EGXPhys
Functions
Planet Criteria
EGXPhys Library » Astrophysics

Functions

template<typename T >
T EGXPhys::PlanetSimilarityIndex (const T &planetMeanRadius, const T &referenceMeanRadius, const T &planetBulkDensity, const T &referenceBulkDensity, const T &planetEscapeVelocity, const T &referenceEscapeVelocity, const T &planetSurfaceTemperature, const T &referenceSurfaceTemperature)
 Calculates Planet Similarity Index \((PSI)\) of a planet when comparing it to a reference planet. More...
 
template<typename T >
T EGXPhys::EarthSimilarityIndex (const T &planetMeanRadius, const T &planetBulkDensity, const T &planetEscapeVelocity, const T &planetSurfaceTemperature)
 Calculates Earth Similarity Index \((ESI)\) of a planet. More...
 
template<typename T >
T EGXPhys::PlanetSimilarityIndexInterior (const T &planetMeanRadius, const T &referenceMeanRadius, const T &planetBulkDensity, const T &referenceBulkDensity)
 Calculates Interior Planet Similarity Index \((PSI_I)\) of a planet when comparing it to a reference planet. More...
 
template<typename T >
T EGXPhys::EarthSimilarityIndexInterior (const T &planetMeanRadius, const T &planetBulkDensity)
 Calculates Interior Earth Similarity Index \((ESI_I)\) of a planet. More...
 
template<typename T >
T EGXPhys::PlanetSimilarityIndexSurface (const T &planetEscapeVelocity, const T &referenceEscapeVelocity, const T &planetSurfaceTemperature, const T &referenceSurfaceTemperature)
 Calculates Surface Planet Similarity Index \((PSI_S)\) of a planet when comparing it to a reference planet. More...
 
template<typename T >
T EGXPhys::EarthSimilarityIndexSurface (const T &planetEscapeVelocity, const T &planetSurfaceTemperature)
 Calculates Surface Earth Similarity Index \((ESI_S)\) of a planet. More...
 

Detailed Description

Function Documentation

◆ EarthSimilarityIndex()

template<typename T >
T EGXPhys::EarthSimilarityIndex ( const T &  planetMeanRadius,
const T &  planetBulkDensity,
const T &  planetEscapeVelocity,
const T &  planetSurfaceTemperature 
)

Calculates Earth Similarity Index \((ESI)\) of a planet.

The earth similarity index is a number that denotes how similar a planet is to that of earth. 1 is being exactly earth like.

\[ESI=\sqrt{ESI_I ESI_S}\]

See http://phl.upr.edu/projects/earth-similarity-index-esi and https://en.wikipedia.org/wiki/Earth_Similarity_Index.

Equations taken from "A Two-Tiered Approach to Assessing the Habitability of Exoplanets" https://doi.org/10.1089/ast.2010.0592.

Parameters
planetMeanRadius\(r\ (m)\) is the mean radius of a planet.
planetBulkDensity\(\rho\ (\frac{kg}{m^3})\) is the bulk density of the planet.
planetEscapeVelocity\(v_e\ (\frac{m}{s})\) is the escape velocity. The velocity needed to escape the planet's gravitational pull.
planetSurfaceTemperature\(T\ (K)\) is the average surface temperature of the planet.
Returns
\(ESI\)(dimensionless) Earth Similarity Index for a planet.
See also
PlanetSimilarityIndex() for \(ESI\) equation using any planet as reference.
EarthSimilarityIndexInterior() for \(ESI_I\) equation.
EarthSimilarityIndexSurface() for \(ESI_S\) equation.

◆ EarthSimilarityIndexInterior()

template<typename T >
T EGXPhys::EarthSimilarityIndexInterior ( const T &  planetMeanRadius,
const T &  planetBulkDensity 
)

Calculates Interior Earth Similarity Index \((ESI_I)\) of a planet.

The interior earth similarity index is a number that denotes how similar the interior of a planet is to the earth. 1 is being exactly earth like.

\[ESI_I=\sqrt{ESI_r ESI_\rho}\]

\[ESI_I=\sqrt{\left ( 1 - \left | \frac{r-r_\oplus}{r+r_\oplus} \right | \right )^{0.57} \left ( 1 - \left | \frac{\rho-\rho_\oplus}{\rho+\rho_\oplus} \right | \right )^{1.07}}\]

See http://phl.upr.edu/projects/earth-similarity-index-esi and https://en.wikipedia.org/wiki/Earth_Similarity_Index.

Equations taken from "A Two-Tiered Approach to Assessing the Habitability of Exoplanets" https://doi.org/10.1089/ast.2010.0592.

Parameters
planetMeanRadius\(r\ (m)\) is the mean radius of a planet.
planetBulkDensity\(\rho\ (\frac{kg}{m^3})\) is the bulk density of the planet.
Returns
\(ESI_I\)(dimensionless) Interior Earth Similarity Index for a planet when comparing it to a reference planet.
See also
EarthSimilarityIndex() Uses \(ESI_S\) for calculations.
PlanetSimilarityIndexInterior() for \(ESI_I\) equation using any planet as reference.
EarthSimilarityIndexSurface() for \(ESI_S\) equation.

◆ EarthSimilarityIndexSurface()

template<typename T >
T EGXPhys::EarthSimilarityIndexSurface ( const T &  planetEscapeVelocity,
const T &  planetSurfaceTemperature 
)

Calculates Surface Earth Similarity Index \((ESI_S)\) of a planet.

The interior planet similarity index is a number that denotes how similar the surface of a planet is to the earth. 1 is being exactly earth like.

\[PSI_S=\sqrt{PSI_{v_e} PSI_T}\]

\[PSI_S=\sqrt{\left ( 1 - \left | \frac{v_e-v_{e,\oplus}}{v_e+v_{e,\oplus}} \right | \right )^{0.70} \left ( 1 - \left | \frac{T-T_{\oplus}}{T+T_{\oplus}} \right | \right )^{5.58}}\]

See http://phl.upr.edu/projects/earth-similarity-index-esi and https://en.wikipedia.org/wiki/Earth_Similarity_Index.

Equations taken from "A Two-Tiered Approach to Assessing the Habitability of Exoplanets" https://doi.org/10.1089/ast.2010.0592.

Parameters
planetEscapeVelocity\(v_e\ (\frac{m}{s})\) is the escape velocity needed to escape the planet's gravitational pull.
planetSurfaceTemperature\(T\ (K)\) is the average surface temperature of the planet.
Returns
\(ESI_S\)(dimensionless) Surface Earth Similarity Index for a planet.
See also
EarthSimilarityIndex() Uses \(ESI_S\) for calculations.
PlanetSimilarityIndexSurface() for \(ESI_S\) equation using any planet as reference.
EarthSimilarityIndexInterior() for \(ESI_I\) equation.

◆ PlanetSimilarityIndex()

template<typename T >
T EGXPhys::PlanetSimilarityIndex ( const T &  planetMeanRadius,
const T &  referenceMeanRadius,
const T &  planetBulkDensity,
const T &  referenceBulkDensity,
const T &  planetEscapeVelocity,
const T &  referenceEscapeVelocity,
const T &  planetSurfaceTemperature,
const T &  referenceSurfaceTemperature 
)

Calculates Planet Similarity Index \((PSI)\) of a planet when comparing it to a reference planet.

The planet similarity index is a number that denotes how similar a planet is to that of the reference. 1 is being exactly like the reference.

\[PSI=\sqrt{PSI_I PSI_S}\]

See http://phl.upr.edu/projects/earth-similarity-index-esi and https://en.wikipedia.org/wiki/Earth_Similarity_Index.

Equations taken from "A Two-Tiered Approach to Assessing the Habitability of Exoplanets" https://doi.org/10.1089/ast.2010.0592.

Parameters
planetMeanRadius\(r\ (m)\) is the mean radius of a planet.
referenceMeanRadius\(r_{ref}\ (m)\) is the mean radius of the reference planet.
planetBulkDensity\(\rho\ (\frac{kg}{m^3})\) is the bulk density of the planet.
referenceBulkDensity\(\rho\ (\frac{kg}{m^3})\) is the bulk density of the reference planet.
planetEscapeVelocity\(v_e\ (\frac{m}{s})\) is the escape velocity needed to escape the planet's gravitational pull.
referenceEscapeVelocity\(v_{e,ref}\ (\frac{m}{s})\) is the escape velocity needed to escape the reference planet's gravitational pull.
planetSurfaceTemperature\(T\ (K)\) is the average surface temperature of the planet.
referenceSurfaceTemperature\(T_{ref}\ (K)\) is the average surface temperature of the reference planet.
Returns
\(PSI\)(dimensionless) Planet Similarity Index for a planet when comparing it to a reference planet.
See also
EarthSimilarityIndex() for \(PSI\) equation using earth as reference.
PlanetSimilarityIndexInterior() for \(PSI_I\) equation.
PlanetSimilarityIndexSurface() for \(PSI_S\) equation.

◆ PlanetSimilarityIndexInterior()

template<typename T >
T EGXPhys::PlanetSimilarityIndexInterior ( const T &  planetMeanRadius,
const T &  referenceMeanRadius,
const T &  planetBulkDensity,
const T &  referenceBulkDensity 
)

Calculates Interior Planet Similarity Index \((PSI_I)\) of a planet when comparing it to a reference planet.

The interior planet similarity index is a number that denotes how similar the interior of the planet is to that of the reference. 1 is being exactly like the reference.

\[PSI_I=\sqrt{PSI_r PSI_\rho}\]

\[PSI_I=\sqrt{\left ( 1 - \left | \frac{r-r_{ref}}{r+r_{ref}} \right | \right )^{0.57} \left ( 1 - \left | \frac{\rho-\rho_{ref}}{\rho+\rho_{ref}} \right | \right )^{1.07}}\]

See http://phl.upr.edu/projects/earth-similarity-index-esi and https://en.wikipedia.org/wiki/Earth_Similarity_Index.

Equations taken from "A Two-Tiered Approach to Assessing the Habitability of Exoplanets" https://doi.org/10.1089/ast.2010.0592.

Parameters
planetMeanRadius\(r\ (m)\) is the mean radius of a planet.
referenceMeanRadius\(r_{ref}\ (m)\) is the mean radius of the reference planet.
planetBulkDensity\(\rho\ (\frac{kg}{m^3})\) is the bulk density of the planet.
referenceBulkDensity\(\rho_{ref}\ (\frac{kg}{m^3})\) is the bulk density of the reference planet.
Returns
\(PSI_I\)(dimensionless) Interior Planet Similarity Index for a planet when comparing it to a reference planet.
See also
PlanetSimilarityIndex() Uses \(PSI_I\) for calculations.
EarthSimilarityIndexInterior() for \(PSI_I\) equation using earth as reference.
PlanetSimilarityIndexSurface() for \(PSI_S\) equation.

◆ PlanetSimilarityIndexSurface()

template<typename T >
T EGXPhys::PlanetSimilarityIndexSurface ( const T &  planetEscapeVelocity,
const T &  referenceEscapeVelocity,
const T &  planetSurfaceTemperature,
const T &  referenceSurfaceTemperature 
)

Calculates Surface Planet Similarity Index \((PSI_S)\) of a planet when comparing it to a reference planet.

The interior planet similarity index is a number that denotes how similar the interior of the planet is to that of the reference. 1 is being exactly like the reference.

\[PSI_S=\sqrt{PSI_{v_e} PSI_T}\]

\[PSI_S=\sqrt{\left ( 1 - \left | \frac{v_e-v_{e,ref}}{v_e+v_{e,ref}} \right | \right )^{0.70} \left ( 1 - \left | \frac{T-T_{ref}}{T+T_{ref}} \right | \right )^{5.58}}\]

See http://phl.upr.edu/projects/earth-similarity-index-esi and https://en.wikipedia.org/wiki/Earth_Similarity_Index.

Equations taken from "A Two-Tiered Approach to Assessing the Habitability of Exoplanets" https://doi.org/10.1089/ast.2010.0592.

Parameters
planetEscapeVelocity\(v_e\ (\frac{m}{s})\) is the escape velocity needed to escape the planet's gravitational pull.
referenceEscapeVelocity\(v_{e,ref}\ (\frac{m}{s})\) is the escape velocity needed to escape the reference planet's gravitational pull.
planetSurfaceTemperature\(T\ (K)\) is the average surface temperature of the planet.
referenceSurfaceTemperature\(T_{ref}\ (K)\) is the average surface temperature of the reference planet.
Returns
\(PSI_S\)(dimensionless) Surface Planet Similarity Index for a planet when comparing it to a reference planet.
See also
PlanetSimilarityIndex() Uses \(PSI_S\) for calculations.
EarthSimilarityIndexSurface() for \(PSI_S\) equation using earth as reference.
PlanetSimilarityIndexInterior() for \(PSI_I\) equation.