Mass Of Earth In Kilograms

Unit of measurement of mass equal to that of Earth

Earth mass
19th-century analogy of Archimedes' quip of "give me a lever long enough and a fulcrum on which to place it, and I will motility the earth"[1]
General information
Unit system	astronomy
Unit of	mass
Symbol	M ⊕
Conversions
1M ⊕ in ...	... is equal to ...
SI base unit	(5.9722±0.0006)×1024 kg
U.South. customary	≈ 1.3166×1025 pounds

An Earth mass (denoted as ${\displaystyle M_{\mathrm {E} }}$ or ${\displaystyle M_{\oplus }}$ , where ⊕ is the standard astronomical symbol for Earth), is a unit of mass equal to the mass of the planet Globe. The current best estimate for the mass of Earth is M _⊕ = 5.9722×x²⁴ kg , with a standard doubt of 6×10²⁰ kg (relative doubtfulness ten^−iv).^[2] The recommended value in 1976 was (5.9742±0.0036)×10²⁴ kg.^[3] It is equivalent to an boilerplate density of 5515 kg·m⁻³ .

The Globe mass is a standard unit of mass in astronomy that is used to point the masses of other planets, including rocky terrestrial planets and exoplanets. Ane Solar mass is close to 333,000 Globe masses. The Earth mass excludes the mass of the Moon. The mass of the Moon is well-nigh 1.2% of that of the Earth, so that the mass of the Globe+Moon organization is shut to six.0456×10²⁴ kg.

Most of the mass is accounted for past atomic number 26 and oxygen (c. 32% each), magnesium and silicon (c. 15% each), calcium, aluminium and nickel (c. one.5% each).

Precise measurement of the Earth mass is difficult, as it is equivalent to measuring the gravitational constant, which is the fundamental concrete constant known with least accuracy, due to the relative weakness of the gravitational force. The mass of the Globe was first measured with any accuracy (within about twenty% of the correct value) in the Schiehallion experiment in the 1770s, and within i% of the modernistic value in the Cavendish experiment of 1798.

Unit of measurement of mass in astronomy [edit]

The mass of Earth is estimated to be:

${\displaystyle M_{\oplus }=(5.9722\;\pm \;0.0006)\times ten^{24}\;\mathrm {kg} }$ ,

which can exist expressed in terms of solar mass as:

${\displaystyle M_{\oplus }={\frac {1}{332\;946.0487\;\pm \;0.0007}}\;M_{\odot }\approx 3.003\times x^{-half dozen}\;M_{\odot }}$ .

The ratio of Earth mass to lunar mass has been measured to not bad accuracy. The current best estimate is:^{[4] [5]}

${\displaystyle M_{\oplus }/M_{L}=81.3005678\;\pm \;0.0000027}$

Masses of noteworthy astronomical objects relative to the mass of Earth

Object	Globe mass M World	Ref
Moon	0.012300 0371(4)	[4]
Sunday	332946.0487±0.0007	[2]
Mercury	0.0553	[vi]
Venus	0.815	[6]
Globe	1	Past definition
Mars	0.107	[6]
Jupiter	317.8	[six]
Saturn	95.2	[6]
Uranus	14.5	[6]
Neptune	17.ane	[6]
Pluto	0.0025	[6]
Eris	0.0027
Gliese 667 Cc	3.8	[7]
Kepler-442b	ane.0 – 8.two	[eight]

The G G _Earth product for the World is called the geocentric gravitational constant and equals (398600 441.8±0.viii)×10⁶ m³ south^−two . It is determined using light amplification by stimulated emission of radiation ranging information from Earth-orbiting satellites, such equally LAGEOS-1.^{[ix] [10]} The G Thousand _Globe production tin also be calculated past observing the motion of the Moon^[11] or the period of a pendulum at various elevations. These methods are less precise than observations of bogus satellites.

The relative uncertainty of the geocentric gravitational constant is simply 2×10⁻⁹ , i.e. l000 times smaller than the relative uncertainty for Thousand _Earth itself. G _Globe can exist institute out only by dividing the K M _Earth product past Yard , and G is known only to a relative incertitude of iv.6×10⁻⁵ (2014 NIST recommended value), and then Chiliad _Earth volition have the aforementioned uncertainty at all-time. For this reason and others, astronomers prefer to employ the united nations-reduced Chiliad M _World production, or mass ratios (masses expressed in units of Earth mass or Solar mass) rather than mass in kilograms when referencing and comparison planetary objects.

Limerick [edit]

Earth'due south density varies considerably, between less than 2700 kg⋅m⁻³ in the upper crust to as much as 13000 kg⋅thousand⁻³ in the inner cadre.^[12] The Earth's core accounts for xv% of Earth's volume but more 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 i% of the mass.^[12] Almost 90% of the mass of the Earth is equanimous of the iron–nickel alloy (95% iron) in the core (30%), and the silicon dioxides (c. 33%) and magnesium oxide (c. 27%) in the drapery and crust. Pocket-size contributions are from iron(Two) oxide (v%), aluminium oxide (3%) and calcium oxide (2%),^[13] besides numerous trace elements (in elementary terms: atomic number 26 and oxygen c. 32% each, magnesium and silicon c. xv% each, calcium, aluminium and nickel c. ane.5% each). Carbon accounts for 0.03%, h2o for 0.02%, and the atmosphere for about one part per 1000000.^[xiv]

History of measurement [edit]

Pendulums used in Mendenhall gravimeter apparatus, from 1897 scientific journal. The portable gravimeter developed in 1890 by Thomas C. Mendenhall provided the near authentic relative measurements of the local gravitational field of the Earth.

The mass of Earth is measured indirectly by determining other quantities such equally Globe'southward density, gravity, or gravitational constant. The first measurement in the 1770s Schiehallion experiment resulted in a value about twenty% also low. The Cavendish experiment of 1798 found the correct value within ane%. Doubt was reduced to almost 0.2% by the 1890s,^[15] to 0.1% by 1930.^[16]

The effigy of the World has been known to better than 4 significant digits since the 1960s (WGS66), so that since that time, the doubtfulness 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,^[17] and at 0.01% (10⁻⁴) by the 2000s. The current relative incertitude of 10⁻⁴ amounts to vi×10²⁰ kg in accented terms, of the gild of the mass of a small-scale planet (lxx% of the mass of Ceres).

Early estimates [edit]

Before the direct measurement of the gravitational constant, estimates of the Earth mass were limited to estimating Earth's mean density from ascertainment of the crust and estimates on Globe's volume. Estimates on the volume of the Earth in the 17th century were based on a circumference estimate of sixty miles (97 km) to the degree of latitude, corresponding to a radius of 5,500 km (86% of the World'southward bodily radius of about vi,371 km), resulting in an estimated volume of about one third smaller than the correct value.^[18]

The average density of the Earth was non accurately known. Globe was assumed to consist either mostly of water (Neptunism) or generally of igneous stone (Plutonism), both suggesting boilerplate densities far likewise low, consequent with a total mass of the lodge of 10²⁴ kg. Isaac Newton estimated, without admission to reliable measurement, that the density of World would be five or six times every bit great as the density of water,^[19] which is surprisingly accurate (the modern value is 5.515). Newton under-estimated the Globe's volume by about thirty%, so that his estimate would exist roughly equivalent to (four.two±0.5)×10²⁴ kg.

In the 18th century, knowledge of Newton's law of universal gravitation permitted indirect estimates on the mean density of the Globe, via estimates of (what in modern terminology is known every bit) the gravitational constant. Early on estimates on the mean density of the Earth were made by observing the slight deflection of a pendulum almost a mountain, every bit in the Schiehallion experiment. Newton considered the experiment in Principia, simply pessimistically concluded that the effect would be too small to be measurable.

An expedition from 1737 to 1740 past Pierre Bouguer and Charles Marie de La Condamine attempted to make up one's mind the density of Earth past measuring the menstruation of a pendulum (and therefore the strength of gravity) equally a part of acme. The experiments were carried out in Republic of ecuador and Peru, on Pichincha Volcano and mountain Chimborazo.^[20] 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 hateful density of the World, only Bouguer stated that it was at least sufficient to testify that the Earth was not hollow.^[15]

Schiehallion experiment [edit]

That a further try should exist made on the experiment was proposed to the Royal Lodge in 1772 past Nevil Maskelyne, Astronomer Royal.^[21] He suggested that the experiment would "practice honor to the nation where it was made" and proposed Whernside in Yorkshire, or the Blencathra-Skiddaw massif in Cumberland equally suitable targets. The Imperial Society formed the Committee of Attraction to consider the thing, appointing Maskelyne, Joseph Banks and Benjamin Franklin amongst its members.^[22] The Commission 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 fundamental Scottish Highlands.^[22] The mount stood in isolation from any nearby hills, which would reduce their gravitational influence, and its symmetrical e–west ridge would simplify the calculations. Its steep northern and southern slopes would allow the experiment to exist 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 ${\displaystyle {\tfrac {nine}{5}}}$ that of Schiehallion mountain.^[23] This corresponds to a mean density most 4 one⁄2 higher than that of water (i.east., about 4.5 grand/cm^three ), about twenty% beneath the modernistic value, merely still significantly larger than the mean density of normal rock, suggesting for the get-go fourth dimension that the interior of the Earth might be substantially equanimous of metal. Hutton estimated this metal portion to occupy some twenty⁄31 (or 65%) of the diameter of the Earth (modern value 55%).^[24] With a value for the mean density of the Earth, Hutton was able to set some values to Jérôme Lalande'due south planetary tables, which had previously only been able to limited the densities of the major Solar Arrangement objects in relative terms.^[23]

Cavendish experiment [edit]

Henry Cavendish (1798) was the outset to effort 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, and Newton's police force of universal gravitation.

In modern notation, the mass of the Earth is derived from the gravitational constant and the mean Earth radius by

${\displaystyle M_{\oplus }={\frac {GM_{\oplus }}{K}}={\frac {gR_{\oplus }^{ii}}{G}}.}$

Where gravity of Earth, "little grand", is

${\displaystyle g=Thou{\frac {M_{\oplus }}{R_{\oplus }^{2}}}}$ .

Cavendish plant a mean density of 5.45 grand/cm^three , about 1% below the modern value.

19th century [edit]

While the mass of the World is implied by stating the World's radius and density, it was not usual to state the accented mass explicitly prior to the introduction of scientific annotation using powers of x in the later 19th century, because the accented numbers would have been besides bad-mannered. Ritchie (1850) gives the mass of the Earth's atmosphere as "11,456,688,186,392,473,000 lbs." ( one.1×x¹⁹ lb = five.0×10¹⁸ kg, modern value is v.15×10¹⁸ kg) and states that "compared with the weight of the globe this mighty sum dwindles to insignificance".^[25]

Absolute figures for the mass of the Earth are cited only kickoff in the second one-half of the 19th century, mostly in popular rather than expert literature. An early such effigy was given as "xiv septillion pounds" (14 Quadrillionen Pfund) [ 6.5×10²⁴ kg] in Masius (1859). ^[26] Beckett (1871) cites the "weight of the earth" as "5842 quintillion tons" [ 5.936×x²⁴ kg].^[27] The "mass of the globe in gravitational measure" is stated as "nine.81996×6370980²" in The New Volumes of the Encyclopaedia Britannica (Vol. 25, 1902) with a "logarithm of earth's mass" given equally "xiv.600522" [ 3.98586 ×10^xiv ]. This is the gravitational parameter in 1000ⁱⁱⁱ·southward^−two (modernistic value 3.98600 ×10¹⁴ ) and not the accented mass.

Experiments involving pendulums connected to be performed in the starting time half of the 19th century. By the second half of the century, these were outperformed past repetitions of the Cavendish experiment, and the modern value of G (and hence, of the Globe mass) is even so derived from high-precision repetitions of the Cavendish experiment.

In 1821, Francesco Carlini determined a density value of ρ = 4.39 g/cmⁱⁱⁱ through measurements fabricated with pendulums in the Milan area. This value was refined in 1827 past Edward Sabine to 4.77 g/cmⁱⁱⁱ , and so in 1841 by Carlo Ignazio Giulio to iv.95 thousand/cmⁱⁱⁱ . On the other hand, George Biddell Airy sought to determine ρ by measuring the deviation in the flow of a pendulum between the surface and the lesser of a mine.^[28] The first tests took place in Cornwall between 1826 and 1828. The experiment was a failure due to a fire and a flood. Finally, in 1854, Blusterous got the value 6.6 g/cm³ past measurements in a coal mine in Harton, Sunderland. Airy'due south method assumed that the Globe had a spherical stratification. Afterwards, 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 betwixt v.0 and 6.3 g/cmⁱⁱⁱ . This led to the concept of isostasy, which limits the power to accurately measure ρ, past either the divergence from vertical of a plumb line or using pendulums. Despite the petty chance of an accurate gauge of the average density of the World in this way, Thomas Corwin Mendenhall in 1880 realized a gravimetry experiment in Tokyo and at the top of Mountain Fuji. The event was ρ = 5.77 g/cm³ .^{[ citation needed ]}

Modern value [edit]

The uncertainty in the modernistic value for the Earth'south mass has been entirely due to the uncertainty in the gravitational constant G since at least the 1960s.^[29] G is notoriously difficult to measure, and some high-precision measurements during the 1980s to 2010s take yielded mutually exclusive results.^[30] Sagitov (1969) based on the measurement of Thousand past Heyl and Chrzanowski (1942) cited a value of M _Earth = 5.973(3)×x²⁴ kg (relative doubtfulness 5×10^−four ).

Accuracy has improved only slightly since so. Most mod measurements are repetitions of the Cavendish experiment, with results (inside standard incertitude) ranging between 6.672 and 6.676 ×ten⁻¹¹  chiliad³ kg⁻¹southward⁻ⁱⁱ (relative uncertainty 3×ten^−iv) in results reported since the 1980s, although the 2014 NIST recommended value is close to 6.674×x^−eleven  1000³ kg^−ones⁻² with a relative dubiety below ten⁻⁴. The Astronomical Almanach Online every bit of 2016 recommends a standard uncertainty of 1×ten^−iv for Earth mass, Chiliad _Earth 5.9722(6)×10²⁴ kg ^[ii]

Variation [edit]

Earth's mass is variable, subject area to both proceeds 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 result is a net loss of cloth, estimated at 5.v×10⁷ kg (5.four×x⁴ long tons) per year. This amount is 10 ⁻¹⁷ of the total earth mass.^{[ citation needed ]} The 5.5×10⁷ kg annual net loss is essentially due to 100,000 tons lost due to atmospheric escape, and an average of 45,000 tons gained from in-falling dust and meteorites. This is well inside the mass uncertainty of 0.01% ( vi×10²⁰ kg), 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^[31] ( 3 kg/s) and ane,600 tons of helium per year^[32] are lost through atmospheric escape. The main factor in mass gain is in-falling cloth, catholic grit, meteors, etc. are the most significant contributors to Earth'south increment in mass. The sum of textile is estimated to be 37000 to 78000 tons annually,^{[33] [34]} although this tin vary significantly; to take an farthermost instance, the Chicxulub impactor, with a midpoint mass estimate of 2.3×ten¹⁷ kg,^[35] added 900 one thousand thousand times that annual dustfall corporeality to the Earth'due south mass in a unmarried consequence.

Boosted changes in mass are due to the mass–free 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 twelvemonth.^{[ commendation needed ]}

An additional loss due to spacecraft on escape trajectories has been estimated at 65 tons per year since the mid-20th century. Globe lost about 3473 tons in the initial 53 years of the space age, just the trend is currently decreasing.^{[ commendation needed ]}

Run across as well [edit]

• Abundance of elements in Earth's crust
• Cavendish experiment
• Earth radius
• Gravitational constant
• Orders of magnitude (mass)
• Planetary mass
• Schiehallion experiment
• Solar mass
• Structure of the Earth

References [edit]

1. ^ Attributed by Pappus of Alexandria (Synagoge [Συναγωγή] Viii, 4th century), as « Δός μοί ποῦ στῶ, καὶ κινῶ τὴν Γῆν » . Engraving from Mechanic's Magazine (cover of spring Volume Ii, Knight & Lacey, London, 1824).
2. ^ ^{a b c} The cited value is the recommended value published by the International Astronomical Wedlock in 2009 (encounter 2016 "Selected Astronomical Constants" in "The Astronomical Almanac Online". USNO/UKHO. ).
3. ^ Run across IAU (1976) System of Astronomical Constants.
4. ^ ^{a b} Pitjeva, E.V.; Standish, Eastward.M. (one April 2009). "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit". Celestial Mechanics and Dynamical Astronomy. 103 (four): 365–372. Bibcode:2009CeMDA.103..365P. doi:10.1007/s10569-009-9203-8. S2CID 121374703.
5. ^ Luzum, Brian; Capitaine, Nicole; Fienga, Agnès; et al. (x July 2011). "The IAU 2009 organization of astronomical constants: the report of the IAU working group on numerical standards for Fundamental Astronomy". Celestial Mechanics and Dynamical Astronomy. 110 (4): 293–304. Bibcode:2011CeMDA.110..293L. doi:10.1007/s10569-011-9352-iv.
6. ^ ^{a b c d e f g h} "Planetary Fact Canvass – Ratio to Earth". nssdc.gsfc.nasa.gov . Retrieved 12 February 2016.
7. ^ "The Habitable Exoplanets Catalog – Planetary Habitability Laboratory @ UPR Arecibo".
8. ^ "HEC: Data of Potential Habitable Worlds".
9. ^ Ries, J.C.; Eanes, R.J.; Shum, C.M.; Watkins, One thousand.Chiliad. (xx March 1992). "Progress in the decision of the gravitational coefficient of the Earth". Geophysical Enquiry Letters. 19 (6): 529. Bibcode:1992GeoRL..19..529R. doi:x.1029/92GL00259.
10. ^ Lerch, Francis J.; Laubscher, Roy E.; Klosko, Steven 1000.; Smith, David E.; Kolenkiewicz, Ronald; Putney, Barbara H.; Marsh, James Thou.; Brownd, Joseph Due east. (December 1978). "Determination of the geocentric gravitational constant from laser ranging on near-Earth satellites". Geophysical Enquiry Letters. 5 (12): 1031–1034. Bibcode:1978GeoRL...5.1031L. doi:10.1029/GL005i012p01031.
11. ^ Shuch, H. Paul (July 1991). "Measuring the mass of the world: the ultimate moonbounce experiment" (PDF). Proceedings, 25th Briefing of the Cardinal States VHF Club: 25–thirty. Retrieved 28 Feb 2016.
12. ^ ^{a b} See structure of the Earth: inner core book 0.7%, density 12,600–13,000, mass c. 1.vi%; outer core vol. 14.iv%, density nine,900–12,200 mass c. 28.7–31.7%. Hazlett, James Southward.; Monroe, Reed; Wicander, Richard (2006). Physical Geology: Exploring the World (half dozen. ed.). Belmont: Thomson. p. 346.
13. ^ Jackson, Ian (1998). The Globe'south Mantle – Limerick, Structure, and Evolution. Cambridge University Press. pp. 311–378.
14. ^ The hydrosphere (Globe's oceans) account for nearly 0.02% 2.three×10^−four of total mass, Carbon for about 0.03% of the crust, or three×10⁻⁶ of full mass, Earth'south atmosphere for about 8.half dozen×10⁻⁷ of total mass. Biomass is estimated at ten⁻¹⁰ ( five.5×10¹⁴ kg, see Bar-On, Yinon One thousand.; Phillips, Rob; Milo, Ron. "The biomass distribution on Earth" Proc. Natl. Acad. Sci. United states., 2018).
15. ^ ^{a b} Poynting, J.H. (1913). The Earth: its shape, size, weight and spin. Cambridge. pp. 50–56.
16. ^ P. R. Heyl, A redetermination of the constant of gravitation, National Agency of Standards Journal of Research 5 (1930), 1243–1290.
17. ^ IAU (1976) System of Astronomical Constants
18. ^ Mackenzie, A. Stanley, The laws of gravitation; memoirs past Newton, Bouguer and Cavendish, together with abstracts of other important memoirs, American Book Visitor (1900 [1899]), p. 2.
19. ^ "Sir Isaac Newton thought it probable, that the hateful density of the earth might exist five or half-dozen times as great equally the density of h2o; and we have now found, by experiment, that it is very little less than what he had thought it to exist: and so much justness was even in the surmises of this wonderful man!" Hutton (1778), p. 783
20. ^ Ferreiro, Larrie (2011). Measure out of the World: The Enlightenment Trek that Reshaped Our Globe. New York: Bones Books. ISBN978-0-465-01723-two.
21. ^ Maskelyne, N. (1772). "A proposal for measuring the allure of some hill in this Kingdom". Philosophical Transactions of the Majestic Social club. 65: 495–499. Bibcode:1775RSPT...65..495M. doi:10.1098/rstl.1775.0049.
22. ^ ^{a b} Danson, Edwin (2006). Weighing the Globe. Oxford University Press. pp. 115–116. ISBN978-0-xix-518169-2.
23. ^ ^{a b} Hutton, C. (1778). "An Account of the Calculations Made from the Survey and Measures Taken at Schehallien". Philosophical Transactions of the Majestic Society. 68: 689–788. doi:10.1098/rstl.1778.0034.
24. ^ Hutton (1778), p. 783.
25. ^ Archibald Tucker Ritchie, The Dynamical Theory of the Formation of the Earth vol. 2 (1850), Longman, Brown, Green and Longmans, 1850, p. 280.
26. ^ J.Thou.Mädler in: Masius, Hermann, Dice gesammten Naturwissenschaften, vol. three (1859), p. 562.
27. ^ Edmund Beckett Baron Grimthorpe, Astronomy Without Mathematics (1871), p. 254. Max Eyth, Der Kampf um dice Cheopspyramide: Erster Band (1906), p. 417 cites the "weight of the world" (Das Gewicht des Erdballs) equally "5273 quintillion tons".
28. ^ Poynting, John Henry (1894). The Mean Density of the Earth. London: Charles Griffin. pp. 22–24.
29. ^ "Since the geocentric gravitational abiding [...] is at present adamant to a relative accuracy of ten⁻⁶, our noesis of the mass of the globe is entirely limited by the low accuracy of our knowledge of the Cavendish gravitational constant." Sagitov (1970 [1969]), p. 718.
30. ^ Schlamminger, Stephan (18 June 2014). "Fundamental constants: A cool way to measure big G". Nature. 510 (7506): 478–480. Bibcode:2014Natur.510..478S. doi:10.1038/nature13507. PMID 24965646. S2CID 4396011.
31. ^ "Fantasy and Science Fiction: Science by Pat Irish potato & Paul Doherty".
32. ^ "Earth Loses 50,000 Tonnes of Mass Every Yr". SciTech Daily. 5 February 2012.
33. ^ Zook, Herbert A. (2001), "Spacecraft Measurements of the Catholic Dust Flux", Accession of Extraterrestrial Matter Throughout Earth's History, pp. 75–92, doi:10.1007/978-one-4419-8694-8_5, ISBN978-1-4613-4668-5
34. ^ Carter, Lynn. "How many meteorites hit Earth each year?". Ask an Astronomer. The Curious Team, Cornell University. Retrieved 6 Feb 2016.
35. ^ Durand-Manterola, H. J.; Cordero-Tercero, Thousand. (2014). "Assessments of the energy, mass and size of the Chicxulub Impactor". arXiv:1403.6391 [astro-ph.EP].

Mass Of Earth In Kilograms,

Source: https://en.wikipedia.org/wiki/Earth_mass

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