User Manual 4.8 Celestial bodies

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Introduction

Scope

The celestial bodies are described by their main features : position and geometry. The positions are ephemeris that must be loaded from models, the geometries are created as one axis ellipsoids. The package provides a factory able to create any celestial body of the solar system.

Javadoc

The classes for bodies description are available in the package bodies of Patrius.

Library Javadoc
Orekit Package fr.cnes.sirius.patrius.bodies
Patrius Package fr.cnes.sirius.patrius.bodies

Links

Orekit bodies : Orekit Bodies architecture description

IAU report : Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009

Useful Documents

None as of now.

Package Overview

Bodiesorekit.JPG

This package overview is from the OREKIT website, under apache license.

Features Description

Celestial bodies

The Moon, the Sun and planets of the solar system are all represented by the CelestialBody interface. This class associates a name (eg Sun) to :

  • a gravitational coefficient GM
  • a body centered inertial frame (which can be retrieved with method getInertiallyOrientedFrame()).
  • a body centered rotating frame (which can be retrieved with method getBodyOrientedFrame()).

Inertially-oriented and body-oriented frames are defined in the following way:

  • Body-centered inertial frame is centered on the celestial body centered and pole axis (Z axis) is shifted by right ascension α and declination δ.
  • Body-centered rotating frame is linked to inertially-oriented frame by a rotation of angle W(t) (reference values for W(t) is provided by IAU).
CelestialBodyFrame.png

To build a celestial body, the user can:

  • use the static methods of the CelestialBodyFactory to create instances of the most common celestial bodies (Moon, Sun, Jupiter, etc.). JPL Ephemeris data are used. Warning: using the factory requires to load JPL Ephemeris data beforehand.
  • use the simplified models (Meeus, etc.).
  • creates its own celestial body using the class UserCelestialBody as well as its own pole motion using the class UserIAUPole.

These methods are detailed in the following sections.

Ephemeris Loader

For any celestial body of the Solar System, the actual computation of its position and velocity relies on the JPL planetary ephemerides files. These files are binary files and loaded thanks to the JPLEphemeridesLoader object.

For the moment, this object is able to load JPL DE XXX files and IMCCE INPOP files which are the most commonly used data files (see below for an exact list of accepted files). For instance with the most common files, the JPL DE 405 covers the years 1600 to 2200 at maximum precision, the JPL DE 406 covers the years-3000 to +3000 at only slightly reduced precision. The DE 405 file is the basis for the Astronomical Almanac and leads to sufficiently accurate results and, for most purposes, even the accuracy of DE 406 is sufficient.

JPLEphemeridesLoader

In order to generate the ephemerides of one celestial body of the Solar System, one has to use the JPLEphemeridesLoader as follows : 

 
final JPLEphemeridesLoader loaderEMB = new JPLEphemeridesLoader(fileName, 
                   JPLEphemeridesLoader.EphemerisType.EARTH_MOON);
final JPLEphemeridesLoader loaderSSB = new JPLEphemeridesLoader(fileName, 
                   JPLEphemeridesLoader.EphemerisType.SOLAR_SYSTEM_BARYCENTER);
CelestialBodyFactory.addCelestialBodyLoader(CelestialBodyFactory.EARTH_MOON, loaderEMB);
CelestialBodyFactory.addCelestialBodyLoader(CelestialBodyFactory.SOLAR_SYSTEM_BARYCENTER, loaderSSB);
 
// Reference frame
Frame icrf = FramesFactory.getICRF();
 
// Ephemeris of the Sun
JPLEphemeridesLoader loader = new JPLEphemeridesLoader("unxp2000.405", 
                JPLEphemeridesLoader.EphemerisType.SUN);
 
// Creation of the Sun
CelestialBody sun = loader.loadCelestialBody(CelestialBodyFactory.SUN);
 
// Coordinates of the Sun given a date and a reference frame
PVCoordinates pvSun = sun.getPVCoordinates(date, icrf);

When the user wants to create a JPLEphemeridesLoader, first of all, he must supply the folder where the DE XXX files are stored. Then he has to give the name of the file which contains the data (DE XXX), the type of celestial body and a date (desired central date) as entries of the JPLEphemeridesLoader.

The first argument (name of the data file) may be null. In this case, Patrius takes the first compatible file found. If one wants only files from the DE 405 ephemerides, for instance, he has to give the String "^unx[mp](\\d\\d\\d\\d)\\.(?:405)$". The last argument can also be null. If the central date is not mentionned an arbitrary 100 days range will be loaded whereas if it is mentionned all data within a +/-50 days range around this date will be loaded.

Once the data is loaded, thanks to the JPLEphemeridesLoader, the user can create the celestial body with the method loadCelestialBody() of the JPLEphemeridesLoader class. To do so, the user has to be sure that all required data is loaded. Indeed, apart from the Moon, the Earth and the Earth-Moon barycenter, the creation of a celestial body requires some data on the Earth Moon barycenter and the Solar System barycenter in order to instanciate the frame in which the ephemerides of the celestial body will be defined. Therefore, the user has to create a JPLEphemeridesLoader for the Earth-Moon barycenter and the Solar System barycenter prior to creating the celestial body, otherwise Patrius will arbitrarily load a DE file to generate the corresponding ephemerides that are used afterwards for the generation of the frame. Then the user has to complete the list of the loaders of the CelestialBodyFactory with these two loaders before calling the method loadCelestialBody().

NB : The user has to clean the CelestialBodyFactory memory if he does not want to work with the previously defined celestial bodies.

JPL ephemerides

The JPL ephemerides data is available on the JPL FTP server [R3].

Available ephemerides :


Development Ephemerides Created in... Description
DE200 September 1981 includes nutations but not librations.

Referred to the dynamical equator and equinox of 2000.
Covers JED 2305424.8 (1599 DEC 09) to JED 2513360.5 (2169 MAR 31).

This ephemeris was used for the Astronomical Almanac from 1984 to 2003. (See Standish, 1982 and Standish, 1990).

DE202 October 1987 includes nutations and librations.

Referred to the dynamical equator and equinox of 2000.
Covers JED 2414992.5 (1899 DEC 04) to JED 2469808.5 (2050 JAN 02).

DE403 May 1993 includes nutations and librations.

Referred to the International Celestial Reference Frame.
Covers JED 2305200.5 (1599 APR 29) to JED 2524400.5 (2199 JUN 22).

Fit to planetary and lunar laser ranging data.(See Folkner et al. 1994).

DE405, DE406 May 1997 For the DE405:

includes both nutations and librations.
Referred to the International Celestial Reference Frame.
Covers JED 2305424.80 (1599 DEC 09) to JED 2525008.50 (2201 FEB 20)

For the DE406 :

the same as the DE405 except the time span : Spans JED 0624976.50 (-3001 FEB 04) to 2816912.50 (+3000 MAY 06)

This is the same integration as DE405, with the accuracy of the interpolating polynomials has been lessened to reduce file size for the longer time span covered by the file.

DE410 April 2003 includes nutations and librations.

Referred to the International Celestial Reference Frame.
Covers JED 2415056.5 (1900 FEB 06) to JED 2458832.5 (2019 DEC 15).

Ephemeris used for Mars Exploration Rover navigation.

DE413 November 2004 includes nutations and librations.

Referred to the International Celestial Reference Frame.
Covers JED 2414992.5, (1899 DEC 04) to JED 2469872.5 (2050 MAR 07).

Created to update the orbit of Pluto to aid in planning for an occultation of a relatively bright star by Charon on 11 July 2005.

DE414 May 2005 includes nutations and librations.

Covers JED 2414992.5, (1899 DEC 04) to JED 2469872.5 (2050 MAR 07).

Fit to ranging data from MGS and Odyssey through 2003. (See Konopliv et al., 2006.)

DE418 August 2007 includes nutations and librations.

Covers JED 2414864.8 (1899 JUL 29) to JED 2470192.5 (2051 JAN 21)

DE421 February 2008 includes nutations and librations.

Referred to the International Celestial Reference Frame.
Covers JED 2414864.8 (1899 JUL 29) to JED 2471184.8 (2053 OCT 09)

Fit to planetary and lunar laser ranging data. (See Folkner et al., 2009)

DE422 September 2009 includes nutations and librations.

Referred to the International Celestial Reference Frame.
Covers JED 625648.5, (-3000 DEC 07) to JED 2816816.5, (3000 JAN 30).

Intended for the MESSENGER mission to Mercury.
Extended integration time to serve as successor to DE406.
Fit to ranging data from MGS and Odyssey through 2003. (See Konopliv et al., 2010.)

DE423 February 2010 includes nutations and librations.

Referred to the International Celestial Reference Frame version 2.0.
Covers JED 2378480.5, (1799 DEC 16) to JED 2524624.8, (2200 FEB 02).

Intended for the MESSENGER mission to Mercury.

IMCCE INPOP ephemerides

The IMCCE INPOP ephemeris is available on IMCCE website.

Available INPOP ephemerides :

  • 06b
  • 06c
  • 08a
  • 10a
  • 10b
  • 10e
  • 13c
  • 17a
  • 19a

Simplified analytical models

Meeus Model

The Meeus Model is a simplified model which gives the position of the Sun and the Moon with respect to the time T expressed in centuries (TT time scale). This model is an analytical model less precise than the DE ephemerides given by JPL. It is adapted for onboard applications. The class implementing the Meeus Model allows three different models computing the position of the Sun with appropriate equations : the standard model (provided by Jean Meeus), the Stela model and an onboard model. The main differences between these model is the computation of the obliquity of the ecliptic : indeed, its value is fixed to 0 for the standard model, given by an expression involving [math]T, T^{2}[/math]for Stela model and [math]T, T^{2}, T^{3}[/math] for the onboard model. Moreover, the onboard model computed the position in J2000 frame, whereas standard and Stela models use respectively EOD and MOD frame.

Regarding the precision, one has to expect a maximum difference of 25593km in position for the Sun and a maximum angular difference of 34.8 (wrt DE405 ephemerides). For the Moon, one has to expect a maximum difference of 26 km in position and a maximum angular difference of 15.2 (wrt DE405 ephemerides). As for the performances (in terms of execution time), the Meeus model for the Sun is faster than the DE405 ephemerides. However, we did not come to the same conclusion for the Moon even by decreasing the degree of precision (number of terms taken into account to compute the latitude, longitude and distance which are needed to compute in fine the position of the Moon).

Deviation in position wrt DE423 Angular deviation wrt DE423
Sun 12000 km 34.8
Moon 62x66x46 12.4 km 15.2
Moon 26x13x13 225 km 122
Moon 9x4x3 1591 km 889
Deviation in position wrt DE405 Angular deviation wrt DE405
Sun 25593km 34.8
Moon 62x66x46 26 km 15.2


Number of elementary operations Number of trigonometric operations
Sun 89 10
Moon 62x66x46 2671 182
Moon 26x13x13 917 60
Moon 9x4x3 401 24

References for the tables :

  • "Modèles d'éphémérides luni-solaires", CNES DCT/SB/MS, 03/14/2011
  • "Modèle MEEUS pour éphémérides Lune-Soleil : Compléments sur le nombre d'opérations", CNES DCT/SB/MS
execution time - DE405 execution time- MEEUS
Sun 59 s 548 ms 19 s 938 ms
Moon 62x66x46 11 s 625 ms 3 mn 22 s 323 ms
Moon 26x13x13 11 s 625 ms 1 mn 17 s 74 ms
Moon 9x4x3 11 s 625 ms 40 s 326 ms

In order to build such a Sun or Moon, one has to use the object MeeusSun or MeeusMoon which both extend AbstractCelestialBody. Note that it is not possible to build those celestial bodies from the CelestialBodyFactory, for the moment.

Basic board Sun model

The basic board Sun model is a simplified analytical model which gives the direction of the Sun (the normalized position) with respect to time. This model is similar to the Meeus model (the constants of the model are different) and is adapted for onboard applications. The reference inertial frame is the CIRF.

User-defined celestial bodies

User can defined its own celestial body by using UserCelestialBody. This class requires to provide:

  • Its name.
  • Its position-velocity through time using a PVCoordinateProvider implementation.
  • Its gravitational constant.
  • Its pole motion using IAUPole implementation or directly the UserIAUPole implementation.

The UserIAUPole is a simple way to build standard pole motion from IAU note. It requires to provide for each component (α, δ and W) a list of functions of duration in days and duration in centuries (from a reference epoch) as defined in IAU note. This functions are UnivariateDifferentiableFunction. Available functions in PATRIUS include:

  • PolynomialFunction: polynomial function
  • SineFunction: function of the form k.sin(f) with f an UnivariateDifferentiableFunction
  • CosineFunction: function of the form k.cos(f) with f an UnivariateDifferentiableFunction

Example: building Ceres. According to the IAU report, Ceres has the following parameters:

  • α = 291◦ ± 5◦
  • δ = 59◦ ± 5◦
  • W = 170.90◦ + 952.1532◦d

With d being the interval in days from the standard epoch (the standard epoch is JD 2451545.0, i.e. 2000 January 1 12 hours TDB)

Ceres gravitational constant is 6.263E10 m^^3^^kg^^-1^^s^^-2^^.

If one knows Ceres motion given for instance by a PVCoordinatePropagator pv, then one can build Ceres with the following code: 

// Gravitational parameter
final double gm = 6.263E10;
 
// Pole motion - Method 1 - Implementation if IAUPole interface
final IAUPole pole = new IAUPole() {
    @Override
    public double getPrimeMeridianAngle(final AbsoluteDate date) {
        // W
        final double d = date.durationFrom(AbsoluteDate.J2000_EPOCH) / Constants.JULIAN_DAY;
        return FastMath.toRadians(170.90) + FastMath.toRadians(952.1532)* d;
    }
 
    @Override
    public Vector3D getPole(final AbsoluteDate date) {
        // Pole bias: alpha and delta
        return new Vector3D(FastMath.toRadians(291), FastMath.toRadians(59));
    }
};
 
// Pole motion - Method 2 - Use of UserIAUPole class
// Alpha 0 coefficients
final List<UnivariateDifferentiableFunction> alpha0fDays = new ArrayList<UnivariateDifferentiableFunction>();
alpha0fDays.add(new PolynomialFunction(new double[] { 291 }));
final List<UnivariateDifferentiableFunction> alpha0fCenturies = new ArrayList<UnivariateDifferentiableFunction>();
final IAUPoleCoefficients1D alpha0Coeffs = new IAUPoleCoefficients1D(alpha0fDays, alpha0fCenturies);
// Delta 0 coefficients
final List<UnivariateDifferentiableFunction> delta0fDays = new ArrayList<UnivariateDifferentiableFunction>();
delta0fDays.add(new PolynomialFunction(new double[] { 59 }));
final List<UnivariateDifferentiableFunction> delta0fCenturies =  new ArrayList<UnivariateDifferentiableFunction>();
final IAUPoleCoefficients1D delta0Coeffs = new IAUPoleCoefficients1D(delta0fDays, delta0fCenturies);
// W coefficients
final List<UnivariateDifferentiableFunction> wfDays = new ArrayList<UnivariateDifferentiableFunction>();
wfDays.add(new PolynomialFunction(new double[] { 170.9, 952.1532 }));
final List<UnivariateDifferentiableFunction> wfCenturies = new ArrayList<UnivariateDifferentiableFunction>();
final IAUPoleCoefficients1D wCoeffs = new IAUPoleCoefficients1D(wfDays, wfCenturies);
// Build pole
final IAUPole pole = new UserIAUPole(new IAUPoleCoefficients(alpha0Coeffs, delta0Coeffs, wCoeffs));
 
// Build Ceres body
final CelestialBody ceres = new UserDefinedCelestialBody("Ceres", pv, gm, pole);

Then ceres object possesses all features of:

  • A CelestialBody: retrieve body-centered inertial frame or body-centered rotating frame
  • A PVCoordinateProvider: retrieve position and velocity at any time

Body shapes

The one-axis ellipsoid is a good approximate model for most planet-size and larger natural bodies. It is the equilibrium shape reached by a fluid body under its own gravity field when it rotates. The symmetry axis is the rotation or polar axis.

OneAxisEllipsoid

This type is used to represent the shape of a planet. One very useful implementation represents an ellipsoid (OneAxisEllipsoid). It is constructed from an equatorial radius, a flattening coefficient, and a reference frame that will be used to localize Geodetic points on the shape.

It could be interesting to obtained the geodetic coordinates of the nadir point of the satellite. To that purpose, one can use the method getIntersectionPoint(Line, Vector3D, Frame, AbsoluteDate) of the object OneAxisEllipsoid. 

 
AbsoluteDate date = new AbsoluteDate(new DateComponents(2008, 03, 21),
                                             TimeComponents.H12,
                                             TimeScalesFactory.getUTC());       
Frame frame = FramesFactory.getITRF();
// Body shape model
OneAxisEllipsoid earth = new OneAxisEllipsoid(6378136.460, 1 / 298.257222101, frame);
 
// Satellite on any position
 
circ = new CircularOrbit(7178000.0, 0.5e-4, 0., FastMath.toRadians(50.), FastMath.toRadians(0.),
                                   FastMath.toRadians(90.), PositionAngle.MEAN, 
                                   FramesFactory.getEME2000(), date, mu);
 
// Transform satellite position to position/velocity parameters in EME2000 and ITRF200B
PVCoordinates pvSatEME2000 = circ.getPVCoordinates();
PVCoordinates pvSatItrf  = frame.getTransformTo(FramesFactory.getEME2000(), date).transformPVCoordinates(pvSatEME2000);
Vector3D pSatItrf  = pvSatItrf.getPosition();
 
// Nadir point of the satellite
Vector3D pointItrf     = new Vector3D.ZERO;
Vector3D direction = Vector3D(1., pSatItrf,-1., pointItrf);
Line line = new Line(pSatItrf, direction);
// intersection point between the ellipsoid and the line that joins the satellite and the center of the body
GeodeticPoint nadir = earth.getIntersectionPoint(line, pSatItrf, frame, date);

GeometricBodyShape and ExtendedOneAxisEllipsoid

The GeometricBodyShape interface extends BodyShape for more complex computations. ExtendedOneAxisEllipsoid implements it. See the [MIS_SENSORS_PatriusBodySpheroid specific page] for more details.

Facet celestial body

FacetCelestialBody is a class used to define a celestial body as a mesh. This is particularly useful for small irregular bodies such as asteroids. For example, Phobos contains here 100 000 vertices and 200 000 facets:

Phobos.jpg

This class:

  • Inherits the GeometricBodyShape interface and hence can be used together with EclipseDetector and SensorModel.
  • Inherits the CelestialBody interface and hence can be used as any celestial bodies with classes such as ThirdBodyAttraction, SunPointing and event detectors.
  • Provides some useful and optimised methods for small body handling. Facets are connected to each other allowing some methods to be writen in a recursive or iterative way and hence being very fast. If n is the number of vertices of the body, fast recursive or iterative methods are in O(log(n)).
Mesh provider

A mesh is described by a list of facets Triangle and or vertices Vertex. A Triangle contains three vertices. Mesh is provided by the generic interface MeshProvider. This interface currently possesses two implementation:

  • ObjMeshLoader: in this case, the mesh is provided under official .obj file format. See This page for more information on the format.
  • GeodeticMeshLoader: in this case, the mesh is provided in an ASCII column file listing each vertex in the format [Latitude Longitude Altitude].
Available methods

Noe that most methods return exact results. For example, distanceTo methods returns exact distance to mesh body. Only transform() and getLocalRadius() methods simplify the mesh in a one axis ellipsoid.

FacetCelestialBody provides the following methods:

  • getIntersection(final Line line, final Vector3D close, final Frame frame, final AbsoluteDate date) and similar which returns an Intersection object.This object contains the intersection point as well as the Triangle containing the intersection point. This method is recursive and is in O(log(n)).
  • transform() methods which converts a point or a geodetic point using reference ellipsoid. Reference ellipsoid is the closest one axis ellipsoid to the body.
  • getLocalRadius() methods which provides the local radius from an object and an occulted body using reference ellipsoid. Reference ellipsoid is the closest one axis ellipsoid to the body. This method is to be used only by EclipseDetector.
  • distanceTo() method which returns the distance to the body. This method is recursive and is hence in O(log(n)).
  • getNeighbors() methods which returns the neighbors triangles to:
    • A point or a triangle given a "neighborhood distance"
    • A triangle given a "neighborhood order". In this case, order 1 returns the immediate neighbors of the triangles, order 2 returns also the neighbors' neighbors and so on.

This method is recursive and is hence in O(log(n)).

  • getSurfacePointedDataEphemeris() method which returns for each provided SpacecraftState a container SurfacePointedData, containing all pointed surface-related data.
  • getFieldData() which returns a container FieldData containing data related to the field of view:
    • Visible triangles from the satellite field of view IFieldOfView. A visible triangle must be entirely in the field of view and not masked by any other triangle.
    • Contour of the seen triangles. Contour is strictly contained in the field of view

If main direction of the field of view is provided, this method is recursive and is in O(log(n)). Otherwise, it is in O(n) and is much slower.

  • isInEclipse() method which returns true if the satellite is currently in eclipse, false otherwise. Penumbra is not taken into account. This method is in O(log(n)).
  • getNeverVisibleTriangles() which returns a list of facets which are never visible from the provided ephemeris. Visibility criteria is the same as for getFieldData() method. This method is in O((n)).
  • getNeverEnlightenedTriangles() which returns a list of facets which are never enlightened by the Sun. Visibility criteria is the same as for getFieldData() method. This method is in O((n)).
  • getVisibleAndEnlightenedTriangles() which returns a list of facets which are visible and enlightened at the same time, at least once on the provided ephemeris. Visibility criteria is the same as for getFieldData() method. This method is in O((n)).

GeodeticPoint

The geodetic point is defined by a latitude, a longitude and an altitude in the frame associated to the body. It could be interesting to know the position of a satellite in terms of geodetic coordinates rather than Cartesian ones and vice versa (the corresponding methods in OneAxisEllipsoid). 

// equatorial radius of the celestial body
double ae = 6378137.0;
// flatness of the celestial body
double f = 1.0 / 298.257222101;
// date        
AbsoluteDate date = AbsoluteDate.J2000_EPOCH;
// reference frame attached to the body        
Frame frame = FramesFactory.getITRF();
// body shape model (ellipsoid)     
OneAxisEllipsoid model = new OneAxisEllipsoid(ae, f, frame);
 
// transformation with jacobian matrix : cartesian to geodetic
 
// initial cartesian point that will be transformed
Vector3D cp = new Vector3D(4637885.347, 121344.808, 4362452.869);
// coresponding geodetic point        
GeodeticPoint gp = model.transform(cp, frame, date);
 
// transformation with jacobian matrix : geodetic to cartesian
 
// initial geodetic point that will be transformed
GeodeticPoint gp2 = new GeodeticPoint(0.852479154923577, 0.0423149994747243, 111.6);
// coresponding Cartesian point        
Vector3D cp2 = model.transform(gp2);

It could be also interesting to obtain the jacobian matrix of the transformation. 

// transformation : cartesian to geodetic
 
double[][] jacobianGeodesicWrtCartesian = new double[3][3];
gp = model.transformAndComputeJacobian(cp, frame, date, jacobianGeodesicWrtCartesian);
 
// transformation : geodetic to cartesian
 
double[][] jacobianCartesianWrtGeodesic = new double[3][3];       
Vector3D cp2 = model.transformAndComputeJacobian(gp2, jacobianCartesianWrtGeodesic );

Getting Started

TBD

Contents

Interfaces

Interface Summary Javadoc
BodyShape Interface representing the rigid surface shape of a natural body. ...
CelestialBody Interface for celestial bodies like Sun, Moon or solar system planets. ...
MeshLoader Interface for FacetCelestialBody mesh provider. ...

Classes

Class Summary Javadoc
CelestialBodyFactory Factory class for bodies of the solar system. ...
GeodeticPoint Point location relative to a 2D body surface. ...
JPLEphemeridesLoader Loader for JPL ephemerides binary files (DE 405, DE 406, ...). ...
OneAxisEllipsoid Modeling of a one-axis ellipsoid. ...
MeeusSun Position of the Sun according to Meeus model. Three models with there appropriate equations are avaible : the standard model (former MeeusSun), Stela model (former MeeuSunStela) and an on-board model ...
MeeusMoon Position of the Moon according to Meeus model. ...
BasicBoardSun Direction of the Sun according to a basic board Sun model. ...
UserCelestialBody User-defined celestial body ...
UserIAUPole User-defined IAU pole motion ...
FacetCelestialBody Celestial body defined by a mesh. ...
Triangle Unitary facet (triangle) for a FacetCelestialBody. ...
ObjMeshLoader .obj 3D file mesh loader. ...
GeodeticMeshLoader Mesh loader for ASCII files describing the body with latitude/longitude/altitude components (1 per line). ...
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