STELA propagation model

Overview of STELA

The Semi-analytic Tool for End of Life Analysis software (STELA) has been designed by CNES (French Space Agency) to support the French Space Operations Act.

The STELA features available in Celestlab include:

• Long term propagation of orbits around Earth
• Computation of state vector's time derivatives due to various forces
• Computation of cross sectional area (not described in this section)

Force model (propagation or computation of derivatives)

STELA takes into account the effects of Earth gravity, third body (Sun and Moon) perturbations, atmospheric drag, solar radiation pressure and apparent acceleration (effect of non-inertiallity of the frame in which the motion is integrated).

The perturbations are modeled as follows (see STELA user's manual for more details):

• Earth gravity: Potential with degree and order up to 15 (including the effect of J2^2).

• Sun and Moon gravity: the computation is based on Sun and Moon positions computed using a simplified Meeus model for the Moon and Brown model for the Sun. The model for the Moon consists in expansion series including: 6 terms for longitude, 4 terms for latitude, and 4 terms for distance from Earth.

• Atmospheric drag: the atmosphere is supposed to be co-rotating with the Earth. No wind effect is considered. The averaged equations are obtained by quadrature (Simpson).

• Solar radiation pressure: eclipses are taken into account (analytical computation assuming a spherical Earth). The averaged equations are obtained by quadrature (Simpson) over the orbit arc out of the eclipse region.

• Apparent acceleration: The motion is integrated in CIRS, and the reference frame (the frame considered as inertial) can be either CIRS, ICRS or MOD. The acceleration along the orbit path is obtained using a simplified CIRS->ICRS conversion model (to minimize computation time). The averaged equations are obtained by quadrature (Simpson).

Model parameters

The main model parameters used by STELA and available in CelestLab are the following:

Name	Type	Description	Standard value
mass	double > 0	Spacecraft mass (kg)	1000
central_enabled	boolean	Specifies whether or not central force is taken into account	%t
zonal_enabled	boolean	Specifies whether or not zonal harmonics perturbation is taken into account	%t
zonal_maxDeg	integer	Number of zonal harmonics to be used	7
tesseral_enabled	boolean	Specifies whether or not tesseral harmonics are taken into account	%t
tesseral_maxDeg	integer	Number of tesseral harmonics to be used	7
tesseral_minPeriod	double > 0	Minimum period of periodic terms due to tesseral harmonics (s)	86400 * 5
thirdbody_enabled	boolean	Specifies whether or not third body perturbation is taken into account	%t
thirdbody_bodies	string 1xN	Third body names	["Sun", "Moon"]
drag_enabled	boolean	Specifies whether or not drag perturbation is taken into account	%t
drag_coefType	string	Drag coefficient type: "constant", "variable" or "cook"	"constant"
drag_area	double >= 0	Cross sectional area for drag computation (m^2)	10.0
drag_coef	double	Drag coefficient value (if coefficient type is "constant")	2.2
drag_solarActivityType	string	Solar activity type for drag computation: "constant" or "variable"	"constant"
drag_solarActivityFlux	double	Solar flux for drag computation if type is "constant" (sfu)	140.0
drag_solarActivityAp	double	Geomagnetic index value for drag computation (if type is "constant")	15.0
srp_enabled	boolean	Specifies whether or not radiation pressure is taken into account	%t
srp_area	double >= 0	Cross sectional area for SRP computation (m^2)	10.0
srp_coef	double >= 0	Reflectivity coefficient for SRP computation (between 1 and 2)	1.5
ref_frame	string	Frame considered as inertial in propagation: "ECI", "ICRS" or "MOD"	"ICRS"
integrator_step	double	Integration step (s)	86400

Optional (and more advanced) parameters are:

Name	Type	Description	Default value
reentryAltitude	double >= 0	Altitude under which propagation stops (m)	80000
drag_atmosphericModel	string	Atmospheric model to be used	"NRLMSISE-00"
drag_nbQuadPoints	integer > 0, odd	Number of quadrature points for drag computation	33
drag_nbComputeSteps	integer > 0	Number of time steps between drag computations	1
drag_cookWallTemp	double > 0	Wall temperature for "cook" drag coefficient computation (K)	300
drag_cookAccomodCoef	double > 0	Accomodation parameter for "cook" drag coefficient computation	4.0
srp_nbQuadPoints	integer > 0, odd	Number of quadrature points for SRP computation	11
appAcc_nbQuadPoints	integer > 0, odd	Number of quadrature points for apparent acceleration computation	7
thirdbody_degree	integer > 0	Third body potential expansion degree (Sun or Moon)	4

Additional parameters (for advanced users) may be specified:

Name	Type	Description	Default value
solarActivityFile	string	Solar and geomagnetic data file path	"" (= default file path)
aeroCoefFile	string	Aerodynamic coefficient file path	"" (= default file path)

Note: The solar activity and aero coefficient file paths can be either absolute, or relative to the STELA configuration directory (= default location for these files).

Specific aspects of CelestLab version

Differences in parameter definitions:

• The parameter tesseral_minPeriod is a duration rather than a multiple of the integration step.
• The parameter central_enabled specifies whether or not the central force should be taken into account. It must be true for propagation, true or false for the computation of derivatives.
• The parameter thirdbody_bodies has been added. "Sun" and "Moon" are the only accepted body names.
• The parameter ref_frame gives the name of the frame considered as inertial. It can be "ICRS", "CIRS" or "MOD". The interface also accepts "ECI" which actually means "CIRS".
• Model constants (gravitational parameters, potential coefficients...) can be changed through CelestLab. The constants used can be either the one defined STELA or the one defined in CelestLab. See the configuration menu for the option currently selected.

Notes:

• The default area to mass ratio (both for drag and SRP computation) is 0.01 m^2/kg, which is a value commonly seen in practical applications.
• The default (constant) solar activity and geomagnetic values corresponds to a medium solar activity level.

References

1) STELA software and associated user manual on CNES freeware server.