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Precession-Nutation Model

Brahe evaluates the IAU 2006/2000A precession-nutation model by default. The truncated IAU 2000B model, IAU 2000 precession with the abridged IAU 2000B nutation series, is selectable with a single global setting. The setting applies to every subsequent transformation that depends on the orientation of the Celestial Intermediate Pole: the GCRF ↔ ITRF and ECI ↔ ECEF transformations, the GCRF ↔ MOD ↔ TOD equinox chain, the reference frame router, the batch forms, and the Earth-rotation-dependent force models used during propagation.

Querying and Setting the Model

get_precession_nutation_model returns the model in effect and set_precession_nutation_model replaces it. The setting is crate-wide and persists until it is changed again, so a program that switches models temporarily should restore the previous value when it is done.

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import numpy as np

import brahe as bh

bh.initialize_eop()

print(f"Default precession-nutation model: {bh.get_precession_nutation_model()}")

epc = bh.Epoch(2040, 3, 1, 0, 0, 0.0, time_system=bh.UTC)
print(f"Epoch: {epc}")

R_2006a = bh.rotation_gcrf_to_itrf(epc)

bh.set_precession_nutation_model(bh.PrecessionNutationModel.IAU2000B)
print(f"Selected precession-nutation model: {bh.get_precession_nutation_model()}")

R_2000b = bh.rotation_gcrf_to_itrf(epc)

# Rotation angle between the two matrices, in the form that keeps its precision
# for the very small angles separating the two models
frobenius = np.linalg.norm(R_2006a - R_2000b, "fro")
theta_mas = 2.0 * np.arcsin(frobenius / (2.0 * np.sqrt(2.0))) * bh.RAD2AS * 1000.0

print("\nGCRF to ITRF rotation difference between the two models:")
print(f"  Angle: {theta_mas:.4f} mas")

rc2i_2006a = bh.bias_precession_nutation_model(epc, bh.PrecessionNutationModel.IAU2006A)
rc2i_2000b = bh.bias_precession_nutation_model(epc, bh.PrecessionNutationModel.IAU2000B)

print("\nBias-precession-nutation matrices evaluated per call:")
print(f"  Max absolute difference: {np.max(np.abs(rc2i_2006a - rc2i_2000b)):.2e}")

bh.set_precession_nutation_model(bh.PrecessionNutationModel.IAU2006A)
print(f"\nRestored precession-nutation model: {bh.get_precession_nutation_model()}")

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use brahe as bh;

fn main() {
    bh::initialize_eop().unwrap();

    println!("Default precession-nutation model: {}", bh::get_precession_nutation_model());

    let epc = bh::Epoch::from_datetime(2040, 3, 1, 0, 0, 0.0, 0.0, bh::TimeSystem::UTC);
    println!("Epoch: {}", epc);

    let r_2006a = bh::rotation_gcrf_to_itrf(epc);

    bh::set_precession_nutation_model(bh::PrecessionNutationModel::IAU2000B);
    println!("Selected precession-nutation model: {}", bh::get_precession_nutation_model());

    let r_2000b = bh::rotation_gcrf_to_itrf(epc);

    // Rotation angle between the two matrices, in the form that keeps its precision
    // for the very small angles separating the two models
    let frobenius = (r_2006a - r_2000b).norm();
    let theta_mas = 2.0 * (frobenius / (2.0 * 2.0_f64.sqrt())).asin() * bh::RAD2AS * 1000.0;

    println!("\nGCRF to ITRF rotation difference between the two models:");
    println!("  Angle: {:.4} mas", theta_mas);

    let rc2i_2006a = bh::bias_precession_nutation_model(epc, bh::PrecessionNutationModel::IAU2006A);
    let rc2i_2000b = bh::bias_precession_nutation_model(epc, bh::PrecessionNutationModel::IAU2000B);

    println!("\nBias-precession-nutation matrices evaluated per call:");
    println!("  Max absolute difference: {:.2e}", (rc2i_2006a - rc2i_2000b).abs().max());

    bh::set_precession_nutation_model(bh::PrecessionNutationModel::IAU2006A);
    println!("\nRestored precession-nutation model: {}", bh::get_precession_nutation_model());
}
Output 
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Default precession-nutation model: IAU 2006/2000A
Epoch: 2040-03-01 00:00:00.000 UTC
Selected precession-nutation model: IAU 2000B

GCRF to ITRF rotation difference between the two models:
  Angle: 0.2311 mas

Bias-precession-nutation matrices evaluated per call:
  Max absolute difference: 1.00e-09

Restored precession-nutation model: IAU 2006/2000A

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Default precession-nutation model: IAU 2006/2000A
Epoch: 2040-03-01 00:00:00.000 UTC
Selected precession-nutation model: IAU 2000B

GCRF to ITRF rotation difference between the two models:
  Angle: 0.2311 mas

Bias-precession-nutation matrices evaluated per call:
  Max absolute difference: 1.00e-9

Restored precession-nutation model: IAU 2006/2000A

Accuracy and Speed

IAU 2000B evaluates the Celestial Intermediate Pole about eight times faster than IAU 2006/2000A, because its nutation series has 77 terms instead of roughly 1300. The two models place the pole within 0.3 mas RMS and 1.2 mas at worst over 1990 to 2040, which moves a position by at most 25 cm at geostationary altitude and 4 cm in low Earth orbit. Use IAU 2000B where throughput matters more than that difference, and the default elsewhere.

Per-Call Model Selection

bias_precession_nutation_model, bias_precession, nutation, and gast_rotation take the model as an explicit argument instead of reading the global setting, so a caller can evaluate either model without changing it for the rest of the program.

See Also