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An Earth mass (denoted as M🜨, M♁ or ME, where and are the astronomical Earth symbol), 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 of 10−4.The cited value is the recommended value published by the International Astronomical Union in 2009 (see 2016 "Selected Astronomical Constants" in ). It is equivalent to an average density of . Using the nearest metric prefix, the Earth mass is approximately six , or 6.0 Rg.
The Earth mass is a standard unit of mass in astronomy that is used to indicate the masses of other , including rocky terrestrial planets and . One Solar mass is close to Earth masses. The Earth mass excludes the mass of the Moon. 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 and oxygen (c. 32% each), magnesium and silicon (c. 15% each), calcium, aluminium and nickel (c. 1.5% each).
Precise measurement of the Earth mass is difficult, as it is equivalent to measuring the gravitational constant, which is the fundamental physical constant known with least accuracy, due to the relative weakness of the gravitational force. The mass of the Earth was first measured with any accuracy (within about 20% of the correct value) in the Schiehallion experiment in the 1770s, and within 1% of the modern value in the Cavendish experiment of 1798.
The ratio of Earth mass to lunar mass has been measured to great accuracy. The current best estimate is:
| + Masses of noteworthy astronomical objects relative to the mass of Earth | ||
| Moon | ||
| Sun | ||
| Mercury | 0.0553 | |
| Venus | 0.815 | |
| Earth | 1 | by definition |
| Mars | 0.107 | |
| Jupiter | 317.8 | |
| Saturn | 95.2 | |
| Uranus | 14.5 | |
| Neptune | 17.1 | |
| Pluto | 0.0025 | |
| Eris | 0.0027 | |
| Gliese 667 Cc | 3.8 | |
| Kepler-442b | 1.0 – 8.2 |
The product of M🜨 and the universal gravitational constant () is known as the geocentric gravitational constant ( M🜨) and equals . It is determined using laser ranging data from Earth-orbiting satellites, such as LAGEOS. 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) rather than mass in kilograms when referencing and comparing planetary objects.
The figure of the Earth 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. Relative uncertainty was cited at 0.06% in the 1970s,IAU (1976) System of Astronomical Constants 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 (70% of the mass of Ceres).
The average density of the Earth was not accurately known. Earth was assumed to consist either mostly of water (Neptunism) or mostly of igneous rock (Plutonism), both suggesting average densities far too low, consistent with a total mass of the order of . Isaac Newton estimated, without access to reliable measurement, that the density of Earth would be five or six times as great as the density of water,"Sir Isaac Newton thought it probable, that the mean density of the earth might be five or six times as great as the density of water; and we have now found, by experiment, that it is very little less than what he had thought it to be: so much justness was even in the surmises of this wonderful man!" Hutton (1778), p. 783 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 permitted indirect estimates on the mean density of the Earth, via estimates of (what in modern terminology is known as) the gravitational constant. 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. Newton considered the experiment in Principia, but pessimistically concluded that the effect would be too small to be measurable.
An expedition from 1737 to 1740 by Pierre Bouguer and Charles Marie de La Condamine 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 and mount Chimborazo.
Bouguer wrote in a 1749 paper that they had been able to detect a deflection of 8 seconds of arc, 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 Earth.
After a lengthy search over the summer of 1773, Mason reported that the best candidate was Schiehallion, a peak in the central Scottish Highlands. 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, maximising the deflection effect. Nevil Maskelyne, Charles Hutton 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's planetary tables, which had previously only been able to express the densities of the major Solar System objects in relative terms.
In modern notation, the mass of the Earth is derived from the gravitational constant and the mean Earth radius by
Cavendish found a mean density of , about 1% below the modern value.
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 pounds" ( 14 Quadrillionen Pfund) in Masius (1859).J.G.Mädler in: Masius, Hermann, Die gesammten Naturwissenschaften, vol. 3 (1859), p. 562. Beckett (1871) cites the "weight of the earth" as "5842 quintillion long ton" .Edmund Beckett Baron Grimthorpe, Astronomy Without Mathematics (1871), p. 254. Max Eyth, Der Kampf um die Cheopspyramide: Erster Band (1906), p. 417 cites the "weight of the globe" ( Das Gewicht des Erdballs) as "5273 quintillion 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 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 determined a density value of through measurements made with pendulums in the Milan area. This value was refined in 1827 by Edward Sabine to , and then in 1841 by Carlo Ignazio Giulio to . On the other hand, George Biddell Airy 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 in 1880 realized a gravimetry experiment in Tokyo and at the top of Mount Fuji. The result was .
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 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🜨 =
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, meteors, 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, 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 and natural radioactive decay is estimated to amount to 16 tons per year.
An additional loss due to spacecraft on escape velocity 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.
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