ECI ↔ ECEF Transformations¶

Transforms a state vector (position and velocity) from the Earth Centered Inertial (ECI/GCRF) frame to the Earth Centered Earth Fixed (ECEF/ITRF) frame.

This function is an alias for state_gcrf_to_itrf. 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

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

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

# Transform to ECEF
state_ecef = bh.state_eci_to_ecef(epc, state_eci)
print(f"ECEF state: {state_ecef}")

Computes the combined rotation matrix from the inertial to the Earth-fixed reference frame. Applies corrections for bias, precession, nutation, Earth-rotation, and polar motion.

This function is an alias for rotation_gcrf_to_itrf. ECI refers to the GCRF (Geocentric Celestial Reference Frame) implementation, and ECEF refers to the ITRF (International Terrestrial Reference Frame) implementation.

Parameters:

Returns:

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import brahe as bh
import numpy as np

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

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

Transforms a position vector from the Earth Centered Inertial (ECI/GCRF) frame to the Earth Centered Earth Fixed (ECEF/ITRF) frame.

This function is an alias for position_gcrf_to_itrf. 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

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

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

# Transform to ECEF
r_ecef = bh.position_eci_to_ecef(epc, r_eci)
print(f"ECEF position: {r_ecef}")

Transforms a state vector (position and velocity) from the Earth Centered Earth Fixed (ECEF/ITRF) frame to the Earth Centered Inertial (ECI/GCRF) frame.

This function is an alias for state_itrf_to_gcrf. 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

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

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

# Transform to ECI
state_eci = bh.state_ecef_to_eci(epc, state_ecef)
print(f"ECI state: {state_eci}")

Computes the combined rotation matrix from the Earth-fixed to the inertial reference frame. Applies corrections for bias, precession, nutation, Earth-rotation, and polar motion.

This function is an alias for rotation_itrf_to_gcrf. ECEF refers to the ITRF (International Terrestrial Reference Frame) implementation, and ECI refers to the GCRF (Geocentric Celestial Reference Frame) implementation.

Parameters:

Returns:

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import brahe as bh

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

# Get rotation matrix from ECEF to ECI
R = bh.rotation_ecef_to_eci(epc)
print(f"Rotation matrix shape: {R.shape}")

Transforms a position vector from the Earth Centered Earth Fixed (ECEF/ITRF) frame to the Earth Centered Inertial (ECI/GCRF) frame.

This function is an alias for position_itrf_to_gcrf. 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

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

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

# Transform to ECI
r_eci = bh.position_ecef_to_eci(epc, r_ecef)
print(f"ECI position: {r_eci}")