astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

, planetary mass is a measure of the

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

of a

planet A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...

-like

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

. Within the

Solar System The Solar SystemCapitalization 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 "Sola ...

, 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 frequently used unit of mass in astronomy, equal to approximately . It is approximately equal to the mass of the Sun. It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxie ...

(), the mass of the

Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...

. In the study of

extrasolar planet An exoplanet or extrasolar planet is a planet outside the Solar System. The first confirmed detection of an exoplanet was in 1992 around a pulsar, and the first detection around a main-sequence star was in 1995. A different planet, first detect ...

s, the unit of measure is typically the mass of

Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a Jupiter mass, mass more than 2.5 times that of all the other planets in the Solar System combined a ...

() for large

gas giant A gas giant is a giant planet composed mainly of hydrogen and helium. Jupiter and Saturn are the gas giants of the Solar System. The term "gas giant" was originally synonymous with "giant planet". However, in the 1990s, it became known that Uranu ...

planets, and the mass of

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

() for smaller rocky

terrestrial planet A terrestrial planet, tellurian 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 ...

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 colloquially referred to as moons, a deriv ...

s, its mass can be calculated using

Newton's law of universal gravitation Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is Proportionality (mathematics)#Direct proportionality, proportional to the product ...

to derive a generalization of Kepler's third law 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 (also known as orbital revolution) 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 ...

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 Uncrewed spacecraft or robotic spacecraft are spacecraft without people on board. Uncrewed spacecraft may have varying levels of autonomy from human input, such as remote control, or remote guidance. They may also be autonomous, in which th ...

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

MESSENGER Messenger, Messengers, The Messenger or The Messengers may refer to: People * Courier, a person or company that delivers messages, packages, or mail * Messenger (surname) * Bicycle messenger, a bicyclist who transports packages through cities * M ...

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

Varuna Varuna (; , ) is a Hindu god. He is one of the earliest deities in pantheon, whose role underwent a significant transformation from the Vedic to the Puranic periods. In the early Vedic era, Varuna is seen as the god-sovereign, ruling the sky ...

, a potential

dwarf planet A dwarf planet is a small planetary-mass object that is in direct orbit around the Sun, massive enough to be hydrostatic equilibrium, gravitationally rounded, but insufficient to achieve clearing the neighbourhood, orbital dominance like the ...

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

Haumea Haumea ( minor-planet designation: 136108 Haumea) is a dwarf planet located beyond Neptune's orbit. It was discovered in 2004 by a team headed by Mike Brown of Caltech at the Palomar Observatory, and formally announced in 2005 by a team heade ...

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

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

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 referred to as significant digits, are specific digits within a number that is written in positional notation that carry both reliability and necessity in conveying a particular quantity. When presenting the outcom ...

: the same mass, in terms of

kilogram The kilogram (also spelled kilogramme) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg. The word "kilogram" is formed from the combination of the metric prefix kilo- (m ...

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 as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...

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 is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity. It is also known as t ...

, ''G''. This constant is remarkably difficult to measure in practice, and its value is known to a relative precision of only The solar mass is quite a large unit on the scale of the Solar System: . 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. When comparing the planets among themselves, it is often convenient to use the mass of the Earth (''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 are substellar objects that have more mass than the biggest gas giant planets, but less than the least massive main sequence, main-sequence stars. Their mass is approximately 13 to 80 Jupiter mass, times that of Jupiter ()not big en ...

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 Structural system, structure to withstand Structural load, loads tending to reduce size (Compression (physics), compression). It is opposed to ''tensil ...

and achieve a rounded shape (roughly

hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and 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. I ...

). 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 an artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication relay, weather forecasting, navigation ( GPS), broadcasting, scient ...

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—an object larger than a meteoroid that is neither a planet nor an identified comet—that orbits within the Solar System#Inner Solar System, inner Solar System or is co-orbital with Jupiter (Trojan asteroids). As ...

s are classified as "

small Solar System bodies A small Solar System body (SSSB) is an object in the Solar System that is neither a planet, a dwarf planet, nor a natural satellite. The term was first IAU definition of planet, defined in 2006 by the International Astronomical Union (IAU) as fo ...

". 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. Believed to have formed in the Solar System about 4.6 billion years ago, they aid study of its formation. Formation A widely accepted theory of pla ...

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 (pronounced or ), sometimes called the Öpik–Oort cloud, is scientific theory, theorized to be a cloud of billions of Volatile (astrogeology), icy planetesimals surrounding the Sun at distances ranging from 2,000 to 200,000 A ...

. The smaller planets retain only

silicates 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 is also used for an ...

and metals, and are

s like Earth or

Mars Mars is the fourth planet from the Sun. It is also known as the "Red Planet", because of its orange-red appearance. Mars is a desert-like rocky planet with a tenuous carbon dioxide () atmosphere. At the average surface level the atmosph ...

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

plate tectonics Plate tectonics (, ) is the scientific theory that the Earth's lithosphere comprises a number of large tectonic plates, which have been slowly moving since 3–4 billion years ago. The model builds on the concept of , an idea developed durin ...

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 CALLISTO (''Cooperative Action Leading to Launcher Innovation in Stage Toss-back Operations'') is a reusable VTVL Prototype, demonstrator propelled by a small 40 kN Japanese LOX-LH2 rocket engine. It is being developed jointly by the CNES, French ...

, Triton, 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 Su ...

. If the protoplanet grows by accretion to more than about twice the mass of Earth, its gravity becomes large enough to retain

hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

in its

atmosphere An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...

. 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 science ...

. 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 (i.e. Jupiter analogue, Jupiter analogues) but that have very short orbital periods (). The close proximity to 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 (hydrogen-2, symbol H or D, also known as heavy hydrogen) is one of two stable isotopes of hydrogen; the other is protium, or hydrogen-1, H. The deuterium nucleus (deuteron) contains one proton and one neutron, whereas the far more c ...

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 (FFRDC) in La Cañada Flintridge, California, Crescenta Valley, United States. Founded in 1936 by Cali ...

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 Lunar Laser Ranging (LLR) is the practice of measuring Lunar distance (astronomy), the distance between the surfaces of the Earth and the Moon using Lidar, laser ranging. The distance can be calculated from the Round-trip delay, round-trip time ...

(LLR). The geocentric gravitational constant – 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; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...

. 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 constants was approved the 27th General Assembly of the

International Astronomical Union The International Astronomical Union (IAU; , UAI) is an international non-governmental organization (INGO) with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach, education, and developmen ...

(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