# Earth Similarity Index

Though differing in size and temperature, terrestrial planets of the Solar System tend to have high Earth Similarity Indexes - Mercury (0.39), Venus (0.78), Earth (1.00) and Mars (0.64). In true colors, sizes to scale.[1]

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, but 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.[2][3] These parameters are often estimated based on one or more known variables. Such variables depend greatly on the method of observation used. For example, surface temperature is influenced by a variety of factors including irradiance, tidal heating, albedo, insolation and greenhouse warming. Where these are not known, planetary equilibrium temperature is frequently used, or the variable is inferred from other known attributes.

A planet with a high ESI (values in the range from 0.8 and 1.0) is likely to be of terrestrial rocky composition.

ESI is not a measure of habitability, though given the point of reference being Earth, some of its functions match closely to those used by habitability measures. The ESI and habitable zone share in common the use of surface temperature as a primary function (and the terrestrial point of reference).

According to this measure there are no other Earth-like planets or moons in the Solar System (second-ranked Venus is 0.78), though a number of exoplanets have been found with values in this range. Kepler-62e has the highest Earth Similarity of confirmed exoplanets at 0.83, while Kepler candidate KOI-1686.01, if confirmed, would be likely to have an ESI of 0.89. Further, the candidate exomoon HD 222582 b m of a confirmed exoplanet, and several candidate exomoons (KOI 375.01 m, KOI-2933.01 m, KOI-422.01 m) of unconfirmed exoplanets, all have an ESI of 0.86.[1]

On November 4, 2013, astronomers reported, based on Kepler space mission data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy.[4][5] 11 billion of these estimated planets may be orbiting sun-like stars.[6] The nearest such planet may be 12 light-years away, according to the scientists.[4][5]

## Formulation

The ESI is defined by the expression

$ESI = \prod_{i=1}^n \left(1 - \left| \frac{x_i - x_{i_0}}{x_i + x_{i_0}} \right| \right)^\frac{w_i}{n}$

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
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

Comparison of the sizes of planets Kepler-69c, Kepler-62e (0.82), Kepler-62f (0.69), and the Earth. All planets except the Earth are artists' conceptions.

Extrasolar planets dominate the list of known Earth-like objects. However, the classification is made difficult in that many methods of extrasolar planet detection leave ESI parameters unquantified. For example, with the transit method, one of the more successful, measurement of radius can be highly accurate, but mass and density are often estimated; likewise with radial velocity methods, which provide accurate measurements of mass but are less successful measuring 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 been determined to have higher ESI than Venus or Mars:

Planet Global ESI Status/Note/References
KOI-3284.01 0.90[citation needed] Unconfirmed[1]
KOI-1686.01 0.89[citation needed] Unconfirmed[1]
KOI-3010.01 0.87[citation needed] Unconfirmed[1]
Gliese 667C c 0.84[citation needed]
KOI-4742.01 0.83[citation needed] Unconfirmed[1]
Kepler-62 e 0.83[citation needed]
KOI-1422.04 0.82[citation needed] Unconfirmed
Gliese 832 c 0.81[citation needed]
Gliese 581 c 0.70[7]
Kepler-186 f 0.64[8]
HD 69830 d 0.60[7]
55 Cnc c 0.56[7]
Gliese 581 e 0.53[7]

## 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.[9]

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

Object Classification Global ESI
HD 222582 b m Exomoon (unconfirmed) 0.86[citation needed]
Moon Natural satellite 0.56[7]
Io Natural satellite 0.36[citation needed]
Callisto Natural satellite 0.34[citation needed]
Ganymede Natural satellite 0.29[citation needed]
Ceres Dwarf planet, asteroid 0.27[citation needed]
Europa Natural satellite 0.64[citation needed]
4 Vesta Asteroid 0.256[citation needed]
Titan Natural satellite 0.24[citation needed]
2 Pallas Asteroid 0.222[citation needed]
Titania Natural satellite 0.10[citation needed]
Pluto Dwarf planet 0.075[citation needed]
Triton Natural satellite 0.074[citation needed]

Of these, only Titan is known to hold on to a significant atmosphere despite an overall lower size and density.