astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

, planetary mass is a measure of the

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...

of a

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...

-like

astronomical object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often u ...

. Within the

Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...

, planets are usually measured in the

astronomical system of units The astronomical system of units, formerly called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976 via Resolution No. ...

, where the unit of mass is the

solar mass The solar mass () is a standard unit of mass in astronomy, equal to approximately . It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. It is approximately equal to the mass ...

(), the mass of the Sun. In the study of

extrasolar planet An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...

s, the unit of measure is typically the mass of

Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousand ...

() for large

gas giant A gas giant is a giant planet composed mainly of hydrogen and helium. Gas giants are also called failed stars because they contain the same basic elements as a star. Jupiter and Saturn are the gas giants of the Solar System. The term "gas giant" ...

planets, and the mass of

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...

() for smaller rocky

terrestrial planet A terrestrial planet, telluric planet, or rocky planet, is a planet that is composed primarily of silicate rocks or metals. Within the Solar System, the terrestrial planets accepted by the IAU are the inner planets closest to the Sun: Mercury, ...

s. The mass of a planet within the Solar System is an adjusted parameter in the preparation of ephemerides. There are three variations of how planetary mass can be calculated: * If the planet has

natural satellite A natural satellite is, in the most common usage, an astronomical body that orbits a planet, dwarf planet, or small Solar System body (or sometimes another natural satellite). Natural satellites are often colloquially referred to as ''moons'' ...

s, its mass can be calculated using

Newton's law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distan ...

to derive a generalization of

Kepler's third law In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbi ...

that includes the mass of the planet and its moon. This permitted an early measurement of Jupiter's mass, as measured in units of the

. * The mass of a planet can be inferred from its effect on the

orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...

s of other planets. In 1931-1948 flawed applications of this method led to incorrect calculations of the mass of Pluto. * Data from influence collected from the orbits of

space probe A space probe is an artificial satellite that travels through space to collect scientific data. A space probe may orbit Earth; approach the Moon; travel through interplanetary space; flyby, orbit, or land or fly on other planetary bodies; o ...

s can be used. Examples include ''Voyager'' probes to the outer planets and the

MESSENGER ''MESSENGER'' was a NASA robotic space probe that orbited the planet Mercury between 2011 and 2015, studying Mercury's chemical composition, geology, and magnetic field. The name is a backronym for "Mercury Surface, Space Environment, Geochem ...

spacecraft to Mercury. * Also, numerous other methods can give reasonable approximations. For instance,

Varuna Varuna (; sa, वरुण, , Malay: ''Baruna'') is a Vedic deity associated initially with the sky, later also with the seas as well as Ṛta (justice) and Satya (truth). He is found in the oldest layer of Vedic literature of Hinduism, su ...

, a potential

dwarf planet A dwarf planet is a small planetary-mass object that is in direct orbit of the Sun, smaller than any of the eight classical planets but still a world in its own right. The prototypical dwarf planet is Pluto. The interest of dwarf planets to ...

, rotates very quickly upon its axis, as does the dwarf planet

Haumea , discoverer = , discovered = , earliest_precovery_date = March 22, 1955 , mpc_name = (136108) Haumea , pronounced = , adjectives = Haumean , note = yes , alt_names = , named_after = Haumea , mp_category = , orbit_ref = , epoc ...

. Haumea has to have a very high density in order not to be ripped apart by

centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...

s. Through some calculations, one can place a limit on the object's density. Thus, if the object's size is known, a limit on the mass can be determined. See the links in the aforementioned articles for more details on this.

Choice of units

The choice of

, , as the basic unit for planetary mass comes directly from the calculations used to determine planetary mass. In the most precise case, that of the

itself, the mass is known in terms of solar masses to twelve

significant figures Significant figures (also known as the significant digits, ''precision'' or ''resolution'') of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something. If a number expres ...

: the same mass, in terms of

kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...

s or other Earth-based units, is only known to five significant figures, which is less than a millionth as precise.2009 Selected Astronomical Constants
" in The difference comes from the way in which planetary masses are calculated. It is impossible to "weigh" a planet, and much less the Sun, against the sort of mass standards which are used in the laboratory. On the other hand, the orbits of the planets give a great range of observational data as to the relative positions of each body, and these positions can be compared to their relative masses using

(with small corrections for

General Relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

where necessary). To convert these relative masses to Earth-based units such as the kilogram, it is necessary to know the value of the

Newtonian constant of gravitation The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in th ...

, ''G''. This constant is remarkably difficult to measure in practice, and its value is only known to a precision of one part in ten-thousand. The solar mass is quite a large unit on the scale of the Solar System: 1.9884(2) kg. The largest planet,

, is 0.09% the mass of the Sun, while the Earth is about three millionths (0.0003%) of the mass of the Sun. Various different conventions are used in the literature to overcome this problem: for example, inverting the ratio so that one quotes the planetary mass in the 'number of planets' it would take to make up one Sun. Here, we have chosen to list all planetary masses in 'microSuns' – that is the mass of the Earth is just over three 'microSuns', or three millionths of the mass of the Sun – unless they are specifically quoted in kilograms. When comparing the planets among themselves, it is often convenient to use the

mass of the Earth An Earth mass (denoted as M_\mathrm or M_\oplus, where ⊕ is the standard astronomical symbol for Earth), is a unit of mass equal to the mass of the planet Earth. The current best estimate for the mass of Earth is , with a relative uncertainty ...

(''M''_E or ) as a standard, particularly for the

s. For the mass of

s, and also for most

s and

brown dwarf Brown dwarfs (also called failed stars) are substellar objects that are not massive enough to sustain nuclear fusion of ordinary hydrogen ( 1H) into helium in their cores, unlike a main-sequence star. Instead, they have a mass between the most ...

s, the mass of Jupiter () is a convenient comparison.

Planetary mass and planet formation

The mass of a planet has consequences for its structure by having a large mass, especially while it is in the hand of process of formation. A body with enough mass can overcome its

compressive strength In mechanics, compressive strength or compression strength is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). In other words, compres ...

and achieve a rounded shape (roughly

hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planeta ...

). Since 2006, these objects have been classified as

if it orbits around the Sun (that is, if it is not the

satellite A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioiso ...

of another planet). The threshold depends on a number of factors, such as composition, temperature, and the presence of tidal heating. The smallest body that is known to be rounded is Saturn's moon Mimas, at about the mass of Earth; on the other hand, bodies as large as the Kuiper belt object Salacia, at about the mass of Earth, may not have overcome their compressive strengths. Smaller bodies like

asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...

s are classified as " small Solar System bodies". A dwarf planet, by definition, is not massive enough to have gravitationally cleared its neighbouring region of

planetesimal Planetesimals are solid objects thought to exist in protoplanetary disks and debris disks. Per the Chamberlin–Moulton planetesimal hypothesis, they are believed to form out of cosmic dust grains. Believed to have formed in the Solar System ...

s. The mass needed to do so depends on location: Mars clears its orbit in its current location, but would not do so if it orbited in the

Oort cloud The Oort cloud (), sometimes called the Öpik–Oort cloud, first described in 1950 by the Dutch astronomer Jan Oort, is a theoretical concept of a cloud of predominantly icy planetesimals proposed to surround the Sun at distances ranging from ...

. The smaller planets retain only

silicates In chemistry, a silicate is any member of a family of polyatomic anions consisting of silicon and oxygen, usually with the general formula , where . The family includes orthosilicate (), metasilicate (), and pyrosilicate (, ). The name ...

and metals, and are

s like Earth or

Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...

. The interior structure of rocky planets is mass-dependent: for example,

plate tectonics Plate tectonics (from the la, label= Late Latin, tectonicus, from the grc, τεκτονικός, lit=pertaining to building) is the generally accepted scientific theory that considers the Earth's lithosphere to comprise a number of larg ...

may require a minimum mass to generate sufficient temperatures and pressures for it to occur. Geophysical definitions would also include the dwarf planets and moons in the outer Solar System, which are like terrestrial planets except that they are composed of ice and rock rather than rock and metal: the largest such bodies are Ganymede,

Titan Titan most often refers to: * Titan (moon), the largest moon of Saturn * Titans, a race of deities in Greek mythology Titan or Titans may also refer to: Arts and entertainment Fictional entities Fictional locations * Titan in fiction, fictiona ...

, Callisto,

Triton Triton commonly refers to: * Triton (mythology), a Greek god * Triton (moon), a satellite of Neptune Triton may also refer to: Biology * Triton cockatoo, a parrot * Triton (gastropod), a group of sea snails * ''Triton'', a synonym of ''Triturus'' ...

, and

Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the S ...

. If the protoplanet grows by

accretion Accretion may refer to: Science * Accretion (astrophysics), the formation of planets and other bodies by collection of material through gravity * Accretion (meteorology), the process by which water vapor in clouds forms water droplets around nucl ...

to more than about twice the mass of Earth, its gravity becomes large enough to retain

hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...

in its

atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A ...

. In this case, it will grow into an

ice giant An ice giant is a giant planet composed mainly of elements heavier than hydrogen and helium, such as oxygen, carbon, nitrogen, and sulfur. There are two ice giants in the Solar System: Uranus and Neptune. In astrophysics and planetary ...

. As such, Earth and Venus are close to the maximum size a planet can usually grow to while still remaining rocky. If the planet then begins

migration Migration, migratory, or migrate may refer to: Human migration * Human migration, physical movement by humans from one region to another ** International migration, when peoples cross state boundaries and stay in the host state for some minimum le ...

, it may move well within its system's frost line, and become a

hot Jupiter Hot Jupiters (sometimes called hot Saturns) are a class of gas giant exoplanets that are inferred to be physically similar to Jupiter but that have very short orbital periods (). The close proximity to their stars and high surface-atmosphere t ...

orbiting very close to its star, then gradually losing small amounts of mass as the star's radiation strips its atmosphere. The theoretical minimum mass a star can have, and still undergo hydrogen fusion at the core, is estimated to be about , though fusion of

deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one ...

can occur at masses as low as 13 Jupiters.

Values from the DE405 ephemeris

The DE405/LE405 ephemeris from the

Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a Federally funded research and development centers, federally funded research and development center and NASA field center in the City of La Cañada Flintridge, California, La Cañada Flintridge, California ...

is a widely used ephemeris dating from 1998 and covering the whole Solar System. As such, the planetary masses form a self-consistent set, which is not always the case for more recent data (see below).

Earth mass and lunar mass

Where a planet has natural satellites, its mass is usually quoted for the whole system (planet + satellites), as it is the mass of the whole system which acts as a perturbation on the orbits of other planets. The distinction is very slight, as natural satellites are much smaller than their parent planets (as can be seen in the table above, where only the largest satellites are even listed). The Earth and the Moon form a case in point, partly because the Moon is unusually large (just over 1% of the mass of the Earth) in relation to its parent planet compared with other natural satellites. There are also very precise data available for the Earth–Moon system, particularly from the Lunar Laser Ranging Experiment (LLR). The

geocentric gravitational constant In celestial mechanics, the standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of the bodies. For two bodies the parameter may be expressed as G(m1+m2), or as GM when ...

– the product of the mass of the Earth times the

– can be measured to high precision from the orbits of the Moon and of artificial satellites. The ratio of the two masses can be determined from the slight wobble in the Earth's orbit caused by the gravitational attraction of the Moon.

More recent values

The construction of a full, high-precision Solar System ephemeris is an onerous task. It is possible (and somewhat simpler) to construct partial ephemerides which only concern the planets (or dwarf planets, satellites, asteroids) of interest by "fixing" the motion of the other planets in the model. The two methods are not strictly equivalent, especially when it comes to assigning uncertainties to the results: however, the "best" estimates – at least in terms of quoted uncertainties in the result – for the masses of minor planets and asteroids usually come from partial ephemerides. Nevertheless, new complete ephemerides continue to be prepared, most notably the EPM2004 ephemeris from the Institute of Applied Astronomy of the

Russian Academy of Sciences The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...

. EPM2004 is based on separate observations between 1913 and 2003, more than seven times as many as DE405, and gave more precise masses for Ceres and five asteroids.

IAU best estimates (2009)

A new set of "current best estimates" for various

astronomical constant An astronomical constant is any of several physical constants used in astronomy. Formal sets of constants, along with recommended values, have been defined by the International Astronomical Union (IAU) several times: in 1964Resolution No.4 of thXIIt ...

s was approved the 27th General Assembly of the

International Astronomical Union The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreac ...

(IAU) in August 2009..

IAU current best estimates (2012)

The 2009 set of "current best estimates" was updated in 2012 by resolution B2 of the IAU XXVIII General Assembly. Improved values were given for Mercury and Uranus (and also for the Pluto system and Vesta).

Footnotes

References

{{reflist, 25em Mass Planetary science Units of measurement in astronomy