High-Precision Orbit Propagator

High-precision satellite propagation using Runga-Kutta methods for differential equation solving

Force models are mostly pulled from Montenbruck & Gill: https://link.springer.com/book/10.1007/978-3-642-58351-3

The propagator can also compute the state transition matrix, meaning position and velocity covariances can be propagated as well.

The default propagator uses a Runga-Kutta 9(8) integrator with coefficient computed by Verner: https://www.sfu.ca/~jverner/

This works much better than lower-order Runga-Kutta solvers such as Dormund-Prince, and I don’t know why it isn’t more popular in numerical packages

This module includes a function to propagate a position and time directly, and a convenience “satstate” object that represents satellite position, velocity, and optionally covariance and can propagate itself to different times

Forces included in the propagator:

  1. Earth gravity with higher-order zonal terms

  2. Sun, Moon gravity

  3. Radiation pressure

  4. Atmospheric drag: NRL-MISE 2000 density model, with option to include space weather effects (can be large)

satkit.satprop.propagate(pos: numpy.typing.ArrayLike[float], vel: numpy.typing.ArrayLike[float], start: satkit.time, **kwargs)

High-precision orbit propagator

Notes

  • Propagator uses advanced Runga-Kutta integrators and includes the following forces:

    • Earth gravity with higher-order zonal terms

    • Sun, Moon gravity

    • Radiation pressure

    • Atmospheric drag: NRL-MISE 2000 density model, with option to include space weather effects (can be large)

  • Stop time must be set by keyword argument, either explicitely or by duration

  • Solid Earth tides are not (yet) included in the model

Propagate statellite ephemeris (position, velocity in gcrs & time) to new time and output new position and velocity via Runge-Kutta integration.

Inputs and outputs are all in the Geocentric Celestial Reference Frame (GCRF)

Parameters:

  • pos (npt.ArrayLike[float]) – 3-element numpy array representing satellite GCRF position in meters

  • vel (npt.ArrayLike[float]) – 3-element numpy array representing satellite GCRF velocity in m/s

  • tm (satkit.time) – satkit.time object representing instant at which satellite is at “pos” & “vel”

Keyword Arguments:

  • stop_time (satkit.time) – satkit.time object representing instant at which new position and velocity will be computed

  • duration_secs (float) – duration in seconds from “tm” for at which new position and velocity will be computed.

  • duration_days (float) – duration in days from “tm” at which new position and velocity will be computed.

  • duration (satkit.duration) – duration from “tm” at which new position & velocity will be computed.

  • output_phi (bool) – Output 6x6 state transition matrix between “starttime” and “stoptime” (and at intervals, if specified)

  • propsettings (propsettings) – “propsettings” object with input settings for the propagation. if left out, default will be used.

  • satproperties (satproperties_static) – “SatPropertiesStatic” object with drag and radiation pressure succeptibility of satellite. If left out, drag and radiation pressure are neglected

  • output_dense – boolean indicting whether or not dense output should be recorded. Default is false. If true, this will allow for calling the “interp” function to query states at arbitrary times between the start time and the stop time

Returns:

Propagation result object holding state outputs, statistics, and dense output if requested

Return type:

(propresult)

class satkit.satprop.propresult

Results of a satellite propagation

This class lets the user access results of the satellite propagation

interp(output_phi: bool = False)

Interpolate state at given time

Parameters:

time (satkit.time) – Time at which to interpolate state

Keyword Arguments:

output_phi (bool) – Output 6x6 state transition matrix at the interpolated time

Returns:

6-element vector representing state at given time if output_phi, also output 6x6 state transition matrix at given time

property phi

6x6 State transition matrix or None if not computed

property pos

GCRF position of satellite, meters

property state

6-element state (pos + vel) of satellite in meters & meters/second

property stats

Statistics of propagation

property time

Time at which state is valid

property vel

GCRF velocity of satellite, meters/second

class satkit.satprop.propsettings

This class contains settings used in the high-precision orbit propgator part of the “satkit” python toolbox

property abs_error

Maxmum absolute value of error for any element in propagated state following ODE integration

Default: 1e-8

property gravity_order

Earth gravity order to use in ODE integration

Default: 4

property rel_error

Maximum relative error of any element in propagated state following ODE integration

Default: 1e-8

property use_jplephem

Use high-precision but computationally expensive JPL ephemerides for sun and mun when computing their gravitational force

property use_spaceweather

Use space weather data when computing atmospheric density for drag forces

Default: true

Notes

  • Space weather data can have a large effect on the density of the atmosphere

  • This can be important for accurate drag force calculations

  • Space weather data is updated every 3 hours. Most-recent data can be downloaded with satkit.utils.update_datafiles()

class satkit.satprop.propstats
property num_accept

Number of accepted steps in adaptive RK integrator

property num_eval

Number of function evaluations

property num_reject

Number of rejected steps in adaptive RK integrator

class satkit.satprop.satproperties_static(*args, **kwargs)

Satellite properties relevant for drag and radiation pressure

This class lets the satellite radiation pressure and drag paramters be set to static values for duration of propagation