Earth's Mass
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An Earth mass (denoted as ''M''🜨, ''M'' or ''M''E, where 🜨 and are the astronomical symbols for Earth), is a unit of
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 ...
equal to the mass of the planet
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 ...
. The current best estimate for the mass of Earth is , with a relative uncertainty of 10−4.The cited value is the recommended value published by 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 ...
in 2009 (se
2016 "Selected Astronomical Constants"
in ).
It is equivalent to an
average density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be use ...
of . Using the nearest
metric prefix A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pr ...
, the Earth mass is approximately six
ronnagram To help compare different ''orders of magnitude'', the following lists describe various ''mass'' levels between 10−67 kg and 1052 kg. The least massive thing listed here is a graviton, and the most massive thing is the observable universe ...
s, or 6.0 Rg. The Earth mass is a standard
unit of 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 ...
in
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 ...
that is used to indicate the masses of other
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 ...
s, including 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 and
exoplanet 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 det ...
s. One
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 ...
is close to Earth masses. The Earth mass excludes the mass of the
Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...
. The mass of the Moon is about 1.2% of that of the Earth, so that the mass of the Earth–Moon system is close to . Most of the mass is accounted for by
iron Iron is a chemical element; it has symbol Fe () and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, forming much of Earth's o ...
and
oxygen Oxygen is a chemical element; it has chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen group (periodic table), group in the periodic table, a highly reactivity (chemistry), reactive nonmetal (chemistry), non ...
(c. 32% each),
magnesium Magnesium is a chemical element; it has Symbol (chemistry), symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 ...
and
silicon Silicon is a chemical element; it has symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic lustre, and is a tetravalent metalloid (sometimes considered a non-metal) and semiconductor. It is a membe ...
(c. 15% each),
calcium Calcium is a chemical element; it has symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air. Its physical and chemical properties are most similar to it ...
,
aluminium Aluminium (or aluminum in North American English) is a chemical element; it has chemical symbol, symbol Al and atomic number 13. It has a density lower than that of other common metals, about one-third that of steel. Aluminium has ...
and
nickel Nickel is a chemical element; it has symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive, but large pieces are slo ...
(c. 1.5% each). Precise measurement of the Earth mass is difficult, as it is equivalent to measuring the
gravitational constant 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 general relativity, theory of general relativity. It ...
, which is the fundamental
physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a ...
known with least accuracy, due to the relative weakness of the
gravitational force 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 proportional to the product of their masses and inversely proportional to the sq ...
. The mass of the Earth was first measured with any accuracy (within about 20% of the correct value) in the
Schiehallion experiment The Schiehallion experiment was an 18th-century experiment to determine the Arithmetic mean, mean density of the Earth. Funded by a grant from the Royal Society, it was conducted in the summer of 1774 around the Scottish Mountains and hills of S ...
in the 1770s, and within 1% of the modern value in the
Cavendish experiment The Cavendish experiment, performed in 1797–1798 by English scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational cons ...
of 1798.


Unit of mass in astronomy

The mass of Earth is estimated to be: : M_\oplus=(5.9722\;\pm\;0.0006)\times10^\;\mathrm, which can be expressed in terms of
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 ...
as: : M_\oplus=\frac\;M_\odot \approx 3.003\times10^\;M_\odot . The ratio of Earth mass to lunar mass has been measured to great accuracy. The current best estimate is: : M_\oplus/M_L=81.3005678\;\pm\;0.0000027 The product of ''M''🜨 and the
universal gravitational constant 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 ...
() is known as the
geocentric gravitational constant The standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of that body. For two bodies, the parameter may be expressed as , or as when one body is much larger than the o ...
(''M''🜨) and equals . It is determined using laser ranging data from Earth-orbiting satellites, such as LAGEOS-1. ''M''🜨 can also be calculated by observing the motion of the Moon or the period of a pendulum at various elevations, although these methods are less precise than observations of artificial satellites. The relative uncertainty of ''M''🜨 is just , considerably smaller than the relative uncertainty for ''M''🜨 itself. ''M''🜨 can be found out only by dividing ''M''🜨 by , and is known only to a relative uncertainty of so ''M''🜨 will have the same uncertainty at best. For this reason and others, astronomers prefer to use ''M''🜨, or mass ratios (masses expressed in units of Earth mass or
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 ...
) rather than mass in kilograms when referencing and comparing planetary objects.


Composition

Earth's density varies considerably, between less than in the upper crust to as much as in the
inner core Earth's inner core is the innermost internal structure of Earth, geologic layer of the planet Earth. It is primarily a solid ball (mathematics), ball with a radius of about , which is about 20% of Earth's radius or 70% of the Moon's radius. T ...
. The
Earth's core The internal structure of Earth are the layers of the Earth, excluding its atmosphere and hydrosphere. The structure consists of an outer silicate solid crust, a highly viscous asthenosphere, and solid mantle, a liquid outer core whose flow g ...
accounts for 15% of Earth's volume but more than 30% of the mass, the mantle for 84% of the volume and close to 70% of the mass, while the crust accounts for less than 1% of the mass.See
structure of the Earth The internal structure of Earth are the layers of the Earth, excluding its atmosphere and hydrosphere. The structure consists of an outer silicate solid crust, a highly viscous asthenosphere, and solid mantle, a liquid outer core whose flow g ...
:
inner core Earth's inner core is the innermost internal structure of Earth, geologic layer of the planet Earth. It is primarily a solid ball (mathematics), ball with a radius of about , which is about 20% of Earth's radius or 70% of the Moon's radius. T ...
volume 0.7%, density 12,600–13,000, mass c. 1.6%;
outer core Earth's outer core is a fluid layer about thick, composed of mostly iron and nickel that lies above Earth's solid Earth's inner core, inner core and below its Earth's mantle, mantle. The outer core begins approximately beneath Earth's surface ...
vol. 14.4%, density 9,900–12,200 mass c. 28.7–31.7%. Hazlett, James S.; Monroe, Reed; Wicander, Richard (2006). ''Physical Geology: Exploring the Earth'' (6. ed.). Belmont: Thomson. p. 346.
About 90% of the mass of the Earth is composed of the iron–nickel alloy (95% iron) in the core (30%), and the
silicon dioxide Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , commonly found in nature as quartz. In many parts of the world, silica is the major constituent of sand. Silica is one of the most complex and abundan ...
s (c. 33%) and
magnesium oxide Magnesium oxide (MgO), or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium (see also oxide). It has an empirical formula of MgO and consists of a lattice of Mg2+ ions and O2− ions ...
(c. 27%) in the mantle and crust. Minor contributions are from
iron(II) oxide Iron(II) oxide or ferrous oxide is the inorganic compound with the formula FeO. Its mineral form is known as wüstite. One of several iron oxides, it is a black-colored powder that is sometimes confused with rust, the latter of which consists ...
(5%),
aluminium oxide Aluminium oxide (or aluminium(III) oxide) is a chemical compound of aluminium and oxygen with the chemical formula . It is the most commonly occurring of several Aluminium oxide (compounds), aluminium oxides, and specifically identified as alum ...
(3%) and
calcium oxide Calcium oxide (formula: Ca O), commonly known as quicklime or burnt lime, is a widely used chemical compound. It is a white, caustic, alkaline, crystalline solid at room temperature. The broadly used term '' lime'' connotes calcium-containing ...
(2%), besides numerous trace elements (in
elementary Elementary may refer to: Arts, entertainment, and media Music * ''Elementary'' (Cindy Morgan album), 2001 * ''Elementary'' (The End album), 2007 * ''Elementary'', a Melvin "Wah-Wah Watson" Ragin album, 1977 Other uses in arts, entertainment, an ...
terms:
iron Iron is a chemical element; it has symbol Fe () and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, forming much of Earth's o ...
and
oxygen Oxygen is a chemical element; it has chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen group (periodic table), group in the periodic table, a highly reactivity (chemistry), reactive nonmetal (chemistry), non ...
c. 32% each,
magnesium Magnesium is a chemical element; it has Symbol (chemistry), symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 ...
and
silicon Silicon is a chemical element; it has symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic lustre, and is a tetravalent metalloid (sometimes considered a non-metal) and semiconductor. It is a membe ...
c. 15% each,
calcium Calcium is a chemical element; it has symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air. Its physical and chemical properties are most similar to it ...
,
aluminium Aluminium (or aluminum in North American English) is a chemical element; it has chemical symbol, symbol Al and atomic number 13. It has a density lower than that of other common metals, about one-third that of steel. Aluminium has ...
and
nickel Nickel is a chemical element; it has symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive, but large pieces are slo ...
c. 1.5% each).
Carbon Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...
accounts for 0.03%,
water Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...
for 0.02%, and the
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 ...
for about one
part per million In science and engineering, the parts-per notation is a set of pseudo-units to describe the small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures ...
.


History of measurement

The mass of Earth is measured indirectly by determining other quantities such as Earth's density, gravity, or gravitational constant. The first measurement in the 1770s
Schiehallion experiment The Schiehallion experiment was an 18th-century experiment to determine the Arithmetic mean, mean density of the Earth. Funded by a grant from the Royal Society, it was conducted in the summer of 1774 around the Scottish Mountains and hills of S ...
resulted in a value about 20% too low. The
Cavendish experiment The Cavendish experiment, performed in 1797–1798 by English scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational cons ...
of 1798 found the correct value within 1%. Uncertainty was reduced to about 0.2% by the 1890s, to 0.1% by 1930. The
figure of the Earth In geodesy, the figure of the Earth is the size and shape used to model planet Earth. The kind of figure depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that is ...
has been known to better than four significant digits since the 1960s ( WGS66), so that since that time, the uncertainty of the Earth mass is determined essentially by the uncertainty in measuring the
gravitational constant 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 general relativity, theory of general relativity. It ...
. Relative uncertainty was cited at 0.06% in the 1970s, and at 0.01% (10−4) by the 2000s. The current relative uncertainty of 10−4 amounts to in absolute terms, of the order of the mass of a
minor planet According to the International Astronomical Union (IAU), a minor planet is an astronomical object in direct orbit around the Sun that is exclusively classified as neither a planet nor a comet. Before 2006, the IAU officially used the term ''minor ...
(70% of the mass of
Ceres Ceres most commonly refers to: * Ceres (dwarf planet), the largest asteroid and first to be discovered * Ceres (mythology), the Roman goddess of agriculture Ceres may also refer to: Places Brazil * Ceres, Goiás, Brazil * Ceres Microregion ...
).


Early estimates

Before the direct measurement of the
gravitational constant 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 general relativity, theory of general relativity. It ...
, estimates of the Earth mass were limited to estimating Earth's mean density from observation of the crust and estimates on Earth's volume. Estimates on the volume of the Earth in the 17th century were based on a circumference estimate of to the degree of latitude, corresponding to a radius of (86% of the Earth's actual radius of about ), resulting in an estimated volume of about one third smaller than the correct value.Mackenzie, A. Stanley,
The laws of gravitation; memoirs by Newton, Bouguer and Cavendish, together with abstracts of other important memoirs
', American Book Company (1900
899 __NOTOC__ Year 899 ( DCCCXCIX) was a common year starting on Monday of the Julian calendar. Events By place Europe * Summer – Arnulf of Carinthia, the King of East Francia, enlists the support of the Magyars, to raid northern Ita ...
, p. 2.
The average density of the Earth was not accurately known. Earth was assumed to consist either mostly of water (
Neptunism Neptunism is a superseded scientific theory of geology proposed by Abraham Gottlob Werner (1749–1817) in the late 18th century, who proposed that rocks formed from the crystallisation of minerals in the early Earth's oceans. The theory took ...
) or mostly of
igneous rock Igneous rock ( ), or magmatic rock, is one of the three main rock types, the others being sedimentary and metamorphic. Igneous rocks are formed through the cooling and solidification of magma or lava. The magma can be derived from partial ...
(
Plutonism Plutonism is the geology, geologic theory that the igneous rocks forming the Earth originated from intrusive Magma, magmatic activity, with a continuing gradual process of weathering and erosion wearing away rocks, which were then deposited on t ...
), both suggesting average densities far too low, consistent with a total mass of the order of .
Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
estimated, without access to reliable measurement, that the density of Earth would be five or six times as great as the density of water, which is surprisingly accurate (the modern value is 5.515). Newton under-estimated the Earth's volume by about 30%, so that his estimate would be roughly equivalent to . In the 18th century, knowledge of
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 ...
permitted indirect estimates on the mean density of the Earth, via estimates of (what in modern terminology is known as) the
gravitational constant 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 general relativity, theory of general relativity. It ...
. Early estimates on the mean density of the Earth were made by observing the slight deflection of a pendulum near a mountain, as in the
Schiehallion experiment The Schiehallion experiment was an 18th-century experiment to determine the Arithmetic mean, mean density of the Earth. Funded by a grant from the Royal Society, it was conducted in the summer of 1774 around the Scottish Mountains and hills of S ...
. Newton considered the experiment in ''
Principia Principia may refer to: * ''Philosophiæ Naturalis Principia Mathematica'', Isaac Newton's three-volume work about his laws of motion and universal gravitation * Principia ( "primary buildings"), the headquarters at the center of Roman forts () * ...
'', but pessimistically concluded that the effect would be too small to be measurable. An expedition from 1737 to 1740 by
Pierre Bouguer Pierre Bouguer () (16 February 1698, Le Croisic – 15 August 1758, Paris) was a French mathematician, geophysicist, geodesist, and astronomer. He is also known as "the father of naval architecture". Career Bouguer's father, Jean Bouguer, ...
and
Charles Marie de La Condamine Charles Marie de La Condamine (; 28 January 1701 – 4 February 1774) was a French explorer, geographer, and mathematician. He spent ten years in territory which is now Ecuador, measuring the length of a degree of latitude at the equator and pre ...
attempted to determine the density of Earth by measuring the period of a pendulum (and therefore the strength of gravity) as a function of elevation. The experiments were carried out in Ecuador and Peru, on
Pichincha Volcano Pichincha is a stratovolcano in Ecuador. The capital Quito wraps around its eastern slopes. The two highest peaks of the mountain are Wawa Pichincha ( Kichwa ''wawa'' child, baby / small, Spanish spelling ''Guagua Pichincha'') () and Ruku Pichinc ...
and mount
Chimborazo Chimborazo () is a stratovolcano situated in Ecuador in the Cordillera Occidental (Ecuador), Cordillera Occidental range of the Andes. Its last known Types of volcanic eruptions, eruption is believed to have occurred around AD 550. Although not ...
. Bouguer wrote in a 1749 paper that they had been able to detect a deflection of 8 
seconds of arc A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of a degree. Since one degree is of a turn, or complete rotation, one arcminute is of a tu ...
, the accuracy was not enough for a definite estimate on the mean density of the Earth, but Bouguer stated that it was at least sufficient to prove that the Earth was not
hollow Hollow may refer to: Natural phenomena *Hollow, a low, wooded area, such as a copse * Hollow (landform), a small vee-shaped, riverine type of valley *Tree hollow, a void in a branch or trunk, which may provide habitat for animals Arts, entertai ...
.


Schiehallion experiment

That a further attempt should be made on the experiment was proposed to the
Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
in 1772 by
Nevil Maskelyne Nevil Maskelyne (; 6 October 1732 – 9 February 1811) was the fifth British Astronomer Royal. He held the office from 1765 to 1811. He was the first person to scientifically measure the mass of the planet Earth. He created '' The Nautical Al ...
,
Astronomer Royal Astronomer Royal is a senior post in the Royal Households of the United Kingdom. There are two officers, the senior being the astronomer royal dating from 22 June 1675; the junior is the astronomer royal for Scotland dating from 1834. The Astro ...
. He suggested that the experiment would "do honour to the nation where it was made" and proposed
Whernside Whernside is a mountain in the Yorkshire Dales in Northern England. It is the highest of the Yorkshire Three Peaks, the other two being Ingleborough and Pen-y-ghent. It is the highest point in the ceremonial county of North Yorkshire Mickle F ...
in
Yorkshire Yorkshire ( ) is an area of Northern England which was History of Yorkshire, historically a county. Despite no longer being used for administration, Yorkshire retains a strong regional identity. The county was named after its county town, the ...
, or the
Blencathra Blencathra, also known as Saddleback, is one of the most northerly of the Cumbrian Mountains, in the English Lake District. It has six separate fell tops, of which the highest is the Hallsfell Top at . Name For many years, Ordnance Surv ...
-
Skiddaw Skiddaw is a mountain in the Lake District National Park in England. Its summit is traditionally considered to be the List of Wainwrights, fourth-highest peak but depending on what topographic prominence is thought to be significant is also ...
massif in
Cumberland Cumberland ( ) is an area of North West England which was historically a county. The county was bordered by Northumberland to the north-east, County Durham to the east, Westmorland to the south-east, Lancashire to the south, and the Scottish ...
as suitable targets. The Royal Society formed the Committee of Attraction to consider the matter, appointing Maskelyne,
Joseph Banks Sir Joseph Banks, 1st Baronet, (19 June 1820) was an English Natural history, naturalist, botanist, and patron of the natural sciences. Banks made his name on the European and American voyages of scientific exploration, 1766 natural-history ...
and
Benjamin Franklin Benjamin Franklin (April 17, 1790) was an American polymath: a writer, scientist, inventor, statesman, diplomat, printer, publisher and Political philosophy, political philosopher.#britannica, Encyclopædia Britannica, Wood, 2021 Among the m ...
amongst its members. The Committee despatched the astronomer and surveyor
Charles Mason Charles Mason (25 April 1728Schiehallion Schiehallion (; , ) is a prominent cone-shaped mountain in the Breadalbane, Scotland, Breadalbane region of the Scottish Highlands, in the county of Perthshire. It rises to and is classed as a Munro. Schiehallion has a rich flora, interesting ...
, a peak in the central
Scottish Highlands The Highlands (; , ) is a historical region of Scotland. Culturally, the Highlands and the Scottish Lowlands, Lowlands diverged from the Late Middle Ages into the modern period, when Scots language, Lowland Scots language replaced Scottish Gae ...
. The mountain stood in isolation from any nearby hills, which would reduce their gravitational influence, and its symmetrical east–west ridge would simplify the calculations. Its steep northern and southern slopes would allow the experiment to be sited close to its
centre of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For a ...
, maximising the deflection effect.
Nevil Maskelyne Nevil Maskelyne (; 6 October 1732 – 9 February 1811) was the fifth British Astronomer Royal. He held the office from 1765 to 1811. He was the first person to scientifically measure the mass of the planet Earth. He created '' The Nautical Al ...
,
Charles Hutton Charles Hutton FRS FRSE LLD (14 August 1737 – 27 January 1823) was an English mathematician and surveyor. He was professor of mathematics at the Royal Military Academy, Woolwich from 1773 to 1807. He is remembered for his calculation of th ...
and Reuben Burrow performed the experiment, completed by 1776. Hutton (1778) reported that the mean density of the Earth was estimated at that of Schiehallion mountain. This corresponds to a mean density about higher than that of water (i.e., about ), about 20% below the modern value, but still significantly larger than the mean density of normal rock, suggesting for the first time that the interior of the Earth might be substantially composed of metal. Hutton estimated this metallic portion to occupy some (or 65%) of the diameter of the Earth (modern value 55%).Hutton (1778), p. 783. With a value for the mean density of the Earth, Hutton was able to set some values to
Jérôme Lalande Joseph Jérôme Lefrançois de Lalande (; 11 July 1732 – 4April 1807) was a French astronomer, freemason and writer. He is known for having estimated a precise value of the astronomical unit (the distance from the Earth to the Sun) using measu ...
's planetary tables, which had previously only been able to express the densities of the major Solar System objects in relative terms.


Cavendish experiment

Henry Cavendish (1798) was the first to attempt to measure the gravitational attraction between two bodies directly in the laboratory. Earth's mass could be then found by combining two equations;
Newton's second law Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
, and
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 ...
. In modern notation, the mass of the Earth is derived from the
gravitational constant 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 general relativity, theory of general relativity. It ...
and the mean
Earth radius Earth radius (denoted as ''R''🜨 or ''R''E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equato ...
by : M_\oplus =\frac = \frac. Where
gravity of Earth The gravity of Earth, denoted by , is the net force, net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a Eucl ...
, "little g", is : g = G\frac. Cavendish found a mean density of , about 1% below the modern value.


19th century

While the mass of the Earth is implied by stating the Earth's radius and density, it was not usual to state the absolute mass explicitly prior to the introduction of
scientific notation Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientif ...
using powers of 10 in the later 19th century, because the absolute numbers would have been too awkward. Ritchie (1850) gives the mass of the
Earth's atmosphere The atmosphere of Earth is composed of a layer of gas mixture that surrounds the Earth's planetary surface (both lands and oceans), known collectively as air, with variable quantities of suspended aerosols and particulates (which create weathe ...
as "11,456,688,186,392,473,000 lbs". ( = , modern value is ) and states that "compared with the weight of the globe this mighty sum dwindles to insignificance". Absolute figures for the mass of the Earth are cited only beginning in the second half of the 19th century, mostly in popular rather than expert literature. An early such figure was given as "14
septillion Depending on context (e.g. language, culture, region), some large numbers have names that allow for describing large quantities in a textual form; not mathematics, mathematical. For very large values, the text is generally shorter than a decimal n ...
pounds" (''14 Quadrillionen Pfund'') [] in Masius (1859). Edmund Beckett, 1st Baron Grimthorpe, Beckett (1871) cites the "weight of the earth" as "5842 1e18, quintillion long ton, tons" []. The "mass of the earth in gravitational measure" is stated as "9.81996×63709802" in ''The New Volumes of the Encyclopaedia Britannica'' (Vol. 25, 1902) with a "logarithm of earth's mass" given as "14.600522" []. This is the standard gravitational parameter, gravitational parameter in m3·s−2 (modern value ) and not the absolute mass. Experiments involving pendulums continued to be performed in the first half of the 19th century. By the second half of the century, these were outperformed by repetitions of the Cavendish experiment, and the modern value of (and hence, of the Earth mass) is still derived from high-precision repetitions of the Cavendish experiment. In 1821,
Francesco Carlini Francesco Carlini (January 7, 1783 – August 29, 1862) was an Italian astronomer. Born in Milan, he became director of the Brera Astronomical Observatory there in 1832. He published ''Nuove tavole de moti apparenti del sole'' in 1832. In 1810, ...
determined a density value of through measurements made with pendulums in the
Milan Milan ( , , ; ) is a city in northern Italy, regional capital of Lombardy, the largest city in Italy by urban area and the List of cities in Italy, second-most-populous city proper in Italy after Rome. The city proper has a population of nea ...
area. This value was refined in 1827 by
Edward Sabine Sir Edward Sabine (; 14 October 1788 – 26 June 1883) was an Irish physicist, geodesist,astronomer, geophysicist, ornithologist, polar explorer, soldier, and the 30th president of the Royal Society. He led the effort to establish a system o ...
to , and then in 1841 by Carlo Ignazio Giulio to . On the other hand,
George Biddell Airy Sir George Biddell Airy (; 27 July 18012 January 1892) was an English mathematician and astronomer, as well as the Lucasian Professor of Mathematics from 1826 to 1828 and the seventh Astronomer Royal from 1835 to 1881. His many achievements inc ...
sought to determine ρ by measuring the difference in the period of a pendulum between the surface and the bottom of a mine. The first tests and experiments took place in Cornwall between 1826 and 1828. The experiment was a failure due to a fire and a flood. Finally, in 1854, Airy got the value by measurements in a coal mine in Harton, Sunderland. Airy's method assumed that the Earth had a spherical stratification. Later, in 1883, the experiments conducted by Robert von Sterneck (1839 to 1910) at different depths in mines of Saxony and Bohemia provided the average density values ''ρ'' between 5.0 and . This led to the concept of isostasy, which limits the ability to accurately measure ''ρ'', by either the deviation from vertical of a plumb line or using pendulums. Despite the little chance of an accurate estimate of the average density of the Earth in this way,
Thomas Corwin Mendenhall Thomas Corwin Mendenhall (October 4, 1841 – March 23, 1924) was an American autodidact physicist and meteorologist. He was the first professor hired at Ohio State University in 1873 and the superintendent of the United States Coast and Geodeti ...
in 1880 realized a gravimetry experiment in Tokyo and at the top of
Mount Fuji is an active stratovolcano located on the Japanese island of Honshu, with a summit elevation of . It is the highest mountain in Japan, the second-highest volcano on any Asian island (after Mount Kerinci on the Indonesian island of Sumatra), a ...
. The result was .


Modern value

The uncertainty in the modern value for the Earth's mass has been entirely due to the uncertainty in the
gravitational constant 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 general relativity, theory of general relativity. It ...
''G'' since at least the 1960s. ''G'' is notoriously difficult to measure, and some high-precision measurements during the 1980s to 2010s have yielded mutually exclusive results. Sagitov (1969) based on the measurement of ''G'' by Heyl and Chrzanowski (1942) cited a value of ''M''🜨 (relative uncertainty ). Accuracy has improved only slightly since then. Most modern measurements are repetitions of the Cavendish experiment, with results (within standard uncertainty) ranging between 6.672 and (relative uncertainty ) in results reported since the 1980s, although the 2014
CODATA The Committee on Data of the International Science Council (CODATA) was established in 1966 as the Committee on Data for Science and Technology, originally part of the International Council of Scientific Unions, now part of the International ...
recommended value is close to with a relative uncertainty below 10−4. The ''Astronomical Almanach Online'' as of 2016 recommends a standard uncertainty of for Earth mass, ''M''🜨 =


Variation

Earth's mass is variable, subject to both gain and loss due to the accretion of in-falling material, including micrometeorites and cosmic dust and the loss of hydrogen and helium gas, respectively. The combined effect is a net loss of material, estimated at per year. The annual net loss is essentially due to 100,000 tons lost due to
atmospheric escape Atmospheric escape is the loss of planetary atmospheric gases to outer space. A number of different mechanisms can be responsible for atmospheric escape; these processes can be divided into thermal escape, non-thermal (or suprathermal) escape, and ...
, and an average of 45,000 tons gained from in-falling dust and meteorites. This is well within the mass uncertainty of 0.01% (), so the estimated value of Earth's mass is unaffected by this factor. Mass loss is due to atmospheric escape of gases. About 95,000 tons of hydrogen per year () and 1,600 tons of helium per year are lost through atmospheric escape. The main factor in mass gain is in-falling material,
cosmic dust Cosmic dustalso called extraterrestrial dust, space dust, or star dustis dust that occurs in outer space or has fallen onto Earth. Most cosmic dust particles measure between a few molecules and , such as micrometeoroids (30 μm). Cosmic dust can ...
,
meteors A meteor, known colloquially as a shooting star, is a glowing streak of a small body (usually meteoroid) going through Earth's atmosphere, after being heated to incandescence by collisions with air molecules in the upper atmosphere, creating a ...
, etc. are the most significant contributors to Earth's increase in mass. The sum of material is estimated to be annually, although this can vary significantly; to take an extreme example, the
Chicxulub impactor The Chicxulub crater is an impact crater buried underneath the Yucatán Peninsula in Mexico. Its center is offshore, but the crater is named after the onshore community of Chicxulub Pueblo (not the larger coastal town of Chicxulub Puerto). I ...
, with a midpoint mass estimate of , added 900 million times that annual dustfall amount to the Earth's mass in a single event. Additional changes in mass are due to the mass–energy equivalence principle, although these changes are relatively negligible. Mass loss due to the combination of
nuclear fission Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactiv ...
and natural
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ...
is estimated to amount to 16 tons per year. An additional loss due to
spacecraft A spacecraft is a vehicle that is designed spaceflight, to fly and operate in outer space. Spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth observation, Weather s ...
on escape trajectories has been estimated at since the mid-20th century. Earth lost about 3473 tons in the initial 53 years of the space age, but the trend is currently decreasing.


See also

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Abundance of elements in Earth's crust The abundance of elements in Earth's crust is shown in tabulated form with the estimated Earth's crust, crustal abundance for each chemical element shown as mg/kg, or parts-per notation, parts per million (ppm) by mass (10,000 ppm = 1%). Res ...
*
Cavendish experiment The Cavendish experiment, performed in 1797–1798 by English scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational cons ...
*
Earth radius Earth radius (denoted as ''R''🜨 or ''R''E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equato ...
*
Orders of magnitude (mass) To help compare different ''orders of magnitude'', the following lists describe various ''mass'' levels between 10−67 kg and 1052 kg. The least massive thing listed here is a graviton, and the most massive thing is the observable universe ...
*
Planetary mass In astronomy, planetary mass is a measure of the mass of a planet-like astronomical object. Within the Solar System, planets are usually measured in the astronomical system of units, where the unit of mass is the solar mass (), the mass of the Sun ...
*
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 ...
*
Internal structure of Earth The internal structure of Earth are the layers of the Earth, excluding its atmosphere and hydrosphere. The structure consists of an outer silicate solid crust, a highly viscous asthenosphere, and solid mantle, a liquid outer core whose flow ge ...


References

{{Portal bar, Mathematics, Astronomy, Stars, Outer space, Science Units of mass Planetary science Planetary geology Units of measurement in astronomy
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 ...