GCRF ↔ ITRF Transformations¶

Transforms a state vector (position and velocity) from GCRF (Geocentric Celestial Reference Frame) to ITRF (International Terrestrial Reference Frame).

Applies the full IAU 2006/2000A transformation including bias, precession, nutation, Earth rotation, and polar motion corrections using global Earth orientation parameters. The velocity transformation accounts for the Earth's rotation rate.

Parameters:

Returns:

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import brahe as bh
import numpy as np

bh.initialize_eop()

# Create epoch
epc = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)

# State vector in GCRF [x, y, z, vx, vy, vz] (meters, m/s)
state_gcrf = np.array([bh.R_EARTH + 500e3, 0.0, 0.0, 0.0, 7600.0, 0.0])

# Transform to ITRF
state_itrf = bh.state_gcrf_to_itrf(epc, state_gcrf)
print(f"ITRF state: {state_itrf}")

Computes the combined rotation matrix from GCRF (Geocentric Celestial Reference Frame) to ITRF (International Terrestrial Reference Frame). Applies corrections for bias, precession, nutation, Earth-rotation, and polar motion.

The transformation is accomplished using the IAU 2006/2000A, CIO-based theory using classical angles. The method as described in section 5.5 of the SOFA C transformation cookbook.

The function will utilize the global Earth orientation and loaded data to apply corrections for Celestial Intermediate Pole (CIP) and polar motion drift derived from empirical observations.

Parameters:

Returns:

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import brahe as bh
import numpy as np

bh.initialize_eop()

# Create epoch
epc = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)

# Get rotation matrix from GCRF to ITRF
R = bh.rotation_gcrf_to_itrf(epc)
print(f"Rotation matrix shape: {R.shape}")
# Output: Rotation matrix shape: (3, 3)

Transforms a position vector from GCRF (Geocentric Celestial Reference Frame) to ITRF (International Terrestrial Reference Frame).

Applies the full IAU 2006/2000A transformation including bias, precession, nutation, Earth rotation, and polar motion corrections using global Earth orientation parameters.

Parameters:

Returns:

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import brahe as bh
import numpy as np

bh.initialize_eop()

# Create epoch
epc = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)

# Position vector in GCRF (meters)
r_gcrf = np.array([7000000.0, 0.0, 0.0])

# Transform to ITRF
r_itrf = bh.position_gcrf_to_itrf(epc, r_gcrf)
print(f"ITRF position: {r_itrf}")

# Batch: one row per position, one shared epoch
positions = np.tile(r_gcrf, (10, 1))                     # shape (10, 3)
positions_itrf = bh.position_gcrf_to_itrf(epc, positions)  # shape (10, 3)

# One position at a sequence of epochs
epochs = [epc + 60.0 * i for i in range(5)]
track = bh.position_gcrf_to_itrf(epochs, r_gcrf)         # shape (5, 3)

Transforms a state vector (position and velocity) from ITRF (International Terrestrial Reference Frame) to GCRF (Geocentric Celestial Reference Frame).

Applies the full IAU 2006/2000A transformation including bias, precession, nutation, Earth rotation, and polar motion corrections using global Earth orientation parameters. The velocity transformation accounts for the Earth's rotation rate.

Parameters:

Returns:

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import brahe as bh
import numpy as np

bh.initialize_eop()

# Create epoch
epc = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)

# State vector in ITRF [x, y, z, vx, vy, vz] (meters, m/s)
state_itrf = np.array([4000000.0, 3000000.0, 4000000.0, 100.0, -50.0, 200.0])

# Transform to GCRF
state_gcrf = bh.state_itrf_to_gcrf(epc, state_itrf)
print(f"GCRF state: {state_gcrf}")

Computes the combined rotation matrix from ITRF (International Terrestrial Reference Frame) to GCRF (Geocentric Celestial Reference Frame). Applies corrections for bias, precession, nutation, Earth-rotation, and polar motion.

The transformation is accomplished using the IAU 2006/2000A, CIO-based theory using classical angles. The method as described in section 5.5 of the SOFA C transformation cookbook.

The function will utilize the global Earth orientation and loaded data to apply corrections for Celestial Intermediate Pole (CIP) and polar motion drift derived from empirical observations.

Parameters:

Returns:

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import brahe as bh

bh.initialize_eop()

# Create epoch
epc = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)

# Get rotation matrix from ITRF to GCRF
R = bh.rotation_itrf_to_gcrf(epc)
print(f"Rotation matrix shape: {R.shape}")

Transforms a position vector from ITRF (International Terrestrial Reference Frame) to GCRF (Geocentric Celestial Reference Frame).

Applies the full IAU 2006/2000A transformation including bias, precession, nutation, Earth rotation, and polar motion corrections using global Earth orientation parameters.

Parameters:

Returns:

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import brahe as bh
import numpy as np

bh.initialize_eop()

# Create epoch
epc = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)

# Position in ITRF (ground station)
r_itrf = np.array([4000000.0, 3000000.0, 4000000.0])

# Transform to GCRF
r_gcrf = bh.position_itrf_to_gcrf(epc, r_itrf)
print(f"GCRF position: {r_gcrf}")

Computes the Bias-Precession-Nutation matrix transforming the GCRS to the CIRS intermediate reference frame. This transformation corrects for the bias, precession, and nutation of Celestial Intermediate Origin (CIO) with respect to inertial space.

This formulation computes the Bias-Precession-Nutation correction matrix using a CIO based model, evaluating the precession-nutation model selected by set_precession_nutation_model (IAU 2006/2000A by default).

The function will utilize the global Earth orientation and loaded data to apply corrections to the Celestial Intermediate Pole (CIP) derived from empirical observations.

Parameters:

Returns:

Computes the Earth rotation matrix transforming the CIRS to the TIRS intermediate reference frame. This transformation corrects for the Earth rotation.

Parameters:

Returns:

Computes the Earth rotation matrix transforming the TIRS to the ITRF reference frame.

The function will utilize the global Earth orientation and loaded data to apply corrections to compute the polar motion correction based on empirical observations of polar motion drift.

Parameters:

Returns:

Set the crate-wide precession-nutation model evaluated by the Earth orientation transformations.

The setting applies to every subsequent call of the GCRF to ITRF and GCRF to MOD to TOD transformations, including the frame router and the batch forms. Functions that take a model argument explicitly are unaffected.

Parameters:

Returns:

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import brahe as bh

bh.set_precession_nutation_model(bh.PrecessionNutationModel.IAU2000B)

Get the crate-wide precession-nutation model evaluated by the Earth orientation transformations.

Returns:

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import brahe as bh

model = bh.get_precession_nutation_model()

Computes the Bias-Precession-Nutation matrix transforming the GCRS to the CIRS intermediate reference frame using an explicitly chosen precession-nutation model.

The Celestial Intermediate Pole corrections from the global Earth orientation data are applied for either model.

Parameters:

Returns:

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import brahe as bh

bh.initialize_eop()
epc = bh.Epoch.from_datetime(2024, 1, 1, 12, 0, 0.0, 0.0, bh.TimeSystem.UTC)
rc2i = bh.bias_precession_nutation_model(epc, bh.PrecessionNutationModel.IAU2000B)