EME2000 ↔ GCRF Transformations¶

Transforms a state vector (position and velocity) from EME2000 (Earth Mean Equator and Equinox of J2000.0) to GCRF (Geocentric Celestial Reference Frame).

Applies the inverse frame bias correction to both position and velocity. Because the transformation does not vary with time, the velocity is directly rotated without additional correction terms.

Parameters:

Returns:

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import brahe as bh
import numpy as np

# State vector in EME2000 [x, y, z, vx, vy, vz] (meters, m/s)
state_eme2000 = np.array([bh.R_EARTH + 500e3, 0.0, 0.0, 0.0, 7600.0, 0.0])

# Transform to GCRF
state_gcrf = bh.state_eme2000_to_gcrf(state_eme2000)
print(f"GCRF state: {state_gcrf}")

Transforms a position vector from EME2000 (Earth Mean Equator and Equinox of J2000.0) to GCRF (Geocentric Celestial Reference Frame).

Applies the inverse frame bias correction to account for the small offset between the J2000.0 mean equator and equinox and GCRF. This is a constant transformation that does not vary with time.

Parameters:

Returns:

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import brahe as bh
import numpy as np

# Position vector in EME2000 (meters)
r_eme2000 = np.array([bh.R_EARTH + 500e3, 0.0, 0.0])

# Transform to GCRF
r_gcrf = bh.position_eme2000_to_gcrf(r_eme2000)
print(f"GCRF position: {r_gcrf}")

Computes the rotation matrix from EME2000 (Earth Mean Equator and Equinox of J2000.0) to GCRF (Geocentric Celestial Reference Frame).

This transformation applies the inverse frame bias correction to account for the difference between EME2000 (J2000.0 mean equator/equinox) and GCRF (ICRS-aligned). The transformation is constant and does not depend on time.

Returns:

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import brahe as bh

# Get rotation matrix
R = bh.rotation_eme2000_to_gcrf()
print(f"Rotation matrix shape: {R.shape}")
# Output: Rotation matrix shape: (3, 3)

Transforms a state vector (position and velocity) from GCRF (Geocentric Celestial Reference Frame) to EME2000 (Earth Mean Equator and Equinox of J2000.0).

Applies the frame bias correction to both position and velocity. Because the transformation does not vary with time, the velocity is directly rotated without additional correction terms.

Parameters:

Returns:

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import brahe as bh
import numpy as np

# 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 EME2000
state_eme2000 = bh.state_gcrf_to_eme2000(state_gcrf)
print(f"EME2000 state: {state_eme2000}")

Transforms a position vector from GCRF (Geocentric Celestial Reference Frame) to EME2000 (Earth Mean Equator and Equinox of J2000.0).

Applies the frame bias correction to account for the small offset between GCRF and the J2000.0 mean equator and equinox. This is a constant transformation that does not vary with time.

Parameters:

Returns:

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import brahe as bh
import numpy as np

# Position vector in GCRF (meters)
r_gcrf = np.array([bh.R_EARTH + 500e3, 0.0, 0.0])

# Transform to EME2000
r_eme2000 = bh.position_gcrf_to_eme2000(r_gcrf)
print(f"EME2000 position: {r_eme2000}")

Computes the rotation matrix from GCRF (Geocentric Celestial Reference Frame) to EME2000 (Earth Mean Equator and Equinox of J2000.0).

This transformation applies the frame bias correction to account for the difference between GCRF (ICRS-aligned) and EME2000 (J2000.0 mean equator/equinox). The transformation is constant and does not depend on time.

Returns:

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import brahe as bh
import numpy as np

# Get rotation matrix
R = bh.rotation_gcrf_to_eme2000()
print(f"Rotation matrix shape: {R.shape}")
# Output: Rotation matrix shape: (3, 3)

Computes the frame bias matrix transforming GCRF (Geocentric Celestial Reference Frame) to EME2000 (Earth Mean Equator and Equinox of J2000.0).

The bias matrix accounts for the small offset between the GCRF and the J2000.0 mean equator and equinox due to the difference in their definitions. This is a constant transformation that does not vary with time.

Returns:

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import brahe as bh

# Get the bias matrix
B = bh.bias_eme2000()
print(f"Bias matrix shape: {B.shape}")
# Output: Bias matrix shape: (3, 3)