Trajectory interpolation

This section focuses on building interpolated trajectories by propagators in Nyx.

For details on interpolation methods for trajectories, including Chebyshev, Lagrange, and Hermite interpolators, refer the ANISE math spec reference on interpolation.

Interpolated trajectories are computed in parallel leading to a negligible impact in computational performance. To build a trajectory from a propagation event, call the for_duration_with_traj() function on the propagator. Note that all of the event finding requires an interpolated trajectory.

Trajectories in Nyx are a simple list of discrete states interpolated using the Hermite interpolator. They are akin to the NASA/SPICE Hermite Type 13 interpolator.

Spacecraft trajectories can be transformed into another frame by transforming each of the individual states into the desired frame.

Warning

Transforming a trajectory into another frame is different from propagating the original spacecraft in that other frame. A propagator will advance with a different step depending on the central body, refer to the reference on propagator.

For example, propagating a spacecraft defined in the Earth J2000 inertial frame when accounting for the gravitational forces of the Earth and the Moon, and transforming that trajectory into a Moon J2000 centered frame will lead to a different trajectory that propagating that same inertial state defined in the Moon J2000 frame.

Trajectory Ephemeris Integration Test¶

Details of the traj_ephem_forward integration test.

Test Configuration¶

Initial epoch: 2021-01-01 12:00:00 UTC
Initial state: LEO orbit in Earth J2000 frame
Propagation duration: 31 days
Dynamics: Two-body
Integration method: variable step Runge-Kutta 8-9

Success Criteria¶

Metric	Requirement
Position Error (Direct)	0 m
Velocity Error (Direct)	0 m/s
Position Error (Post frame conv.)	< 1 m
Velocity Error (Post frame conv.)	< 0.01 m/s
Temporal Precision	< 1 μs

Test Structure¶

Trajectory Generation and Basic Validation¶

Builds a trajectory
Validates conservation of semi-major axis
Verifies initial and final states match propagation
Ensures STM (State Transition Matrix) is properly unset
Confirms interpolation bounds are respected

Interpolation Accuracy¶

Parallel truth generation
Compares interpolated states against truth trajectory
Validates position and velocity errors at exact timesteps
Expected accuracy: machine precision for stored states

Persistence Testing¶

Exports trajectory to Parquet format
Includes eclipse event detection
Reloads trajectory and verifies:
- State count consistency
- Temporal boundaries
- State vector equality
- Microsecond-level epoch precision

Frame Transformation Validation¶

Double conversion test: Earth J2000 → Moon J2000 → Earth J2000
Samples every 5 minutes
Validates:
- Temporal consistency
- Position error < 1 meter
- Velocity error < 0.01 m/s

Run log

$ RUST_LOG=info RUST_BACKTRACE=1 /usr/bin/time cargo test traj_ephem --release -- --nocapture
INFO  nyx_space::propagators::instance > Propagating for 31 days until 2021-02-01T12:00:00 UTC
INFO  nyx_space::propagators::instance >       ... done in 247 ms 822 μs 611 ns
[TIMING] 293 ms 488 μs 896 ns
Average SMA: 7712.186 km        Should be: 7712.186
Ephem: Trajectory in Earth J2000 (μ = 398600.435436096 km^3/s^2, eq. radius = 6378.14 km, polar radius = 6356.75 km, f = 0.0033536422844278) from 2021-01-01T12:00:00 UTC to 2021-02-01T12:00:00 UTC (31 days, or 2678400.000 s) [32289 states]
INFO  nyx_space::propagators::instance > Propagating for 31 days until 2021-02-01T12:00:00 UTC
INFO  nyx_space::propagators::instance >       ... done in 274 ms 970 μs 367 ns
[traj_ephem] Maximum error on exact step: pos: 0.00e0 m         vel: 0.00e0 m/s
INFO  nyx_space::md::trajectory::traj  > Exporting trajectory to parquet file...
INFO  nyx_space::md::trajectory::traj  > Serialized 32289 states from 2021-01-01T12:00:00 UTC to 2021-02-01T12:00:00 UTC
INFO  nyx_space::md::trajectory::traj  > Evaluating 1 event(s)
INFO  nyx_space::md::trajectory::traj  > Trajectory written to /home/chris/Workspace/nyx-space/nyx/output_data/ephem_forward-2024-10-27T06-36-19.parquet in 2 s 245 ms 95 μs 680 ns
INFO  nyx_space::io::trajectory_data   > File: /home/chris/Workspace/nyx-space/nyx/output_data/ephem_forward-2024-10-27T06-36-19.parquet
INFO  nyx_space::io::trajectory_data   > Created on: 2024-10-27T06:36:20.258980864 UTC
INFO  nyx_space::io::trajectory_data   > nyx-space License: AGPL 3.0
INFO  nyx_space::io::trajectory_data   > Created by: Chris Rabotin (chris) on Linux
INFO  nyx_space::io::trajectory_data   > Purpose: Trajectory data
INFO  nyx_space::io::trajectory_data   > Generated by: Nyx v2.0.0-rc
INFO  nyx_space::md::trajectory::sc_traj > Converted trajectory from Earth J2000 (μ = 398600.435436096 km^3/s^2, eq. radius = 6378.14 km, polar radius = 6356.75 km, f = 0.0033536422844278) to Moon J2000 in 300 ms: Trajectory in Moon J2000 (μ = 4902.800066163796 km^3/s^2, radius = 1737.4 km) from 2021-01-01T12:00:00 UTC to 2021-02-01T12:00:00 UTC (31 days, or 2678400.000 s) [32289 states]
ephem_luna Trajectory in Moon J2000 (μ = 4902.800066163796 km^3/s^2, radius = 1737.4 km) from 2021-01-01T12:00:00 UTC to 2021-02-01T12:00:00 UTC (31 days, or 2678400.000 s) [32289 states]
INFO  nyx_space::md::trajectory::sc_traj > Converted trajectory from Moon J2000 (μ = 4902.800066163796 km^3/s^2, radius = 1737.4 km) to Earth J2000 (μ = 398600.435436096 km^3/s^2, eq. radius = 6378.14 km, polar radius = 6356.75 km, f = 0.0033536422844278) in 299 ms: Trajectory in Earth J2000 (μ = 398600.435436096 km^3/s^2, eq. radius = 6378.14 km, polar radius = 6356.75 km, f = 0.0033536422844278) from 2021-01-01T12:00:00 UTC to 2021-02-01T12:00:00 UTC (31 days, or 2678400.000 s) [32289 states]
Ephem back: Trajectory in Earth J2000 (μ = 398600.435436096 km^3/s^2, eq. radius = 6378.14 km, polar radius = 6356.75 km, f = 0.0033536422844278) from 2021-01-01T12:00:00 UTC to 2021-02-01T12:00:00 UTC (31 days, or 2678400.000 s) [32289 states]
2.328666121016051e-11
Eval: total mass = 0.000 kg @  [Earth J2000] 2021-01-01T12:05:00 UTC    position = [-834.810409, -3848.218391, 6622.529651] km  velocity = [5.519092, -4.261593, -1.778298] km/s  Coast
Conv: total mass = 0.000 kg @  [Earth J2000] 2021-01-01T12:05:00 UTC    position = [-834.810409, -3848.218391, 6622.529651] km  velocity = [5.519092, -4.261593, -1.778298] km/s  Coast 0.000 m

(...)

[traj_ephem] Maximum interpolation error after double conversion: pos: 3.76e-8 m                vel: 1.13e-9 m/s
test propagation::trajectory::traj_ephem_forward ... ok