 = bh.state_lfpa_to_lci(epc, x_lfpa)

LCI ↔ LFME¶

rotation_lci_to_lfme `builtin` ¶

rotation_lci_to_lfme(epc: Epoch) -> ndarray

Computes the rotation matrix from Lunar-Centered Inertial (LCI) to Lunar-Fixed Mean Earth/polar-axis (LFME).

Auto-loads the moon_pa_de440 PCK (downloading it to ~/.cache/brahe/naif if needed).

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation matrix	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: 3x3 rotation matrix transforming LCI -> LFME

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
r = bh.rotation_lci_to_lfme(epc)

rotation_lfme_to_lci `builtin` ¶

rotation_lfme_to_lci(epc: Epoch) -> ndarray

Computes the rotation matrix from Lunar-Fixed Mean Earth/polar-axis (LFME) to Lunar-Centered Inertial (LCI). Inverse of rotation_lci_to_lfme.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation matrix	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: 3x3 rotation matrix transforming LFME -> LCI

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
r = bh.rotation_lfme_to_lci(epc)

position_lci_to_lfme `builtin` ¶

position_lci_to_lfme(epc: Epoch, x_lci: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-inertial (LCI) position into the equivalent Cartesian Lunar-Fixed Mean Earth/polar-axis (LFME) position.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lci`	`ndarray or list`	Cartesian LCI position (m), shape `(3,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LFME position (m), shape `(3,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lfme = bh.position_lci_to_lfme(epc, [bh.R_MOON + 100e3, 0.0, 0.0])

position_lfme_to_lci `builtin` ¶

position_lfme_to_lci(epc: Epoch, x_lfme: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-Fixed Mean Earth/polar-axis (LFME) position into the equivalent Cartesian Lunar-inertial (LCI) position.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lfme`	`ndarray or list`	Cartesian LFME position (m), shape `(3,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LCI position (m), shape `(3,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lci = bh.position_lfme_to_lci(epc, [bh.R_MOON, 0.0, 0.0])

state_lci_to_lfme `builtin` ¶

state_lci_to_lfme(epc: Epoch, x_lci: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-inertial (LCI) state (position and velocity) into the equivalent Cartesian Lunar-Fixed Mean Earth/polar-axis (LFME) state.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lci`	`ndarray or list`	Cartesian LCI state `[position (m), velocity (m/s)]`, shape `(6,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LFME state `[position (m), velocity (m/s)]`, shape `(6,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lci = [bh.R_MOON + 100e3, 0.0, 0.0, 0.0, 1.6e3, 0.0]
x_lfme = bh.state_lci_to_lfme(epc, x_lci)

state_lfme_to_lci `builtin` ¶

state_lfme_to_lci(epc: Epoch, x_lfme: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-Fixed Mean Earth/polar-axis (LFME) state (position and velocity) into the equivalent Cartesian Lunar-inertial (LCI) state. Inverse of state_lci_to_lfme.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lfme`	`ndarray or list`	Cartesian LFME state `[position (m), velocity (m/s)]`, shape `(6,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LCI state `[position (m), velocity (m/s)]`, shape `(6,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lci = [bh.R_MOON + 100e3, 0.0, 0.0, 0.0, 1.6e3, 0.0]
x_lfme = bh.state_lci_to_lfme(epc, x_lci)
x_lci2 = bh.state_lfme_to_lci(epc, x_lfme)

LFPA ↔ LFME (Constant Rotation)¶

rotation_lfpa_to_lfme `builtin` ¶

rotation_lfpa_to_lfme() -> ndarray

Computes the constant rotation matrix from Lunar-Fixed Principal Axis (LFPA) to Lunar-Fixed Mean Earth/polar-axis (LFME). Inverse of rotation_lfme_to_lfpa.

Returns:

Type	Description
`ndarray`	numpy.ndarray: 3x3 rotation matrix transforming LFPA -> LFME

Example

import brahe as bh

r = bh.rotation_lfpa_to_lfme()

rotation_lfme_to_lfpa `builtin` ¶

rotation_lfme_to_lfpa() -> ndarray

Computes the constant rotation matrix from Lunar-Fixed Mean Earth/polar-axis (LFME) to Lunar-Fixed Principal Axis (LFPA).

Returns:

Type	Description
`ndarray`	numpy.ndarray: 3x3 rotation matrix transforming LFME -> LFPA

Example

import brahe as bh

r = bh.rotation_lfme_to_lfpa()

ECI ↔ LCI¶

position_eci_to_lci `builtin` ¶

position_eci_to_lci(epc: Epoch, x_eci: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Earth-inertial (ECI) position into the equivalent Cartesian Lunar-inertial (LCI) position.

The LCI origin is the Moon's body center (NAIF ID 301). Auto-initializes the default de440s ephemeris if no SPK kernel is loaded.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_eci`	`ndarray or list`	Cartesian ECI position (m), shape `(3,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LCI position (m), shape `(3,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lci = bh.position_eci_to_lci(epc, [1e7, 2e7, 3e7])

position_lci_to_eci `builtin` ¶

position_lci_to_eci(epc: Epoch, x_lci: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-inertial (LCI) position into the equivalent Cartesian Earth-inertial (ECI) position.

Auto-initializes the default de440s ephemeris if no SPK kernel is loaded.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lci`	`ndarray or list`	Cartesian LCI position (m), shape `(3,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian ECI position (m), shape `(3,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_eci = bh.position_lci_to_eci(epc, [1e7, 2e7, 3e7])

state_eci_to_lci `builtin` ¶

state_eci_to_lci(epc: Epoch, x_eci: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Earth-inertial (ECI) state (position and velocity) into the equivalent Cartesian Lunar-inertial (LCI) state.

The LCI origin is the Moon's body center (NAIF ID 301). Auto-initializes the default de440s ephemeris if no SPK kernel is loaded.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_eci`	`ndarray or list`	Cartesian ECI state `[position (m), velocity (m/s)]`, shape `(6,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian LCI state `[position (m), velocity (m/s)]`, shape `(6,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_lci = bh.state_eci_to_lci(epc, [1e7, 2e7, 3e7, 1.0, 2.0, 3.0])

state_lci_to_eci `builtin` ¶

state_lci_to_eci(epc: Epoch, x_lci: Union[ndarray, List]) -> ndarray

Transforms a Cartesian Lunar-inertial (LCI) state (position and velocity) into the equivalent Cartesian Earth-inertial (ECI) state.

Auto-initializes the default de440s ephemeris if no SPK kernel is loaded.

Parameters:

Name	Type	Description	Default
`epc`	`Epoch`	Epoch instant for computation of the transformation	required
`x_lci`	`ndarray or list`	Cartesian LCI state `[position (m), velocity (m/s)]`, shape `(6,)`	required

Returns:

Type	Description
`ndarray`	numpy.ndarray: Cartesian ECI state `[position (m), velocity (m/s)]`, shape `(6,)`

Example

import brahe as bh

epc = bh.Epoch.from_datetime(2024, 3, 1, 0, 0, 0.0, 0.0, bh.UTC)
x_eci = bh.state_lci_to_eci(epc, [1e7, 2e7, 3e7, 1.0, 2.0, 3.0])

Lunar Frames¶

LCI ↔ LFPA¶

rotation_lci_to_lfpa builtin ¶

rotation_lfpa_to_lci builtin ¶

position_lci_to_lfpa builtin ¶

position_lfpa_to_lci builtin ¶

state_lci_to_lfpa builtin ¶

state_lfpa_to_lci builtin ¶

LCI ↔ LFME¶

rotation_lci_to_lfme builtin ¶

rotation_lfme_to_lci builtin ¶

position_lci_to_lfme builtin ¶

position_lfme_to_lci builtin ¶

state_lci_to_lfme builtin ¶

state_lfme_to_lci builtin ¶

LFPA ↔ LFME (Constant Rotation)¶

rotation_lfpa_to_lfme builtin ¶

rotation_lfme_to_lfpa builtin ¶

ECI ↔ LCI¶

position_eci_to_lci builtin ¶

position_lci_to_eci builtin ¶

state_eci_to_lci builtin ¶

state_lci_to_eci builtin ¶

See Also¶

rotation_lci_to_lfpa `builtin` ¶

rotation_lfpa_to_lci `builtin` ¶

position_lci_to_lfpa `builtin` ¶

position_lfpa_to_lci `builtin` ¶

state_lci_to_lfpa `builtin` ¶

state_lfpa_to_lci `builtin` ¶

rotation_lci_to_lfme `builtin` ¶

rotation_lfme_to_lci `builtin` ¶

position_lci_to_lfme `builtin` ¶

position_lfme_to_lci `builtin` ¶

state_lci_to_lfme `builtin` ¶

state_lfme_to_lci `builtin` ¶

rotation_lfpa_to_lfme `builtin` ¶

rotation_lfme_to_lfpa `builtin` ¶

position_eci_to_lci `builtin` ¶

position_lci_to_eci `builtin` ¶

state_eci_to_lci `builtin` ¶

state_lci_to_eci `builtin` ¶