Earth Similarity Index

Though differing in size and temperature, terrestrial planets of the Solar System tend to have high Earth Similarity Indexes - Mercury (0.60), Venus (0.44), Earth (1.0) and Mars (0.66-0.70) in true colors, sizes to scale.

The Earth Similarity Index, ESI or "easy scale" is a measure of how physically similar a Planetary mass object is to Earth. It is a scale from zero to one, with Earth having a value of one. The ESI was designed to measure planets however the formula can also be applied to large natural satellites and other objects. The ESI is a function of the planet's radius, density, escape velocity, and surface temperature.

ESI values between 0.8 and 1.0 correspond to Earth-like planets with a terrestrial rocky composition that is able to hold an atmosphere under temperate conditions. According to this measure there are no other Earth-like planets or moons in the Solar System (second-ranked Mars falls between 0.66-0.70), though a number of exoplanets have been found with values in this range. Gliese 667C c has the highest Earth Similarity of confirmed exoplanets at 0.85, while Kepler candidate KOI1686.01, if confirmed, would rank at an Earth Similarity of 0.93.

It ESI, however,is not a measure of habitability, and the Planetary Habitability Index is used to measure this instead.

Formulation

The ESI is defined by the expression

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

where $x_{i}$ is one of the planetary properties (e.g. surface temperature), $x_{i_{0}}$ is the corresponding terrestrial reference value (e.g. 288 K) for the property, $w_{i}$ is a weight exponent for the property, and n is the total number of planetary properties. The weight exponents adjust the sensitivity of the scale and equalize their meanings across the different properties. The set of properties, their reference values, and their weight exponents are found in the following table.

Property	Reference Value	Weight Exponent
Mean radius	1.0	0.57
Bulk density	1.0	1.07
Escape velocity	1.0	0.70
Surface temperature	288 K	5.58

ESI has been split into two components to measure different aspects of physical similarity - the Interior ESI and the Surface ESI. The Mean radius and bulk density comprise the Interior ESI, while the escape velocity and surface temperature comprise the Surface ESI. Global ESI is typically cited as the global measure.

Planets with relatively High ESI

Artist's conception of extrasolar planet Kepler-22b which has a predicted high ESI due to its similar size and temperature though its density is currently unknown.

Extrasolar planets dominate the list of known Earth-like objects. However the classification is made difficult in that of the methods of extrasolar planet detection, many methods leave ESI parameters unquantified. For example, with the transit method, one of the more successful methods, measurement of radius can be highly accurate, however mass and density is often estimated. Likewise with radial velocity methods, which provide more accurate measures of mass it can be difficult to successfully measure radius. Planets observed via a number of different methods therefore have the most accurate measures of ESI, though this is not possible in many situations.

The following planets have high ESI scores nearing "Earth-like" composition:

Planet	Global ESI
Gliese 581 g	0.92
Gliese 667C c	0.85
Kepler 22b	0.79-0.81
HD 40307 g	7.9
HD 85512 b	0.77
Tau Ceti e	0.77
Gliese 581 d	0.739
Gliese 163 c	0.73
Tau Ceti f	0.71
Gliese 581c	0.70

ESIs of Non-Planets

The Moon, Io and Earth shown to scale. Although significantly smaller, some of the Solar System's moons and dwarf planets share similarities to Earth's density and temperature resulting in relatively high ESIs. It is theoretically possible for Earth-sized Extrasolar moons and other non-planets to have high ESIs

The ESI can be applied to objects other than planets, including natural satellites, dwarf planets and asteroids though comparisons typically draw lower global ESI due to the lower average density and temperature of these objects, at least for those known in the Solar System.

The following non-planetary objects have have relatively high global ESIs:

Object	Classification	Global ESI
KOI-433.02m	Exomoon (unconfirmed)	0.93
The Moon	Natural satellite	0.56
Io	Natural satellite	0.36
Callisto	Natural satellite	0.34
Ganymede	Natural satellite	0.29
Ceres	Dwarf Planet/Asteroid	0.27
Europa	Natural satellite	0.26
4 Vesta	Asteroid	0.256
Titan	Natural satellite	0.24
2 Pallas	Asteroid	0.222
Titania	Natural satellite	0.10
Enceladus	Natural satellite	0.094
Pluto	Dwarf Planet	0.075
Triton	Natural satellite	0.074

Note that of these, only Titan is known to hold onto a significant atmosphere despite an overall lower size and density.

See also

• Earth analog
• Planetary Habitability Index
• List of potential habitable exoplanets

External links

• "HEC: Data of Potential Habitable Exoplanets and Exomoons". Retrieved 2013-01-05.