KeplerOrbit Class Reference

KeplerOrbit describes an undisturbed orbit in a two-body system. More...

#include <Orbit.hpp>

Public Member Functions
	KeplerOrbit (double epochJDE, double pericenterDistance, double eccentricity, double inclination, double ascendingNode, double argOfPerhelion, double timeAtPerihelion, double orbitGoodDays, double meanMotion, double parentRotObliquity, double parentRotAscendingnode, double parentRotJ2000Longitude, double centralMass=1.0)
	Constructor. More...
void	positionAtTimevInVSOP87Coordinates (double JDE, double *v) override
	Compute the object position for a specified Julian day. More...
void	positionAtMeanAnomalyInVSOP87Coordinates (const double meanAnomaly, double *v)
	Compute the object position for a specified mean anomaly. More...
double	eccentricAnomaly (double M)
	Compute eccentric anomaly E from mean anomaly M. [radians].
void	positionAtEccentricAnomalyInVSOP87Coordinates (const double E, double *v)
	Compute the object position for a specified eccentric anomaly. More...
bool	getUpdateTails () const
	updating comet tails is a bit expensive. try not to overdo it.
void	setUpdateTails (const bool update)
Vec3d	getVelocity () const override
	return speed value [AU/d] last computed by positionAtTimevInVSOP87Coordinates(JDE, v)
void	getVelocity (double *vel) const override
	write speed value [AU/d] into first 3 elements of vel. (zero in the base class)
double	getSemimajorAxis () const override
	Returns semimajor axis [AU] for elliptic orbit, 0 for a parabolic orbit, and a negative value [AU] for hyperbolic orbit.
double	getEccentricity () const override
	return orbit eccentricity. (zero in the base class)
double	meanAnomaly (const double JDE) const
	Return mean anomaly M for JDE (or W, in case of parabolae)
bool	objectDateValid (const double JDE) const
	return whether a position returned for JDE can be regarded accurate enough for telescope use. More...
bool	objectDateGoodEnoughForOrbits (const double JDE) const
	return whether a position returned for JDE would be good enough for at least plotting the orbit. More...
Vec2d	objectDateValidRange (const bool strict) const
	Return minimal and maximal JDE values where this orbit should be used. More...
double	calculateSiderealPeriod () const
	Calculate sidereal period in days from semi-major axis and central mass. If SMA<=0 (hyperbolic orbit), return 0.
double	getEpochJDE () const
double	getOrbitGood () const
Public Member Functions inherited from Orbit
void	setParentOrientation (const double parentRotObliquity, const double parentRotAscendingNode, const double parentRotJ2000Longitude)
	For planet moons which have orbits given in relation to their parent planet's equator. More...

Static Public Member Functions
static double	calculateSiderealPeriod (const double semiMajorAxis, const double centralMass)

Additional Inherited Members
Protected Attributes inherited from Orbit
double	rotateToVsop87 [9]

Detailed Description

KeplerOrbit describes an undisturbed orbit in a two-body system.

This is used for minor bodies orbiting the sun, but also for planet moons. Orbital elements are considered valid for a relatively short time span (orbitGood) around epoch only and should be updated periodically, because the other planets perturbate the orbiting bodies. To avoid using outdated elements, the KeplerOrbit object can be queried using objectDateValid(JDE) whether it makes sense to assume the retrieved positions are close enough to reality to find the object in a telescope. Another test is objectDateGoodEnoughForOrbits(JDE), which test a bit more relaxed, for the sake of retrieving positions for graphics.

Note

This class was called CometOrbit previously, but was now recombined with the former EllipticalOrbit class. They did almost the same.

Algorithms from:

• Meeus: Astronomical Algorithms 1998
• Heafner: Fundamental Ephemeris Computations 1999

Constructor & Destructor Documentation

KeplerOrbit()

KeplerOrbit::KeplerOrbit	(	double	epochJDE,
		double	pericenterDistance,
		double	eccentricity,
		double	inclination,
		double	ascendingNode,
		double	argOfPerhelion,
		double	timeAtPerihelion,
		double	orbitGoodDays,
		double	meanMotion,
		double	parentRotObliquity,
		double	parentRotAscendingnode,
		double	parentRotJ2000Longitude,
		double	centralMass = 1.0
	)

Constructor.

Parameters

epochJDE	JDE epoch of orbital elements.
pericenterDistance	[AU] pericenter distance
eccentricity	0..>1 (>>1 for Interstellar objects)
inclination	[radians]
ascendingNode	[radians]
argOfPerhelion	[radians]
timeAtPerihelion	JDE
orbitGoodDays	[earth days] can be used to exclude computation for dates too far outside epoch. 0: always good (use that for planet moons. Not really correct, but most users won't care) -1: signal "auto-compute to 1/2 the orbital period or 1000 days if there is no period [e>=1]")
meanMotion	[radians/day] for parabolics, this is W/dt in Heafner's lettering
parentRotObliquity	[radians] Comets/Minor Planets only have parent==sun, no need for these? --> Oh yes, these relate VSOP/J2000 eq frames!
parentRotAscendingnode	[radians]
parentRotJ2000Longitude	[radians]
centralMass	central mass in Solar masses. Velocity value depends on this!

Member Function Documentation

calculateSiderealPeriod()

static double KeplerOrbit::calculateSiderealPeriod ( const double  semiMajorAxis, const double  centralMass  )

static

Parameters

semiMajorAxis	in AU. If SMA<=0 (hyperbolic orbit), return 0.
centralMass	in units of Solar masses

objectDateGoodEnoughForOrbits()

bool KeplerOrbit::objectDateGoodEnoughForOrbits ( const double  JDE ) const

inline

return whether a position returned for JDE would be good enough for at least plotting the orbit.

This is true for dates within orbitGood around epoch. If orbitGood is zero, this is always true.

Note

This relieves conditions of objectDateValid(JDE) somewhat, for the sake of illustratory completeness.

objectDateValid()

bool KeplerOrbit::objectDateValid ( const double  JDE ) const

inline

return whether a position returned for JDE can be regarded accurate enough for telescope use.

This is limited to dates within 1 year or epoch, or within orbitGood around epoch, whichever is smaller. If orbitGood is zero, this is always true.

Note

This will still return false positives after close encounters with major masses which change orbital parameters. However, it should catch the usual case of outdated orbital elements which should be updated at least yearly.

objectDateValidRange()

Vec2d KeplerOrbit::objectDateValidRange

(

const bool

strict

)

const

Return minimal and maximal JDE values where this orbit should be used.

Returns

the limits where objectDateValid returns true

positionAtEccentricAnomalyInVSOP87Coordinates()

void KeplerOrbit::positionAtEccentricAnomalyInVSOP87Coordinates	(	const double	E,
		double *	v
	)

Compute the object position for a specified eccentric anomaly.

Parameters

E	eccentricAnomaly [radians]
v	double vector of at least 3 elements. The first three will receive X/Y/Z values in AU.

Note

: Only used for orbit computation

positionAtMeanAnomalyInVSOP87Coordinates()

void KeplerOrbit::positionAtMeanAnomalyInVSOP87Coordinates	(	const double	meanAnomaly,
		double *	v
	)

Compute the object position for a specified mean anomaly.

Parameters

meanAnomaly	[radians]
v	double vector of at least 3 elements. The first three will receive X/Y/Z values in AU.

positionAtTimevInVSOP87Coordinates()

void KeplerOrbit::positionAtTimevInVSOP87Coordinates ( double  JDE, double *  v  )

overridevirtual

Compute the object position for a specified Julian day.

Parameters

JDE	Julian Ephemeris Day
v	double vector of at least 3 elements. The first three will receive X/Y/Z values in AU.

Reimplemented from Orbit.