KnockeRediffusedForceModel.java
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* this work for additional information regarding copyright ownership.
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package org.orekit.forces.radiation;
import java.util.List;
import java.util.stream.Stream;
import org.hipparchus.Field;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.analysis.polynomials.PolynomialFunction;
import org.hipparchus.analysis.polynomials.PolynomialsUtils;
import org.hipparchus.geometry.euclidean.threed.FieldRotation;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Rotation;
import org.hipparchus.geometry.euclidean.threed.RotationConvention;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.MathUtils;
import org.hipparchus.util.SinCos;
import org.orekit.annotation.DefaultDataContext;
import org.orekit.bodies.OneAxisEllipsoid;
import org.orekit.data.DataContext;
import org.orekit.forces.AbstractForceModel;
import org.orekit.frames.FieldTransform;
import org.orekit.frames.Frame;
import org.orekit.frames.Transform;
import org.orekit.propagation.FieldSpacecraftState;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.events.EventDetector;
import org.orekit.propagation.events.FieldEventDetector;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.time.TimeScale;
import org.orekit.utils.Constants;
import org.orekit.utils.ExtendedPVCoordinatesProvider;
import org.orekit.utils.ParameterDriver;
/** The Knocke Earth Albedo and IR emission force model.
* <p>
* This model is based on "EARTH RADIATION PRESSURE EFFECTS ON SATELLITES", 1988, by P. C. Knocke, J. C. Ries, and B. D. Tapley.
* </p> <p>
* This model represents the effects of radiation pressure coming from the Earth.
* It considers Solar radiation which has been reflected by Earth (albedo) and Earth infrared emissions.
* The planet is considered as a sphere and is divided into elementary areas.
* Each elementary area is considered as a plane and emits radiation according to Lambert's law.
* The flux the satellite receives is then equal to the sum of the elementary fluxes coming from Earth.
* </p> <p>
* The radiative model of the satellite, and its ability to diffuse, reflect or absorb radiation is handled
* by a {@link RadiationSensitive radiation sensitive model}.
* </p> <p>
* <b>Caution:</b> The spacecraft state must be defined in an Earth centered frame.
* </p>
*
* @author Thomas Paulet
* @since 10.3
*/
public class KnockeRediffusedForceModel extends AbstractForceModel {
/** Earth rotation around Sun pulsation in rad/sec. */
private static final double EARTH_AROUND_SUN_PULSATION = MathUtils.TWO_PI / Constants.JULIAN_YEAR;
/** Coefficient for solar irradiance computation. */
private static final double ES_COEFF = 4.5606E-6;
/** First coefficient for albedo computation. */
private static final double A0 = 0.34;
/** Second coefficient for albedo computation. */
private static final double C0 = 0.;
/** Third coefficient for albedo computation. */
private static final double C1 = 0.10;
/** Fourth coefficient for albedo computation. */
private static final double C2 = 0.;
/** Fifth coefficient for albedo computation. */
private static final double A2 = 0.29;
/** First coefficient for Earth emissivity computation. */
private static final double E0 = 0.68;
/** Second coefficient for Earth emissivity computation. */
private static final double K0 = 0.;
/** Third coefficient for Earth emissivity computation. */
private static final double K1 = -0.07;
/** Fourth coefficient for Earth emissivity computation. */
private static final double K2 = 0.;
/** Fifth coefficient for Earth emissivity computation. */
private static final double E2 = -0.18;
/** Sun model. */
private final ExtendedPVCoordinatesProvider sun;
/** Spacecraft. */
private final RadiationSensitive spacecraft;
/** Angular resolution for emissivity and albedo computation in rad. */
private final double angularResolution;
/** Earth equatorial radius in m. */
private double equatorialRadius;
/** Reference date for periodic terms: December 22nd 1981.
* Without more precision, the choice is to set it at midnight, UTC. */
private final AbsoluteDate referenceEpoch;
/** Default Constructor.
* <p>This constructor uses the {@link DataContext#getDefault() default data context}</p>.
* @param sun Sun model
* @param spacecraft the object physical and geometrical information
* @param equatorialRadius the Earth equatorial radius in m
* @param angularResolution angular resolution in rad
*/
@DefaultDataContext
public KnockeRediffusedForceModel (final ExtendedPVCoordinatesProvider sun,
final RadiationSensitive spacecraft,
final double equatorialRadius,
final double angularResolution) {
this(sun, spacecraft, equatorialRadius, angularResolution, DataContext.getDefault().getTimeScales().getUTC());
}
/** General constructor.
* @param sun Sun model
* @param spacecraft the object physical and geometrical information
* @param equatorialRadius the Earth equatorial radius in m
* @param angularResolution angular resolution in rad
* @param utc the UTC time scale to define reference epoch
*/
public KnockeRediffusedForceModel (final ExtendedPVCoordinatesProvider sun,
final RadiationSensitive spacecraft,
final double equatorialRadius,
final double angularResolution,
final TimeScale utc) {
this.sun = sun;
this.spacecraft = spacecraft;
this.equatorialRadius = equatorialRadius;
this.angularResolution = angularResolution;
this.referenceEpoch = new AbsoluteDate(1981, 12, 22, 0, 0, 0.0, utc);
}
/** {@inheritDoc} */
@Override
public boolean dependsOnPositionOnly() {
return false;
}
/** {@inheritDoc} */
@Override
public Stream<EventDetector> getEventsDetectors() {
return Stream.of();
}
/** {@inheritDoc} */
@Override
public <T extends CalculusFieldElement<T>> Stream<FieldEventDetector<T>> getFieldEventsDetectors(final Field<T> field) {
return Stream.of();
}
/** {@inheritDoc} */
@Override
public Vector3D acceleration(final SpacecraftState s,
final double[] parameters) {
// Get date
final AbsoluteDate date = s.getDate();
// Get frame
final Frame frame = s.getFrame();
// Get satellite position
final Vector3D satellitePosition = s.getPVCoordinates().getPosition();
// Get Sun position
final Vector3D sunPosition = sun.getPVCoordinates(date, frame).getPosition();
// Get spherical Earth model
final OneAxisEllipsoid earth = new OneAxisEllipsoid(equatorialRadius, 0.0, frame);
// Project satellite on Earth as vector
final Vector3D projectedToGround = satellitePosition.normalize().scalarMultiply(equatorialRadius);
// Get elementary vector east for Earth browsing using rotations
final Vector3D east = earth.transform(satellitePosition, frame, date).getEast();
// Initialize rediffused flux with elementary flux coming from the circular area around the projected satellite
final double centerArea = MathUtils.TWO_PI * equatorialRadius * equatorialRadius *
(1.0 - FastMath.cos(angularResolution));
Vector3D rediffusedFlux = computeElementaryFlux(s, projectedToGround, sunPosition, earth, centerArea);
// Sectorize the part of Earth which is seen by the satellite into crown sectors with constant angular resolution
for (double eastAxisOffset = 1.5 * angularResolution;
eastAxisOffset < FastMath.asin(equatorialRadius / satellitePosition.getNorm());
eastAxisOffset = eastAxisOffset + angularResolution) {
// Build rotation transformations to get first crown elementary sector center
final Transform eastRotation = new Transform(date,
new Rotation(east, eastAxisOffset, RotationConvention.VECTOR_OPERATOR));
// Get first elementary crown sector center
final Vector3D firstCrownSectorCenter = eastRotation.transformPosition(projectedToGround);
// Browse the entire crown
for (double radialAxisOffset = 0.5 * angularResolution;
radialAxisOffset < MathUtils.TWO_PI;
radialAxisOffset = radialAxisOffset + angularResolution) {
// Build rotation transformations to get elementary area center
final Transform radialRotation = new Transform(date,
new Rotation(projectedToGround, radialAxisOffset, RotationConvention.VECTOR_OPERATOR));
// Get current elementary crown sector center
final Vector3D currentCenter = radialRotation.transformPosition(firstCrownSectorCenter);
// Compute current elementary crown sector area, it results of the integration of an elementary crown sector
// over the angular resolution
final double sectorArea = equatorialRadius * equatorialRadius *
2.0 * angularResolution * FastMath.sin(0.5 * angularResolution) * FastMath.sin(eastAxisOffset);
// Add current sector contribution to total rediffused flux
rediffusedFlux = rediffusedFlux.add(computeElementaryFlux(s, currentCenter, sunPosition, earth, sectorArea));
}
}
return spacecraft.radiationPressureAcceleration(date, frame, satellitePosition, s.getAttitude().getRotation(),
s.getMass(), rediffusedFlux, parameters);
}
/** {@inheritDoc} */
@Override
public <T extends CalculusFieldElement<T>> FieldVector3D<T> acceleration(final FieldSpacecraftState<T> s,
final T[] parameters) {
// Get date
final FieldAbsoluteDate<T> date = s.getDate();
// Get frame
final Frame frame = s.getFrame();
// Get zero
final T zero = date.getField().getZero();
// Get satellite position
final FieldVector3D<T> satellitePosition = s.getPVCoordinates().getPosition();
// Get Sun position
final FieldVector3D<T> sunPosition = sun.getPVCoordinates(date, frame).getPosition();
// Get spherical Earth model
final OneAxisEllipsoid earth = new OneAxisEllipsoid(equatorialRadius, 0.0, frame);
// Project satellite on Earth as vector
final FieldVector3D<T> projectedToGround = satellitePosition.normalize().scalarMultiply(equatorialRadius);
// Get elementary vector east for Earth browsing using rotations
final FieldVector3D<T> east = earth.transform(satellitePosition, frame, date).getEast();
// Initialize rediffused flux with elementary flux coming from the circular area around the projected satellite
final T centerArea = zero.getPi().multiply(2.0).multiply(equatorialRadius).multiply(equatorialRadius).
multiply(1.0 - FastMath.cos(angularResolution));
FieldVector3D<T> rediffusedFlux = computeElementaryFlux(s, projectedToGround, sunPosition, earth, centerArea);
// Sectorize the part of Earth which is seen by the satellite into crown sectors with constant angular resolution
for (double eastAxisOffset = 1.5 * angularResolution;
eastAxisOffset < FastMath.asin(equatorialRadius / satellitePosition.getNorm().getReal());
eastAxisOffset = eastAxisOffset + angularResolution) {
// Build rotation transformations to get first crown elementary sector center
final FieldTransform<T> eastRotation = new FieldTransform<>(date,
new FieldRotation<>(east,
zero.add(eastAxisOffset),
RotationConvention.VECTOR_OPERATOR));
// Get first elementary crown sector center
final FieldVector3D<T> firstCrownSectorCenter = eastRotation.transformPosition(projectedToGround);
// Browse the entire crown
for (double radialAxisOffset = 0.5 * angularResolution;
radialAxisOffset < MathUtils.TWO_PI;
radialAxisOffset = radialAxisOffset + angularResolution) {
// Build rotation transformations to get elementary area center
final FieldTransform<T> radialRotation = new FieldTransform<>(date,
new FieldRotation<>(projectedToGround,
zero.add(radialAxisOffset),
RotationConvention.VECTOR_OPERATOR));
// Get current elementary crown sector center
final FieldVector3D<T> currentCenter = radialRotation.transformPosition(firstCrownSectorCenter);
// Compute current elementary crown sector area, it results of the integration of an elementary crown sector
// over the angular resolution
final T sectorArea = zero.add(equatorialRadius * equatorialRadius *
2.0 * angularResolution * FastMath.sin(0.5 * angularResolution) * FastMath.sin(eastAxisOffset));
// Add current sector contribution to total rediffused flux
rediffusedFlux = rediffusedFlux.add(computeElementaryFlux(s, currentCenter, sunPosition, earth, sectorArea));
}
}
return spacecraft.radiationPressureAcceleration(date, frame, satellitePosition, s.getAttitude().getRotation(),
s.getMass(), rediffusedFlux, parameters);
}
/** {@inheritDoc} */
@Override
public List<ParameterDriver> getParametersDrivers() {
return spacecraft.getRadiationParametersDrivers();
}
/** Compute Earth albedo.
* Albedo value represents the fraction of solar radiative flux that is reflected by Earth.
* Its value is in [0;1].
* @param date the date
* @param phi the equatorial latitude in rad
* @return the albedo in [0;1]
*/
private double computeAlbedo(final AbsoluteDate date, final double phi) {
// Get duration since coefficient reference epoch
final double deltaT = date.durationFrom(referenceEpoch);
// Compute 1rst Legendre polynomial coeficient
final SinCos sc = FastMath.sinCos(EARTH_AROUND_SUN_PULSATION * deltaT);
final double A1 = C0 +
C1 * sc.cos() +
C2 * sc.sin();
// Get 1rst and 2nd order Legendre polynomials
final PolynomialFunction firstLegendrePolynomial = PolynomialsUtils.createLegendrePolynomial(1);
final PolynomialFunction secondLegendrePolynomial = PolynomialsUtils.createLegendrePolynomial(2);
// Get latitude sinus
final double sinPhi = FastMath.sin(phi);
// Compute albedo
return A0 +
A1 * firstLegendrePolynomial.value(sinPhi) +
A2 * secondLegendrePolynomial.value(sinPhi);
}
/** Compute Earth albedo.
* Albedo value represents the fraction of solar radiative flux that is reflected by Earth.
* Its value is in [0;1].
* @param date the date
* @param phi the equatorial latitude in rad
* @param <T> extends CalculusFieldElement
* @return the albedo in [0;1]
*/
private <T extends CalculusFieldElement<T>> T computeAlbedo(final FieldAbsoluteDate<T> date, final T phi) {
// Get duration since coefficient reference epoch
final T deltaT = date.durationFrom(referenceEpoch);
// Compute 1rst Legendre polynomial coeficient
final FieldSinCos<T> sc = FastMath.sinCos(deltaT.multiply(EARTH_AROUND_SUN_PULSATION));
final T A1 = sc.cos().multiply(C1).add(
sc.sin().multiply(C2)).add(C0);
// Get 1rst and 2nd order Legendre polynomials
final PolynomialFunction firstLegendrePolynomial = PolynomialsUtils.createLegendrePolynomial(1);
final PolynomialFunction secondLegendrePolynomial = PolynomialsUtils.createLegendrePolynomial(2);
// Get latitude sinus
final T sinPhi = FastMath.sin(phi);
// Compute albedo
return firstLegendrePolynomial.value(sinPhi).multiply(A1).add(
secondLegendrePolynomial.value(sinPhi).multiply(A2)).add(A0);
}
/** Compute Earth emisivity.
* Emissivity is used to compute the infrared flux that is emitted by Earth.
* Its value is in [0;1].
* @param date the date
* @param phi the equatorial latitude in rad
* @return the emissivity in [0;1]
*/
private double computeEmissivity(final AbsoluteDate date, final double phi) {
// Get duration since coefficient reference epoch
final double deltaT = date.durationFrom(referenceEpoch);
// Compute 1rst Legendre polynomial coefficient
final SinCos sc = FastMath.sinCos(EARTH_AROUND_SUN_PULSATION * deltaT);
final double E1 = K0 +
K1 * sc.cos() +
K2 * sc.sin();
// Get 1rst and 2nd order Legendre polynomials
final PolynomialFunction firstLegendrePolynomial = PolynomialsUtils.createLegendrePolynomial(1);
final PolynomialFunction secondLegendrePolynomial = PolynomialsUtils.createLegendrePolynomial(2);
// Get latitude sinus
final double sinPhi = FastMath.sin(phi);
// Compute albedo
return E0 +
E1 * firstLegendrePolynomial.value(sinPhi) +
E2 * secondLegendrePolynomial.value(sinPhi);
}
/** Compute Earth emisivity.
* Emissivity is used to compute the infrared flux that is emitted by Earth.
* Its value is in [0;1].
* @param date the date
* @param phi the equatorial latitude in rad
* @param <T> extends CalculusFieldElement
* @return the emissivity in [0;1]
*/
private <T extends CalculusFieldElement<T>> T computeEmissivity(final FieldAbsoluteDate<T> date, final T phi) {
// Get duration since coefficient reference epoch
final T deltaT = date.durationFrom(referenceEpoch);
// Compute 1rst Legendre polynomial coeficient
final FieldSinCos<T> sc = FastMath.sinCos(deltaT.multiply(EARTH_AROUND_SUN_PULSATION));
final T E1 = sc.cos().multiply(K1).add(
sc.sin().multiply(K2)).add(K0);
// Get 1rst and 2nd order Legendre polynomials
final PolynomialFunction firstLegendrePolynomial = PolynomialsUtils.createLegendrePolynomial(1);
final PolynomialFunction secondLegendrePolynomial = PolynomialsUtils.createLegendrePolynomial(2);
// Get latitude sinus
final T sinPhi = FastMath.sin(phi);
// Compute albedo
return firstLegendrePolynomial.value(sinPhi).multiply(E1).add(
secondLegendrePolynomial.value(sinPhi).multiply(E2)).add(E0);
}
/** Compute total solar flux impacting Earth.
* @param sunPosition the Sun position in an Earth centered frame
* @return the total solar flux impacting Earth in J/m^3
*/
private double computeSolarFlux(final Vector3D sunPosition) {
// Compute Earth - Sun distance in UA
final double earthSunDistance = sunPosition.getNorm() / Constants.JPL_SSD_ASTRONOMICAL_UNIT;
// Compute Solar flux
return ES_COEFF * Constants.SPEED_OF_LIGHT / (earthSunDistance * earthSunDistance);
}
/** Compute total solar flux impacting Earth.
* @param sunPosition the Sun position in an Earth centered frame
* @param <T> extends CalculusFieldElement
* @return the total solar flux impacting Earth in J/m^3
*/
private <T extends CalculusFieldElement<T>> T computeSolarFlux(final FieldVector3D<T> sunPosition) {
// Compute Earth - Sun distance in UA
final T earthSunDistance = sunPosition.getNorm().divide(Constants.JPL_SSD_ASTRONOMICAL_UNIT);
// Compute Solar flux
return earthSunDistance.multiply(earthSunDistance).reciprocal().multiply(ES_COEFF * Constants.SPEED_OF_LIGHT);
}
/** Compute elementary rediffused flux on satellite.
* @param state the current spacecraft state
* @param elementCenter the position of the considered area center
* @param sunPosition the position of the Sun in the spacecraft frame
* @param earth the Earth model
* @param elementArea the area of the current element
* @return the rediffused flux from considered element on the spacecraft
*/
private Vector3D computeElementaryFlux(final SpacecraftState state,
final Vector3D elementCenter,
final Vector3D sunPosition,
final OneAxisEllipsoid earth,
final double elementArea) {
// Get satellite position
final Vector3D satellitePosition = state.getPVCoordinates().getPosition();
// Get current date
final AbsoluteDate date = state.getDate();
// Get frame
final Frame frame = state.getFrame();
// Get solar flux impacting Earth
final double solarFlux = computeSolarFlux(sunPosition);
// Get satellite viewing angle as seen from current elementary area
final double alpha = Vector3D.angle(elementCenter, satellitePosition);
// Check that satellite sees the current area
if (FastMath.abs(alpha) < MathUtils.SEMI_PI) {
// Get current elementary area center latitude
final double currentLatitude = earth.transform(elementCenter, frame, date).getLatitude();
// Compute Earth emissivity value
final double e = computeEmissivity(date, currentLatitude);
// Initialize albedo
double a = 0.0;
// Check if elementary area is in day light
final double sunAngle = Vector3D.angle(elementCenter, sunPosition);
if (FastMath.abs(sunAngle) < MathUtils.SEMI_PI) {
// Elementary area is in day light, compute albedo value
a = computeAlbedo(date, currentLatitude);
}
// Compute elementary area contribution to rediffused flux
final double albedoAndIR = a * solarFlux * FastMath.cos(sunAngle) +
e * solarFlux * 0.25;
// Compute elementary area - satellite vector and distance
final Vector3D r = satellitePosition.subtract(elementCenter);
final double rNorm = r.getNorm();
// Compute attenuated projected elemetary area vector
final Vector3D projectedAreaVector = r.scalarMultiply(elementArea * FastMath.cos(alpha) /
(FastMath.PI * rNorm * rNorm * rNorm));
// Compute elementary radiation flux from current elementary area
return projectedAreaVector.scalarMultiply(albedoAndIR / Constants.SPEED_OF_LIGHT);
} else {
// Spacecraft does not see the elementary area
return new Vector3D(0.0, 0.0, 0.0);
}
}
/** Compute elementary rediffused flux on satellite.
* @param state the current spacecraft state
* @param elementCenter the position of the considered area center
* @param sunPosition the position of the Sun in the spacecraft frame
* @param earth the Earth model
* @param elementArea the area of the current element
* @param <T> extends CalculusFieldElement
* @return the rediffused flux from considered element on the spacecraft
*/
private <T extends CalculusFieldElement<T>> FieldVector3D<T> computeElementaryFlux(final FieldSpacecraftState<T> state,
final FieldVector3D<T> elementCenter,
final FieldVector3D<T> sunPosition,
final OneAxisEllipsoid earth,
final T elementArea) {
// Get satellite position
final FieldVector3D<T> satellitePosition = state.getPVCoordinates().getPosition();
// Get current date
final FieldAbsoluteDate<T> date = state.getDate();
// Get frame
final Frame frame = state.getFrame();
// Get zero
final T zero = date.getField().getZero();
// Get solar flux impacting Earth
final T solarFlux = computeSolarFlux(sunPosition);
// Get satellite viewing angle as seen from current elementary area
final T alpha = FieldVector3D.angle(elementCenter, satellitePosition);
// Check that satellite sees the current area
if (FastMath.abs(alpha).getReal() < MathUtils.SEMI_PI) {
// Get current elementary area center latitude
final T currentLatitude = earth.transform(elementCenter, frame, date).getLatitude();
// Compute Earth emissivity value
final T e = computeEmissivity(date, currentLatitude);
// Initialize albedo
T a = zero;
// Check if elementary area is in day light
final T sunAngle = FieldVector3D.angle(elementCenter, sunPosition);
if (FastMath.abs(sunAngle).getReal() < MathUtils.SEMI_PI) {
// Elementary area is in day light, compute albedo value
a = computeAlbedo(date, currentLatitude);
}
// Compute elementary area contribution to rediffused flux
final T albedoAndIR = a.multiply(solarFlux).multiply(FastMath.cos(sunAngle)).add(
e.multiply(solarFlux).multiply(0.25));
// Compute elementary area - satellite vector and distance
final FieldVector3D<T> r = satellitePosition.subtract(elementCenter);
final T rNorm = r.getNorm();
// Compute attenuated projected elemetary area vector
final FieldVector3D<T> projectedAreaVector = r.scalarMultiply(elementArea.multiply(FastMath.cos(alpha)).divide(
rNorm.multiply(rNorm).multiply(rNorm).multiply(zero.getPi())));
// Compute elementary radiation flux from current elementary area
return projectedAreaVector.scalarMultiply(albedoAndIR.divide(Constants.SPEED_OF_LIGHT));
} else {
// Spacecraft does not see the elementary area
return new FieldVector3D<T>(zero, zero, zero);
}
}
}