Rotational Flattening/Oblateness

Functions
template<typename T >
T	EGXPhys::RotationalFlattening (const T eccentricity)
	Finds the flattening (oblateness), \(f\), of a planet with eccentricity \(e\): \[ f = 1 - \sqrt{1-e^2} \] . More...
template<typename T >
T	EGXPhys::RotationalFlattening (const T equatorialRadius, const T polarRadius)
	Finds the flattening (oblateness), \(f\), of a planet with equatorial radius \(a\) and polar radius, \(c\): \[ f =\begin{cases} \frac{a-c}{a}{} & oblate \\ \frac{c-a}{a} & prolate \end{cases} \] . More...
template<typename T >
T	EGXPhys::RotationalFlattening (const T massInkg, const T meanRadiusInm, const T angularVelocityInmPersSquared)
	Finds the flattening (oblateness), \(f\), of a planet with mass, \(M\), mean radius, \(a\), and angular velocity of rotation, \(\Omega\). Note that this is a 1st order approximation for a planet that is rotating relatively slowly (small flattening). \[ f = \frac{5}{4} \frac{\Omega^2 a^3}{GM} \] . More...
template<typename T >
T	EGXPhys::RotationalOblateness (const T eccentricity)
	Finds the oblateness (flattening), \(f\), of a planet with eccentricity \(e\): \[ f = 1 - \sqrt{1-e^2} \] . More...
template<typename T >
T	EGXPhys::RotationalOblateness (const T equatorialRadius, const T polarRadius)
	Finds the oblateness (flattening), \(f\), of a planet with equatorial radius \(a\) and polar radius, \(c\): \[ f =\begin{cases} \frac{a-c}{a}{} & oblate \\ \frac{c-a}{a} & prolate \end{cases} \] . More...
template<typename T >
T	EGXPhys::RotationalOblateness (const T massInkg, const T meanRadiusInm, const T angularVelocityInmPersSquared)
	Finds the oblateness (flattening), \(f\), of a planet with mass, \(M\), mean radius, \(a\), and angular velocity of rotation, \(\Omega\). Note that this is a 1st order approximation for a planet that is rotating relatively slowly (small flattening). \[ f = \frac{5}{4} \frac{\Omega^2 a^3}{GM} \] . More...

Detailed Description

Function Documentation

RotationalFlattening() [1/3]

template<typename T >

T EGXPhys::RotationalFlattening

(

const T

eccentricity

)

Finds the flattening (oblateness), \(f\), of a planet with eccentricity \(e\):

\[ f = 1 - \sqrt{1-e^2} \]

.

Equation taken from "Map Projections-A Working Manual" (Snyder, 1987), p. 13

See http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

Parameters

eccentricity

\( e\ (dimensionless)\) Eccentricity of planet.

Returns

\( f\ (dimensionless)\) Flattening of planet.

See also

RotationalOblateness() for alias.

SpheroidFlattening() for alias.

SpheroidEccentricity() for eccentricity of a spheroid.

RotationalFlattening() [2/3]

template<typename T >

T EGXPhys::RotationalFlattening	(	const T	equatorialRadius,
		const T	polarRadius
	)

Finds the flattening (oblateness), \(f\), of a planet with equatorial radius \(a\) and polar radius, \(c\):

\[ f =\begin{cases} \frac{a-c}{a}{} & oblate \\ \frac{c-a}{a} & prolate \end{cases} \]

.

Planet is oblate if the equatorial radius is larger than the polar radius. It is prolate if the polar radius is larger than the equatorial radius.

Equation taken from "Map Projections-A Working Manual" (Snyder, 1987), p. 13

See http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

Parameters

equatorialRadius	\( a\ (m)\) Equatorial radius in meters.
polarRadius	\( c\ (m)\) Polar radius in meters.

Returns

\( f\ (dimensionless)\) Flattening of planet.

See also

RotationalOblateness() for alias.

SpheroidFlattening() for alias.

RotationalFlattening() [3/3]

template<typename T >

T EGXPhys::RotationalFlattening	(	const T	massInkg,
		const T	meanRadiusInm,
		const T	angularVelocityInmPersSquared
	)

Finds the flattening (oblateness), \(f\), of a planet with mass, \(M\), mean radius, \(a\), and angular velocity of rotation, \(\Omega\). Note that this is a 1st order approximation for a planet that is rotating relatively slowly (small flattening).

\[ f = \frac{5}{4} \frac{\Omega^2 a^3}{GM} \]

.

Equation taken from http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node109.html

See http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

Parameters

massInkg	\( M\ (kg)\) Mass of planet in kilograms.
meanRadiusInm	\( e\ (m)\) Mean radius of planet in meters.
angularVelocityInmPersSquared	\( \Omega\ (\frac{m}{s^2})\) Angular velocity of rotation of planet in meter per second squared.

Returns

\( f\ (dimensionless)\) Flattening of planet.

See also

RotationalOblateness() for alias.

RotationalOblateness() [1/3]

template<typename T >

T EGXPhys::RotationalOblateness

(

const T

eccentricity

)

Finds the oblateness (flattening), \(f\), of a planet with eccentricity \(e\):

\[ f = 1 - \sqrt{1-e^2} \]

.

Equation taken from "Map Projections-A Working Manual" (Snyder, 1987), p. 13

See http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

Parameters

eccentricity

\( e\ (dimensionless)\) Eccentricity of planet.

Returns

\( f\ (dimensionless)\) Flattening of planet.

See also

RotationalFlattening() for alias.

SpheroidOblateness() for alias.

SpheroidEccentricity() for eccentricity of a spheroid.

RotationalOblateness() [2/3]

template<typename T >

T EGXPhys::RotationalOblateness	(	const T	equatorialRadius,
		const T	polarRadius
	)

Finds the oblateness (flattening), \(f\), of a planet with equatorial radius \(a\) and polar radius, \(c\):

\[ f =\begin{cases} \frac{a-c}{a}{} & oblate \\ \frac{c-a}{a} & prolate \end{cases} \]

.

Planet is oblate if the equatorial radius is larger than the polar radius. It is prolate if the polar radius is larger than the equatorial radius.

Equation taken from "Map Projections-A Working Manual" (Snyder, 1987), p. 13

See http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

Parameters

equatorialRadius	\( a\ (m)\) Equatorial radius in meters.
polarRadius	\( c\ (m)\) Polar radius in meters.

Returns

\( f\ (dimensionless)\) Flattening of planet.

See also

RotationalFlattening() for alias.

SpheroidOblateness() for alias.

RotationalOblateness() [3/3]

template<typename T >

T EGXPhys::RotationalOblateness	(	const T	massInkg,
		const T	meanRadiusInm,
		const T	angularVelocityInmPersSquared
	)

Finds the oblateness (flattening), \(f\), of a planet with mass, \(M\), mean radius, \(a\), and angular velocity of rotation, \(\Omega\). Note that this is a 1st order approximation for a planet that is rotating relatively slowly (small flattening).

\[ f = \frac{5}{4} \frac{\Omega^2 a^3}{GM} \]

.

Equation taken from http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node109.html

See http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

Parameters

massInkg	\( M\ (kg)\) Mass of planet in kilograms.
meanRadiusInm	\( e\ (m)\) Mean radius of planet in meters.
angularVelocityInmPersSquared	\( \Omega\ (\frac{m}{s^2})\) Angular velocity of rotation of planet in meter per second squared.

Returns

\( f\ (dimensionless)\) Flattening of planet.

See also

RotationalOblateness() for alias.