Functions
template<typename T >
T	EGXPhys::OrbitalPeriod (const T siderealDayIns, const T synodicDayIns)
	Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the length of the celestial object's sidereal day, \(T_{Sidereal}\), and synodic day, \(T_{Synodic}\). The orbital period is the time needed for a celestial object to complete one orbit around another object. \[ T_{Orbit}=\dfrac{T_{Synodic} * T_{Sidereal}}{T_{Synodic} + T_{Sidereal}}\] . More...

template<typename T >
T	EGXPhys::OrbitalPeriodSmallBody (const T semiMajorAxisInm, const T centralBodyMassInKg)
	Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), and the central object's mass that the celestial object is orbiting around, \(M\). It is assumed that the central object's mass is much larger then the celestial objects mass. The orbital period is the time needed for a celestial object to complete one orbit around the central object. \[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{GM}}\] . More...

template<typename T >
T	EGXPhys::OrbitalPeriodSmallBodyFromMass (const T semiMajorAxisInm, const T centralBodyMassInKg)
	Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), and the central object's mass that the celestial object is orbiting around, \(M\). It is assumed that the central object's mass is much larger then the celestial objects mass. The orbital period is the time needed for a celestial object to complete one orbit around the central object. \[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{GM}}\] . More...

template<typename T >
T	EGXPhys::OrbitalPeriodSmallBodyFromSGP (const T semiMajorAxisInm, const T centralBodyStandardGravitationalParameter)
	Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), and the central object's standard gravitational parameter, \(\mu\). It is assumed that the central object's mass is much larger then the celestial objects mass. The orbital period is the time needed for a celestial object to complete one orbit around the central object. \[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{\mu}}\] . More...

template<typename T >
T	EGXPhys::OrbitalPeriodTwoBody (const T semiMajorAxisInm, const T firstBodyMassInKg, const T secondBodyMassInKg)
	Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), its mass, \(M_1\), and the mass of the second celestial object, \(M_2\). The orbital period is the time needed for a celestial object to complete one orbit around the second celestial object. \[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{G(M_1 + M_2)}}\] . More...

template<typename T >
T	EGXPhys::OrbitalPeriodTwoBodyFromMass (const T semiMajorAxisInm, const T firstBodyMassInKg, const T secondBodyMassInKg)
	Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), its mass, \(M_1\), and the mass of the second celestial object, \(M_2\). The orbital period is the time needed for a celestial object to complete one orbit around the second celestial object. \[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{G(M_1 + M_2)}}\] . More...

template<typename T >
T	EGXPhys::OrbitalPeriodTwoBodyFromSGP (const T semiMajorAxisInm, const T firstBodyStandardGravitationalParameter, const T secondBodyStandardGravitationalParameter)
	Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), its standard gravitational parameter, \(\mu_1\), and the standard gravitational parameter of the second celestial object, \(\mu_2\). The orbital period is the time needed for a celestial object to complete one orbit around the second celestial object. \[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{\mu_1 + \mu_2}}\] . More...

Detailed Description

Function Documentation

◆ OrbitalPeriod()

template<typename T >

T EGXPhys::OrbitalPeriod	(	const T	siderealDayIns,
		const T	synodicDayIns
	)

Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the length of the celestial object's sidereal day, \(T_{Sidereal}\), and synodic day, \(T_{Synodic}\). The orbital period is the time needed for a celestial object to complete one orbit around another object.

\[ T_{Orbit}=\dfrac{T_{Synodic} * T_{Sidereal}}{T_{Synodic} + T_{Sidereal}}\]

.

See http://www.celestialnorth.org/FAQtoids/dazed_about_days_(solar_and_sidereal).htm and https://en.wikipedia.org/wiki/Orbital_period

Parameters

siderealDayIns	\( T_{Sidereal}\ (s)\) Sidereal day of the celestial object in seconds. Negative number indicates the planet has retrograde rotation.
synodicDayIns	\( T_{Synodic}\ (s)\) Synodic day (solar day) of the celestial object in seconds.

Returns: \( T_{Orbit}\ (s)\) Orbital period of the celestial object in seconds.

See also: SiderealDay() for period it takes for a celestial body to rotate once in relation to the distant stars. It is a 360 degree rotation.; SolarDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; SynodicDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.

◆ OrbitalPeriodSmallBody()

template<typename T >

T EGXPhys::OrbitalPeriodSmallBody	(	const T	semiMajorAxisInm,
		const T	centralBodyMassInKg
	)

Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), and the central object's mass that the celestial object is orbiting around, \(M\). It is assumed that the central object's mass is much larger then the celestial objects mass. The orbital period is the time needed for a celestial object to complete one orbit around the central object.

\[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{GM}}\]

.

See https://en.wikipedia.org/wiki/Orbital_period

Parameters

semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the celestial object's rotation in meters.
centralBodyMassInKg	\( M\ (kg)\) Mass of the central object that the celestial object is orbiting around in kilograms.

Returns: \( T_{Orbit}\ (s)\) Orbital period of the celestial object in seconds.

See also: OrbitalPeriodSmallBodyFromMass() for alias.; OrbitalPeriodSmallBodyFromSGP() for calculation using standard gravitational parameter.; SiderealDay() for period it takes for a celestial body to rotate once in relation to the distant stars. It is a 360 degree rotation.; SolarDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; SynodicDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.

◆ OrbitalPeriodSmallBodyFromMass()

template<typename T >

T EGXPhys::OrbitalPeriodSmallBodyFromMass	(	const T	semiMajorAxisInm,
		const T	centralBodyMassInKg
	)

Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), and the central object's mass that the celestial object is orbiting around, \(M\). It is assumed that the central object's mass is much larger then the celestial objects mass. The orbital period is the time needed for a celestial object to complete one orbit around the central object.

\[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{GM}}\]

.

See https://en.wikipedia.org/wiki/Orbital_period

Parameters

semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the celestial object's rotation in meters.
centralBodyMassInKg	\( M\ (kg)\) Mass of the central object that the celestial object is orbiting around in kilograms.

Returns: \( T_{Orbit}\ (s)\) Orbital period of the celestial object in seconds.

See also: OrbitalPeriodSmallBody() for alias.; OrbitalPeriodSmallBodyFromSGP() for calculation using standard gravitational parameter.; SiderealDay() for period it takes for a celestial body to rotate once in relation to the distant stars. It is a 360 degree rotation.; SolarDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; SynodicDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.

◆ OrbitalPeriodSmallBodyFromSGP()

template<typename T >

T EGXPhys::OrbitalPeriodSmallBodyFromSGP	(	const T	semiMajorAxisInm,
		const T	centralBodyStandardGravitationalParameter
	)

Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), and the central object's standard gravitational parameter, \(\mu\). It is assumed that the central object's mass is much larger then the celestial objects mass. The orbital period is the time needed for a celestial object to complete one orbit around the central object.

\[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{\mu}}\]

.

See https://en.wikipedia.org/wiki/Orbital_period

Parameters

semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the celestial object's rotation in meters.
centralBodyStandardGravitationalParameter	\( \mu\ (\frac{m^3}{s^2})\) Standard gravitational parameter of the central object that the celestial object is orbiting around in meter cubed per seconds squared.

Returns: \( T_{Orbit}\ (s)\) Orbital period of the celestial object in seconds.

See also: OrbitalPeriodSmallBody() for calculation using mass.; SiderealDay() for period it takes for a celestial body to rotate once in relation to the distant stars. It is a 360 degree rotation.; SolarDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; SynodicDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; StandardGravitationalParameter() for calculating standard gravitational parameter.

◆ OrbitalPeriodTwoBody()

template<typename T >

T EGXPhys::OrbitalPeriodTwoBody	(	const T	semiMajorAxisInm,
		const T	firstBodyMassInKg,
		const T	secondBodyMassInKg
	)

Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), its mass, \(M_1\), and the mass of the second celestial object, \(M_2\). The orbital period is the time needed for a celestial object to complete one orbit around the second celestial object.

\[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{G(M_1 + M_2)}}\]

.

See https://en.wikipedia.org/wiki/Orbital_period

Parameters

semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the celestial object's rotation in meters.
firstBodyMassInKg	\( M\ (kg)\) Mass of the celestial object in kilograms.
secondBodyMassInKg	\( M\ (kg)\) Mass of the second celestial object in kilograms.

Returns: \( T_{Orbit}\ (s)\) Orbital period of the celestial object in seconds.

See also: OrbitalPeriodTwoBodyFromMass() for alias.; OrbitalPeriodTwoBodyFromSGP() for calculation using standard gravitational parameter.; SiderealDay() for period it takes for a celestial body to rotate once in relation to the distant stars. It is a 360 degree rotation.; SolarDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; SynodicDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.

◆ OrbitalPeriodTwoBodyFromMass()

template<typename T >

T EGXPhys::OrbitalPeriodTwoBodyFromMass	(	const T	semiMajorAxisInm,
		const T	firstBodyMassInKg,
		const T	secondBodyMassInKg
	)

Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), its mass, \(M_1\), and the mass of the second celestial object, \(M_2\). The orbital period is the time needed for a celestial object to complete one orbit around the second celestial object.

\[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{G(M_1 + M_2)}}\]

.

See https://en.wikipedia.org/wiki/Orbital_period

Parameters

semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the celestial object's rotation in meters.
firstBodyMassInKg	\( M\ (kg)\) Mass of the celestial object in kilograms.
secondBodyMassInKg	\( M\ (kg)\) Mass of the second celestial object in kilograms.

Returns: \( T_{Orbit}\ (s)\) Orbital period of the celestial object in seconds.

See also: OrbitalPeriodTwoBody() for alias.; OrbitalPeriodTwoBodyFromSGP() for calculation using standard gravitational parameter.; SiderealDay() for period it takes for a celestial body to rotate once in relation to the distant stars. It is a 360 degree rotation.; SolarDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; SynodicDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.

◆ OrbitalPeriodTwoBodyFromSGP()

template<typename T >

T EGXPhys::OrbitalPeriodTwoBodyFromSGP	(	const T	semiMajorAxisInm,
		const T	firstBodyStandardGravitationalParameter,
		const T	secondBodyStandardGravitationalParameter
	)

Calculates the orbital period, \(T_{Orbit}\), of a celestial object in seconds from the semi-major axis of its orbit, \(a\), its standard gravitational parameter, \(\mu_1\), and the standard gravitational parameter of the second celestial object, \(\mu_2\). The orbital period is the time needed for a celestial object to complete one orbit around the second celestial object.

\[ T_{Orbit}=2\pi\sqrt{\dfrac{a^3}{\mu_1 + \mu_2}}\]

.

See https://en.wikipedia.org/wiki/Orbital_period

Parameters

semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the celestial object's rotation in meters.
firstBodyStandardGravitationalParameter	\( \mu_1\ (\frac{m^3}{s^2})\) Standard gravitational parameter of the celestial object in meter cubed per seconds squared.
secondBodyStandardGravitationalParameter	\( \mu_1\ (\frac{m^3}{s^2})\) Standard gravitational parameter of the second celestial object in meter cubed per seconds squared.

Returns: \( T_{Orbit}\ (s)\) Orbital period of the celestial object in seconds.

See also: OrbitalPeriodTwoBody() for calculation using mass.; SiderealDay() for period it takes for a celestial body to rotate once in relation to the distant stars. It is a 360 degree rotation.; SolarDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; SynodicDay() for period it takes for a celestial body to rotate once in relation to the body it is orbiting. It is a 360 + angle degree rotation to account for movement in orbit.; StandardGravitationalParameter() for calculating standard gravitational parameter.

Functions

Detailed Description

Function Documentation

◆ OrbitalPeriod()

◆ OrbitalPeriodSmallBody()

◆ OrbitalPeriodSmallBodyFromMass()

◆ OrbitalPeriodSmallBodyFromSGP()

◆ OrbitalPeriodTwoBody()

◆ OrbitalPeriodTwoBodyFromMass()

◆ OrbitalPeriodTwoBodyFromSGP()