Solar Pressure

For solar pressure, set the following parameters:

Solar Pressure
Parameter Description
Use

Select among:

  • Based on Orbit - Model solar radiation pressure if the apogee of the spacecraft's orbit is above the threshold for the orbit class. Applicable thresholds can be set at the scenario level. This option will always result in the modeling of solar radiation pressure for satellites around non Earth central bodies.
  • No - Do not model solar radiation pressure, even if the apogee is above the threshold.
  • Yes - Model solar radiation pressure, even if the apogee falls below the threshold.
WillUseSolarPressure

This is a read-only field, with a boolean (true/false) value that reflects the result of the selection made in the Use field:

  • If Yes is selected: always true.
  • If No is selected: always false.
  • If Based on Orbit is selected and the central body is the Earth: true if the apogee is above the threshold, otherwise false. For satellites around non Earth central bodies: always true.
EstimateSRP A correction to the nominal solar pressure coefficient, (ΔCr), or to the product Δ (Cr A / M) will be estimated by the filter if set to true and SRP effects are modeled. Also controls if the nominal solar pressure coefficient can be perturbed by the simulator. The estimate flag must also be set to true if this parameter is to be used as a Least Squares Consider State. When used as a consider state it is modeled as a constant.
Model Select either "Spherical" and enter the related parameters immediately below, or select one of the GPS solar pressure models described after the table, or select ReflectionPlugin for a user defined Reflection Plugin model.
SpecModel

Specifies the method for input of solar pressure coefficient information.

  • Cr A / M - If set to this method, the product is entered directly. This is the common case for space surveillance where the individual constituents are not known. Changes to area or mass will cause the Cr value to be updated.
  • MassAreaCr - If set to this method, then the individual constituents (Mass, SRP Area and coefficient of pressure) are entered. This is the common case of satellite operators who have specific knowledge of the satellite physical characteristics. Changes to Cr, area or mass will cause the CrAoverM value to be updated.

Available when "Spherical" Model is selected.

CorrectionType

Specify the estimation solve for to be used in estimating corrections to acceleration due to solar pressure. The area referenced here, A, is that which is associated with solar pressure modeling. Choose between:

  • Cr Additive – estimate an additive correction to Cr
  • CrA/M Additive – estimate an additive correction to (Cr A / M)
  • CrA/M Relative - estimate a relative correction to (Δ(Cr A / M) / (Cr A / M) )
Available when "Spherical" Model is selected.
Cr

Specify the solar pressure coefficient (Cr) to be used in calculating acceleration due to solar pressure.

Available when "Spherical" Model is selected.

Area

Cross-sectional area of the spacecraft in the selected distance unit squared, for computation of solar radiation pressure.


Available when "Spherical" Model is selected.

CrAoverM

Specify the product of the solar pressure coefficient and the solar pressure area divided by the mass (Cr A / M) to be used in calculating acceleration due to solar pressure.

Available when "Spherical" Model is selected.

CrModel

Identifies the Stochastic sequence to be used to represent the Solar Pressure CrModel Coefficient correction, ΔCr or Δ (Cr A / M).

  • GaussMarkov = The correction, ΔCr or Δ (Cr A / M), will be modeled as a scalar exponential Gauss Markov sequence.
  • RandomWalk = The correction, ΔCr or Δ (Cr A / M), will be modeled using a Wiener (Brownian motion) sequence.
  • Vasicek = The correction, ΔCr or Δ (Cr A / M), will be modeled using a Vasicek stochastic sequence. This is a two-parameter model that solves for both a short-term and long-term bias.

Reference the Stochastic Model page for the description and inputs associated with each model.


Available when "Spherical" Model is selected.

Note: Constant is a read-only field whose value is defined by the selected SpecMethod.

ReflectionModel

For Spherical SRP model. Select between:

  • Sphere with diffuse reflection - coefficient of reflectivity (Cr) is scaled by 13/9
  • Sphere with perfect absorption - Cr is not subjected to additional scaling

Available when "Spherical" Model is selected.

SunPosMethod Specifies the algorithm to be used in the computation of the position of the Sun for input to the solar radiation pressure model. Options are to compute the true position of the Sun, apparent position of the Sun to an observer at the center of the Earth or the apparent position of the Sun based on the satellite position.
EclipsingBodies Select from a list of available solar system bodies to include in shadowing computations. The entries in this list are in addition to the central body associated with the satellite unless that satellite is the "Sun" in which case it is not considered as an eclipsing body.
UseInVariationalEquations Set to true to have solar pressure accelerations included in the variational equations for the propagation of covariance. It is recommended that this flag be set to true for high altitude satellites.
AddProcessNoise This controls the addition of white process noise in two components (specified via the EclipticNorthFraction and the EclipticPlaneFraction attributes) normal to the sun-to-satellite line. This is useful when significant solar pressure accelerations exist in these directions, since the solar pressure model cannot account for such accelerations. Process noise along the sun-to-satellite line is added when the solar pressure coefficient is estimated.
EclipticNorthFraction When SRP process noise is added, the acceleration noise added in the direction normal to the sun-to-satellite line and normal to the ecliptic plane is computed as the magnitude of the nominal solar pressure acceleration multiplied by the EclipticNorthFraction. For example, to add white noise equal to 50% of the nominal acceleration in the Ecliptic North direction, specify a value of 0.5.
EclipticPlaneFraction When SRP process noise is added, the acceleration noise added in the direction normal to the sun-to-satellite line and in the ecliptic plane is computed as the magnitude of the nominal solar pressure acceleration multiplied by the EclipticPlaneFraction. For example, to add white noise equal to 50% of the nominal acceleration in the Ecliptic Plane, specify a value of 0.5.

Scripting Examples

set srp  = sat.ForceModel.SolarPressure

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
'  Use Spherical model represented by a Scalar Gauss Markov sequence
'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

srp.Model.Type = "Spherical"
srp.Model.Area.Set 6,"m^2" 
srp.Model.ReflectionModel = "Sphere with perfect absorption"

srp.Model.CPModel.Type = "GaussMarkov"
srp.Model.CPModel.Constant        = 1.1 
srp.Model.CPModel.InitialEstimate = 0 
srp.Model.CPModel.Sigma           = 0.25
srp.Model.CPModel.HalfLife.Set 2880,"min"

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
'  Use Spherical model represented by a Vasicek sequence
'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

srp.Model.Type = "Spherical"
srp.Model.Area.Set 6,"m^2" 
srp.Model.ReflectionModel = "Sphere with perfect absorption"

srp.Model.CPModel.Type = "Vasicek"
srp.Model.CPModel.LongTerm.Constant = 1.1 
srp.Model.CPModel.LongTerm.Sigma    = 0.25
srp.Model.CPModel.ShortTerm.InitialEstimate = 0
srp.Model.CPModel.ShortTerm.Sigma = 0.05
srp.Model.CPModel.ShortTerm.HalfLife.Set 60,"min"
          

GPS Solar Pressure Models & Parameters

The following solar pressure models are intended specifically to be used with GPS satellites.

Models

GPS_BlkIIA_GSPM04a and GPS_BlkIIR_GSPM04a: Implementation of the JPL GSPM.04a models for Block IIA and Block IIR satellites following reference 1, below. This model was derived from a study of non-eclipsing satellites. The model is dependent on the angle of the sun out of the orbit plane (the beta angle), but holds the absolute value of the beta angle at 14.5 degrees for cases where the actual beta angle goes below 14.5, as is the case for eclipsing satellites. The form of the model is the same for Block IIA and Block IIR satellites, but the coefficients are different.

GPS_BlkIIA_GSPM04ae and GPS_BlkIIR_GSPM04ae: Implementation of the JPL GSPM.04ae models for Block IIA and Block IIR satellites following reference 2. This model was derived as an extension of the GSPM.04a models (reference 1), where the models deviate from the GSPM.04a models only for eclipsing satellites. The model is dependent on the angle of the sun out of the orbit plane (the beta angle), but drops one term involving division by the sine of the beta angle when the beta angle goes below one degree. The form of the model is the same for Block IIA and Block IIR satellites, but the coefficients are different.

GPS_BlkIIA_AeroT20: Model for use with Block IIA satellites. Implementation follows reference 3. Model originally presented in reference 4.

GPS_BlkIIR_AeroT30: Model for use with Block IIR satellites. Implementation follows reference 3. Model originally presented in reference 4.

Parameters

The following parameters apply to all of the above models:

GPS Solar Pressure Model Parameters
Parameter Description
K1Model

"K1" refers to the unitless scale parameter for computed acceleration in the satellite body fixed X-Z plane, which contains the sun to satellite line. Nominally the value of K1 is near 1.0. Enter the Stochastic sequence to be used to represent the correction to K1, ΔK1

  • GaussMarkov = K1 will be modeled as a scalar exponential Gauss Markov sequence.
  • RandomWalk = K1 will be modeled using a Wiener (Brownian motion) sequence.
  • Vasicek = K1 will be modeled using a Vasicek stochastic sequence. This is a two-parameter model that solves for both a short-term and long-term bias.
Reference the Stochastic Model page for the description and inputs associated with each model.
K2Model

"K2" refers to the scale parameter for acceleration along the body-fixed Y axis of the satellite. Input is unitless but is multiplied by 1e-12 km/sec^2 to give the acceleration, often referred to as the Y bias. The resulting acceleration is perpendicular to the sun-to-satellite line, and the body-fixed Y axis points in opposite directions for the Block IIA and Block IIR satellites. Nominally the value of K2 is in the range of -1 < K2 < 1.

Enter the Stochastic sequence to be used to represent the correction to K2, ΔK2

  • GaussMarkov = K2 will be modeled as a scalar exponential Gauss Markov sequence.
  • RandomWalk = K2 will be modeled using a Wiener (Brownian motion) sequence.
  • Vasicek = K2 will be modeled using a Vasicek stochastic sequence. This is a two-parameter model that solves for both a short-term and long-term bias.
Reference the Stochastic Model page for the description and inputs associated with each model.

References

  1. Bar-Sever, Y., Kuang, D., "New Empirically Derived Solar Radiation Pressure Model for Global Positioning System Satellites", IPN Progress Report 42-159, November 15, 2004.
  2. Bar-Sever, Y., Kuang, D., "New Empirically Derived Solar Radiation Pressure Model for Global Positioning System Satellites During Eclipse Seasons", IPN Progress Report 42-160, February 15, 2005.
  3. O’Toole, James W., "Mathematical Description of the OMNIS Satellite Orbit Generation Program (OrbGen)", NSWCDD/TR-02/118, May 2004.
  4. Fliegel, H.F., Gallini, T.E., Swift, E.R., "Global Positioning System Radiation Force Model for Geodetic Applications", Journal of Geophysical Research, Volume 97, No. B1, January 1992.
  5. Fliegel, H.F., Gallini, T.E., "Solar Force Modeling of Block IIR Global Positioning System Satellites", Journal of Spacecraft and Rockets, Volume 33, No. 6, November-December 1996.

ODTK 6.5