cascade.dynamics.simple_earth#

cascade.dynamics.simple_earth(J2: bool = True, J3: bool = False, J4: bool = False, C22S22: bool = True, sun: bool = False, moon: bool = False, SRP: bool = False, drag: bool = True) → List[Tuple[expression, expression]]#

Perturbed dynamics around the Earth.

Returns heyoka expressions to be used as dynamics in sim and corresponding to the Earth orbital environment as perturbed by selectable term (all in SI units).

The equations are taken from those used during the ESA Kelvins competition “Space Debris: the Origin” adding a drag term.

The reference frame used is the EME2000 and thus a simulation time of zero will refer to the epoch 2000 JAN 01 12:00:00, or JD 2451545.0

Note

The equations are largely derived from: Celletti, Alessandra, et al. “Dynamical models and the onset of chaos in space debris.” International Journal of Non-Linear Mechanics 90 (2017): 147-163. (arxiv)

Note

If drag is active, the BSTAR coefficient (SI units) of the object must be passed as a first simulation parameter in sim, if SRP is active, the term Cr*AOM (SI units) must be also passed as a simulation parameter (after BSTAR if present), being Cr the coefficient of reflectivity of the spacecraft and AOM the area-to-mass-ratio.

Parameters:

  • J2 (bool, optional) – adds the Earth J2 spherical harmonic (C20 Stokes’ coefficient). Defaults to True.

  • J3 (bool, optional) – adds the Earth J3 spherical harmonic (C30 Stokes’ coefficient). Defaults to False.

  • J4 (bool, optional) – adds the Earth J4 spherical harmonic (C40 Stokes’ coefficient). Defaults to False.

  • C22S22 (bool, optional) – adds the Earth C22 and S22 Stokes’ coefficients. Defaults to True.

  • sun (bool, optional) – adds the Sun gravity. Defaults to False.

  • moon (bool, optional) – adds the Moon gravity. Defaults to False.

  • SRP (bool, optional) – adds the solar radiation pressure. Defaults to False.

  • drag (bool, optional) – adds the drag acceleration (atmosphere is modelled via a fitted isotropic NRLMSISE00). Defaults to True.

Returns:

The dynamics in SI units. Can be used to instantiate a sim.