Numerical Integrators

This example propagates the ISS for 24 hours with two numerical integrators (fixed-step RungeKutta4 and adaptive RungeKutta89) driven by a configurable force model, and prints the SGP4 result at the same time for comparison. Reach for numerical propagation when SGP4's analytic mean-element theory is not accurate enough, or when you need to model specific perturbations.

import {
  RungeKutta4Propagator, RungeKutta89Propagator, ForceModel, EpochUTC, Satellite, TleLine1, TleLine2,
} from 'ootk';

Run it

npm run build
npx tsx ./examples/integrator.ts

Setup Satellite

Build a Satellite from a TLE and define the propagation window. sat.eci(stop) is the SGP4 answer at the stop time (TEME frame), printed as a baseline. sat.toJ2000(start) converts the SGP4 state at the start time into the J2000 state that seeds the numerical integrators.

const start = new Date(2024, 0, 28, 0, 0, 0, 0);
const stop = new Date(2024, 0, 29, 0, 0, 0, 0);
const stopEpoch = EpochUTC.fromDateTime(stop);
const sat = new Satellite({
  tle1: '1 25544U 98067A   24028.54545847  .00031576  00000-0  57240-3 0  9991' as TleLine1,
  tle2: '2 25544  51.6418 292.2590 0002595 167.5319 252.0460 15.49326324436741' as TleLine2,
});

console.log('SGP4 state at stop time (TEME):');
console.log(sat.eci(stop));

Force Model

ForceModel is a builder for the perturbations the integrator will evaluate. This one uses an 8x8 Earth geopotential, lunar and solar third-body gravity, solar radiation pressure, and atmospheric drag (both parameterized by mass in kg and cross-sectional area in m^2).

const forceModel = new ForceModel();

forceModel.setEarthGravity(8, 8);
forceModel.setThirdBodyGravity({
  moon: true,
  sun: true,
});
forceModel.setSolarRadiationPressure(1000, 400);
forceModel.setAtmosphericDrag(1000, 400);

RK4 Propagation

RungeKutta4Propagator is a classic fixed-step integrator. propagate(epoch) steps the seeded J2000 state to the requested EpochUTC under the configured force model.

const rk4 = new RungeKutta4Propagator(sat.toJ2000(start), forceModel);

console.log('\nRungeKutta4 state after 24 hours (J2000):');
console.log(rk4.propagate(stopEpoch));

RK89 Propagation

RungeKutta89Propagator is a high-order adaptive-step integrator. After 24 hours the two integrators agree to a few meters, while both differ from SGP4 by a few hundred kilometers: expected, since SGP4 uses its own simplified force theory and the TLE encodes mean elements fitted for it.

const rkA = new RungeKutta89Propagator(sat.toJ2000(start), forceModel);

console.log('\nRungeKutta89 state after 24 hours (J2000):');
console.log(rkA.propagate(stopEpoch));

Output

SGP4 state at stop time (TEME):
{
  position: { x: -663.6938353817707, y: 6495.793093922628, z: 1874.733222146894 },
  velocity: {
    x: -5.086304552715983,
    y: 1.111360309899012,
    z: -5.625002780548332
  }
}

RungeKutta4 state after 24 hours (J2000):
_J2000 {
  epoch: _EpochUTC { posix: 1706504400 },
  position: _Vector3D {
    x: -964.313601162822,
    y: 6549.750969705299,
    z: 1490.1670220023666
  },
  velocity: _Vector3D {
    x: -5.028176395740335,
    y: 0.5772068247154211,
    z: -5.761952625767482
  }
}

RungeKutta89 state after 24 hours (J2000):
_J2000 {
  epoch: _EpochUTC { posix: 1706504400 },
  position: _Vector3D {
    x: -964.3094290875154,
    y: 6549.750581942014,
    z: 1490.1718512113523
  },
  velocity: _Vector3D {
    x: -5.028177380019933,
    y: 0.5772138007621341,
    z: -5.761950980723573
  }
}

The start and stop dates are constructed in local time, so the exact numbers depend on the machine's timezone.