apparatus, from 1897 scientific journal. The portable gravimeter developed in 1890 by
Thomas C. Mendenhall provided the most accurate relative measurements of the local gravitational field of the Earth. 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 resulted in a value about 20% too low. The
Cavendish experiment 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 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, 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).
Early estimates Before the direct measurement of the
gravitational constant, 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. 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, 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. He suggested that the experiment would "do honour to the nation where it was made" and proposed
Whernside in
Yorkshire, or the
Blencathra-
Skiddaw massif in
Cumberland as suitable targets. The Royal Society formed the Committee of Attraction to consider the matter, appointing Maskelyne,
Joseph Banks and
Benjamin Franklin amongst its members. The Committee despatched the astronomer and surveyor
Charles Mason to find a suitable mountain. After a lengthy search over the summer of 1773, Mason reported that the best candidate was
Schiehallion, a peak in the central
Scottish Highlands. 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%). 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. 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).
Beckett (1871) cites the "weight of the earth" as "5842
quintillion tons" [].
Max Eyth 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, South Shields. 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 .
Modern value The uncertainty in the modern value for the Earth's mass has been entirely due to the uncertainty in the
gravitational constant 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. (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 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 ==