Earth Similarity Index

Size comparison of earth-like planets in our solar system and their ESI: Mercury (0.596), Venus (0.444), Earth (1,000), and Mars (0.697)

The Earth Similarity Index ( English for "Erdähnlichkeitsindex"), short- ESI , one is scale for evaluating the similarity of a celestial body with the earth . The value is between 0 and 1, with the earth having the value 1. It was developed for planets and exoplanets , but can also be applied to other objects. The ESI is calculated from the radius , the density , the cosmic speed and the temperature at the surface. Within our solar system , Mars is the object with the second largest ESI with 0.697 just after Earth.

The ESI was proposed in 2011 by staff at the University of Puerto Rico's Planetary Habitability Laboratory (PHL) . It has in common with the concept of the habitable zone the surface temperature as an essential parameter and the earth as a reference. However, it does not serve as a measure of habitability. In addition to the ESI, the authors proposed the Planetary Habitability Index , or PHI for short.

calculation

One looks at parameters and compares the value of the earth with the corresponding value of the object under consideration . To do this, a kind of symmetrical relative deviation is inverted so that identical values ​​result in 1 and the largest possible deviation in 0: ${\displaystyle n}$ ${\displaystyle x_{i_{0}}}$ ${\displaystyle x_{i}}$

${\displaystyle F_{x_{i}}=1-\left|{\frac {x_{i}-x_{i_{0}}}{x_{i}+x_{i_{0}}}}\right|}$

The ESI is determined as the weighted geometric mean of these deviations:

${\displaystyle \mathrm {ESI} ={\sqrt[{n}]{\prod _{i=1}^{n}\left(F_{x_{i}}\right)^{w_{i}}}}=\prod _{i=1}^{n}\left(1-\left|{\frac {x_{i}-x_{i_{0}}}{x_{i}+x_{i_{0}}}}\right|\right)^{\frac {w_{i}}{n}}}$

The ESI is also used in two sub-aspects: the interior ESI (English for 'inner ESI') is only calculated with the two parameters radius and density; the surface ESI (English for 'surface ESI') from the other two parameters. The following table shows the weightings specified for the ESI and the values ​​for the planet Venus as examples: ${\displaystyle w_{i}}$

parameter	${\displaystyle w_{i}}$	earth ${\displaystyle x_{i_{0}}}$	Venus ${\displaystyle x_{i}}$	${\displaystyle F_{x_{i}}}$	${\displaystyle \left(F_{x_{i}}\right)^{w_{i}}}$
medium radius	0.57	6371 km	6052 km	0.974	0.985	${\displaystyle \mathrm {ESI} _{\mathrm {interior} }={\sqrt {0{,}985\cdot 0{,}973}}=0{,}979}$
Bulk density	1.07	5.515 g / cm³	5.243 g / cm³	0.975	0.973
Cosmic speeds	0.70	11.186 km / s	10.360 km / s	0.962	0.973	${\displaystyle \mathrm {ESI} _{\text{surface}}={\sqrt {0{,}973\cdot 0{,}042}}=0{,}201}$
Surface temperature	5.58	288 K	730 K	0.566	0.042

The ESI for the planet Venus is thus:

${\displaystyle \mathrm {ESI} ={\sqrt {\mathrm {ESI} _{\text{interior}}\cdot \mathrm {ESI} _{\text{surface}}}}={\sqrt {0{,}979\cdot 0{,}201}}=0{,}444}$

See also

• List of potentially habitable planets

Web links

• Planetary Habitability Laboratory (PHL): Earth Similarity Index (ESI)
• picture of science: exoplanets put to the test

Individual evidence

1. ↑ ^{a b} data_solar_ESI.txt referenced in Earth Similarity Index (ESI)
2. ↑ Dirk Schulze-Makuch et al: A Two-Tiered Approach to Assessing the Habitability of Exoplanets . In: Astrobiology . tape 11 , no. 10 , December 2011, p. 1041-1052 , doi : 10.1089 / ast.2010.0592 .