User Manual 4.3 Celestial bodies
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
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).
To build a celestial body, the user can:
- use the static methods of the
CelestialBodyFactoryto 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
UserDefinedCelestialBody
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 only able to load the DE 405 or the DE 406 files which are the most commonly used data files. The former covers the years 1600 to 2200 at maximum precision, the latter covers the years-3000 to +3000 at only slightly reduced precision. The DE 421 file which is the latest JPL ephemeris with fully consistent treatment of planetary and lunar laser ranging data (Folkner et al 2009) is not yet readable by JPLEphemeridesLoader. However 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 405 and DE 406 files are stored. Then he has to give the name of the file which contains the data (DE 405 or DE 406), 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 |
|---|---|---|
| DE102 | September 1981 | includes nutations but not librations. Referred to the dynamical equator and equinox of 1950. |
| DE200 | September 1981 | includes nutations but not librations. Referred to the dynamical equator and equinox of 2000. 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. |
| DE403 | May 1993 | includes nutations and librations. Referred to the International Celestial Reference Frame. 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. 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. Ephemeris used for Mars Exploration Rover navigation. |
| DE413 | November 2004 | includes nutations and librations. Referred to the International Celestial Reference Frame. 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 2414864.5 (1899 JUL 29) to JED 2470192.5 (2051 JAN 21) |
| DE421 | February 2008 | includes nutations and librations. Referred to the International Celestial Reference Frame. 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. Intended for the MESSENGER mission to Mercury. |
| DE423 | February 2010 | includes nutations and librations. Referred to the International Celestial Reference Frame version 2.0. Intended for the MESSENGER mission to Mercury. |
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 34.6 (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 | 34.6 |
| 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 | 34.6 |
| 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 UserDefinedCelestialBody.
This class requires to provide:
- Its name.
- Its position-velocity through time using a
PVCoordinateProviderimplementation. - Its gravitational constant.
- Its pole motion using
IAUPoleimplementation.
Example: building Ceres. According to [FDY_BODY_Links 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 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)); } }; // 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.
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, 121344.608, 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. | ... |
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 | ... |
