Class used to store rotational elements, i.e. More...

#include <RotationElements.hpp>

Data Structures
struct	PlanetCorrections
	0.21+: Axes of planets and moons require terms depending on T=(jde-J2000)/36525, described in Explanatory Supplement 2013, Tables 10.1 and 10.10-14, updated in WGCCRE reports 2009 and 2015. More...

Public Types
enum	ComputationMethod { Traditional , WGCCRE }

enum	PlanetCorrection { EarthMoon =3 , Mars =4 , Jupiter =5 , Saturn =6 , Uranus =7 , Neptune =8 }

typedef double(*	axisRotFuncType) (const double, const double)
	Finetuning correction functions. More...

typedef void(*	axisOriFuncType) (const double, const double, double , double )

Static Public Member Functions
static void	updatePlanetCorrections (const double JDE, const PlanetCorrection planet)
	Update the planet corrections. More...

static double	corrWnil (const double d, const double T)
	These corr* functions can be used as corrW.

static double	corrWMoon (const double d, const double T)

static double	corrWMercury (const double d, const double T)

static double	corrWMars (const double d, const double T)

static double	corrWJupiter (const double d, const double T)
	The default W delivers SystemII longitude. More...

static double	corrWNeptune (const double d, const double T)

static double	corrWPhobos (const double d, const double T)

static double	corrWDeimos (const double d, const double T)

static double	corrWIo (const double d, const double T)

static double	corrWEuropa (const double d, const double T)

static double	corrWGanymede (const double d, const double T)

static double	corrWCallisto (const double d, const double T)

static double	corrWAmalthea (const double d, const double T)

static double	corrWThebe (const double d, const double T)

static double	corrWMimas (const double d, const double T)

static double	corrWTethys (const double d, const double T)

static double	corrWRhea (const double d, const double T)

static double	corrWJanus (const double d, const double T)

static double	corrWEpimetheus (const double d, const double T)

static double	corrWCordelia (const double d, const double T)

static double	corrWOphelia (const double d, const double T)

static double	corrWBianca (const double d, const double T)

static double	corrWCressida (const double d, const double T)

static double	corrWDesdemona (const double d, const double T)

static double	corrWJuliet (const double d, const double T)

static double	corrWPortia (const double d, const double T)

static double	corrWRosalind (const double d, const double T)

static double	corrWBelinda (const double d, const double T)

static double	corrWPuck (const double d, const double T)

static double	corrWAriel (const double d, const double T)

static double	corrWUmbriel (const double d, const double T)

static double	corrWTitania (const double d, const double T)

static double	corrWOberon (const double d, const double T)

static double	corrWMiranda (const double d, const double T)

static double	corrWTriton (const double d, const double T)

static double	corrWNaiad (const double d, const double T)

static double	corrWThalassa (const double d, const double T)

static double	corrWDespina (const double d, const double T)

static double	corrWGalatea (const double d, const double T)

static double	corrWLarissa (const double d, const double T)

static double	corrWProteus (const double d, const double T)

static void	corrOriNil (const double, const double, double , double )
	These functions can be used as corrOri.

static void	corrOriMoon (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriMars (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriJupiter (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriNeptune (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriPhobos (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriDeimos (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriIo (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriEuropa (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriGanymede (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriCallisto (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriAmalthea (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriThebe (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriMimas (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriTethys (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriRhea (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriJanus (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriEpimetheus (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriAriel (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriUmbriel (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriTitania (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriOberon (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriMiranda (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriCordelia (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriOphelia (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriBianca (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriCressida (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriDesdemona (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriJuliet (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriPortia (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriRosalind (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriBelinda (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriPuck (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriTriton (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriNaiad (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriThalassa (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriDespina (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriGalatea (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriLarissa (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static void	corrOriProteus (const double d, const double T, double J2000NPoleRA, double J2000NPoleDE)

static double	getMarsMagLs (const double Ls, const bool albedo)
	Retrieve magnitude variation depending on angle Ls [radians]. More...

Data Fields
double	period

double	offset

double	epoch

double	obliquity

double	ascendingNode

ComputationMethod	method

double	ra0

double	ra1

double	de0

double	de1

double	W0

double	W1

double	currentAxisRA

double	currentAxisDE

double	currentAxisW

axisRotFuncType	corrW

axisOriFuncType	corrOri

Static Public Attributes
static constexpr double	J2000 = 2451545.0

static PlanetCorrections	planetCorrections

static const QMap< QString, axisRotFuncType >	axisRotCorrFuncMap

static const QMap< QString, axisOriFuncType >	axisOriCorrFuncMap

static double	grsJD
	JD (epoch) for calculation of position of Great Red Spot.

static double	grsLongitude
	Longitude of Great Red Spot at grsJD (System II, degrees)

static double	grsDrift
	Annual drift of Great Red Spot position (degrees)

Detailed Description

Class used to store rotational elements, i.e.

axis orientation for the planetary body. Data are read from ssystem_(major|minor).ini in SolarSystem.cpp::loadPlanets().

Notes of early 2021: The original planet axis model in Stellarium seems to be an outdated model untraceable in the literature. Stellarium used to have elements w.r.t. VSOP87 (ecliptical) frame for planets, and elements w.r.t. the host planet's equator for planet moons: ascendingNode obliquity offset period We cannot remove these old data as long as some Moon orbits for the outer planets depend on them. The problem is that without a reference we have no idea whether any of these elements and algorithms are correct.

IAU standards like the Report of the IAU Working Group on Cartographic Coordinates and Rotational elements 2009 (DOI:10.1007/s10569-010-9320-4) has axes given w.r.t. J2000 ICRF.

Between V0.15 and 0.20.*, if the planet elements in ssystem.ini had elements "rot_pole_ra" and "rot_pole_de" given, the poles were transformed to ecliptically-based directions (VSOP87) obliquity/ascendingNode. But these were only ra/de_J2000 poles. Some axes have precession, which need to be modelled/updated. The new way (0.21+): We still allow using the previous 4 elements in Planet::computeTransMatrix(.,.) and Planet::getSiderealTime(), but only if WGCCRE elements are not available.

ra=ra0+T*ra1 de=de0+T*de1 ( --> obliquity, ascendingNode) rot_rotation_offset [degrees] =W0 rot_periode [hours] = computed from rot_pole_W1[deg/day] if that exists. 360 [deg] / rot [hours] --> 360 * rot / 24 [deg/hours]

If rot_pole... values are given, then they are ICRF and transformed on the fly to VSOP87, stored in here.

Since 0.21 we use the WGCCRE elements and orientations directly, so that axes behave properly. In addition, the objects with more complicated element behaviour are updated with two special functions. New keys in ssystem_*.ini, their storage in RotationElements, and their equivalents in the IAU report: rot_pole_ra [degrees] re.ra0 [rad] constant term for alpha_0 rot_pole_de [degrees] re.ra1 [rad/ct] constant term for delta_0 rot_pole_ra1 [degrees/cy] re.de0 [rad] T factor for alpha_0 rot_pole_de1 [degrees/cy] re.de1 [rad/ct] T factor for delta_0 rot_pole_W0 [degrees] re.W0 [degrees] constant term fo W. rot_pole_W1 [degrees/day] re.W1 [degrees/day] d factor for W

Data Structure Documentation

◆ RotationElements::PlanetCorrections

struct RotationElements::PlanetCorrections

0.21+: Axes of planets and moons require terms depending on T=(jde-J2000)/36525, described in Explanatory Supplement 2013, Tables 10.1 and 10.10-14, updated in WGCCRE reports 2009 and 2015.

Others require frequent updates, depending on jde-J2000. (Moon etc.) These should be updated as frequently as needed, optimally with the planet. Light time correction should be applied when needed. best place to call update is the SolarSystem::computePlanets()

Data Fields
double	E1
double	E10
double	E11
double	E12
double	E13
double	E2
double	E3
double	E4
double	E5
double	E6
double	E7
double	E8
double	E9
double	J1
double	J2
double	J3
double	J4
double	J5
double	J6
double	J7
double	J8
double	Ja
double	Jb
double	Jc
double	Jd
double	JDE_E
double	JDE_J
double	JDE_M
double	JDE_N
double	JDE_S
double	JDE_U
double	Je
double	M1
double	M10
double	M2
double	M3
double	M4
double	M5
double	M6
double	M7
double	M8
double	M9
double	N1
double	N2
double	N3
double	N4
double	N5
double	N6
double	N7
double	Na
double	S1
double	S2
double	S3
double	S4
double	S5
double	S6
double	U1
double	U10
double	U11
double	U12
double	U13
double	U14
double	U15
double	U16
double	U2
double	U3
double	U4
double	U5
double	U6
double	U7
double	U8
double	U9

Member Typedef Documentation

◆ axisRotFuncType

typedef double(* RotationElements::axisRotFuncType) (const double, const double)

Finetuning correction functions.

These functions are attached to the planets in Planet::setRotationElements() and called at the right places. This avoids ugly sequences of name query ifelses. arguments are d=JDE-J2000, T=d/36525, J2000NPoleRA, J2000NPoleDE

Member Function Documentation

◆ corrWJupiter()

static double RotationElements::corrWJupiter	(	const double	d,
		const double	T
	)

static

The default W delivers SystemII longitude.

We have to shift by GRS position and texture position. The final value will no longer be W but the rotation value required to show the GRS.

◆ getMarsMagLs()

static double RotationElements::getMarsMagLs	(	const double	Ls,
		const bool	albedo
	)

static

Retrieve magnitude variation depending on angle Ls [radians].

Source: A. Mallama: The magnitude and albedo of Mars. Icarus 192(2007) 404-416.

albedo true to return longitudinal albedo correction, Ls=the average of sub-earth and sub-solar planetographic longitudes false for the Orbital Longitude correction. Ls here is the apparent solar longitude along Mars' "ecliptic". (0=Martian Vernal Equinox)

◆ updatePlanetCorrections()

static void RotationElements::updatePlanetCorrections	(	const double	JDE,
		const PlanetCorrection	planet
	)

static

Update the planet corrections.

planet=3(Moon), 4 (Mars), 5(Jupiter), 6(Saturn), 7(Uranus), 8(Neptune). The values are immediately converted to radians.

Data Structures

Public Types

Static Public Member Functions

Data Fields

Static Public Attributes

Detailed Description

Data Structure Documentation

◆ RotationElements::PlanetCorrections

Member Typedef Documentation

◆ axisRotFuncType

Member Function Documentation

◆ corrWJupiter()

◆ getMarsMagLs()

◆ updatePlanetCorrections()