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'{{Refimprove|date=January 2016}} {{Expand Spanish|date=September 2016}} {{Infobox physical quantity | name = Earth Mass | width = | background = | image = | caption = | unit = [[kilogram]] (kg) | otherunits = [[gram]] (g) [[Centimetre–gram–second system of units|[CGS]]]<br />[[Solar Mass]] (M_⊙) [[Astronomical system of units|[IAU]]] | symbols = <math>M_\oplus</math>, <math>M_\mathrm{T}</math>, <math>M_\mathrm{E}</math> or <math>E</math> | baseunits = {{val|5.9722|0.0006|e=24|u=kg}} | dimension = <math>[M_\oplus]=\mathrm{M}</math> ([[mass]]) | extensive = | intensive = | conserved = | transformsas = | derivations = {{ublist | {{math|1=''{{earth mass}}'' {{=}} ''g{{dot}}R{{su|b=⊕|p=2}}'' ∕ ''G''}} | {{math|1=''{{earth mass}}'' {{=}} ''ρ''{{dot}}''V''}} | {{math|1=''{{earth mass}}'' [[=]] ''μ_⊕'' ∕ ''G''}} }} }} {{Use dmy dates|date=February 2013}} '''Earth mass''' ({{Earth mass}}, where ⊕ is the standard astronomical symbol for planet [[Earth]]) is the unit of [[mass]] equal to that of Earth. This value includes the atmosphere but excludes the moon. The current best estimate for Earth mass is {{math|{{Earth mass}} {{=}} {{val|5.9722|0.0006|e=24|u=kg}}}}<ref name="earth-sse">{{cite web |url=http://solarsystem.nasa.gov/planets/profile.cfm?Object=Earth&Display=Facts |title=Solar System Exploration: Earth: Facts & Figures |work=NASA |date=13 Dec 2012 |accessdate=2012-01-22}}</ref><ref name="AA">"[http://asa.usno.navy.mil/static/files/2016/Astronomical_Constants_2016.pdf 2016 Selected Astronomical Constants]" in {{citation | title = The Astronomical Almanac Online | url = http://asa.usno.navy.mil/ | publisher = [[United States Naval Observatory|USNO]]–[[United Kingdom Hydrographic Office|UKHO]]}}.</ref> Earth mass is a standard [[units of mass|unit of mass]] in [[astronomy]] that is used to indicate the masses of other [[planet]]s, including rocky [[terrestrial planet]]s and [[exoplanet]]s. == Value == The mass of Earth is estimated to be: :<math>M_\oplus=(5.9722\;\pm\;0.0006)\times10^{24}\;\mathrm{kg}</math>, which can be expressed in terms of solar mass as: :<math>M_\oplus=\frac{1}{332\;946.0487\;\pm\;0.0007}\;\mathrm{M_\odot} \approx 3.003\times10^{-6}\;\mathrm{M_\odot} </math>. {| class="wikitable" style="margin-left: 20px;" |+ Masses of noteworthy [[astronomical object]]s relative to the mass of Earth |- ! Object ! '''Earth mass''' {{earth mass}} ! Ref |- | [[Moon]] | {{val|0.0123000371|(4)}} | align="center" |<ref>{{cite journal|last1=Pitjeva|first1=E.V.|last2=Standish|first2=E.M.|title=Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit|journal=Celestial Mechanics and Dynamical Astronomy|date=2009-04-01|volume=103|issue=4|pages=365–372|doi=10.1007/s10569-009-9203-8|url=http://link.springer.com/article/10.1007%2Fs10569-009-9203-8|access-date = 2016-02-12|bibcode = 2009CeMDA.103..365P }}</ref> |- | [[Sun]] | {{val|332946.0487|.0007}} | align="center" | <ref name="AA" /> |- | [[Mercury (planet)|Mercury]] | 0.0553 | align="center" |<ref name=":0">{{Cite web|title = Planetary Fact Sheet – Ratio to Earth|url = http://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.html|website = nssdc.gsfc.nasa.gov|access-date = 2016-02-12}}</ref> |- | [[Venus]] | 0.815 | align="center" |<ref name=":0" /> |- |[[Earth]] |1 |By definition |- | [[Mars]] | 0.107 | align="center" |<ref name=":0" /> |- | [[Jupiter]] | 317.8 | align="center" |<ref name=":0" /> |- | [[Saturn]] |95.2 | align="center" | <ref name=":0" /> |- | [[Uranus]] |14.5 | align="center" | <ref name=":0" /> |- | [[Neptune]] | 17.1 | align="center" | <ref name=":0" /> |- | [[Gliese 667 Cc]] | 3.8 | align="center" | <ref name="PHL">{{cite web|url=http://phl.upr.edu/projects/habitable-exoplanets-catalog|title=The Habitable Exoplanets Catalog – Planetary Habitability Laboratory @ UPR Arecibo|publisher=}}</ref> |- | [[Kepler-442b]] | 1.0 – 8.2 | align="center" | <ref name="UPR-Catalog">{{Cite web|url = http://phl.upr.edu/projects/habitable-exoplanets-catalog/data|title = HEC: Data of Potential Habitable Worlds}}</ref> |} The ratio of Earth mass to lunar mass has been measured to great accuracy. The current best estimate is:<ref>{{cite journal|last1=Konopliv|first1=A|title=A Global Solution for the Gravity Field, Rotation, Landmarks, and Ephemeris of Eros|journal=Icarus|date=December 2002|volume=160|issue=2|pages=289–299|doi=10.1006/icar.2002.6975|url=http://sbn.psi.edu/archive/near/NEAR_A_RSS_1_5_EROS_ORBIT_V1_0/document/gravity/space01v5.pdf|bibcode = 2002Icar..160..289K }}</ref> :<math>M_\oplus/M_L=81.300570\;\pm\;0.000005</math> == History of measurement == The mass of Earth is measured indirectly by determining other quantities such as Earth's density, gravity, or gravitational constant. === Using the ''G''{{Earth mass}} product === Modern methods of determining the mass of Earth involve calculating the [[Gravitational constant#The GM product|gravitational coefficient of the Earth]] and dividing by the [[Gravitational constant|Newtonian constant of gravitation]], : <math> M_\oplus =\frac{ GM_\oplus}{ G }.</math> The ''G''{{Earth mass}} product is determined using laser ranging data from Earth-orbiting satellites.<ref>{{cite journal|last1=Ries|first1=J.C.|last2=Eanes|first2=R.J.|last3=Shum|first3=C.K.|last4=Watkins|first4=M.M.|title=Progress in the determination of the gravitational coefficient of the Earth|journal=Geophysical Research Letters|date=20 March 1992|volume=19|issue=6|doi=10.1029/92GL00259|url=http://onlinelibrary.wiley.com/doi/10.1029/92GL00259/abstract|accessdate=5 February 2016|bibcode = 1992GeoRL..19..529R }}</ref> The ''G''{{Earth mass}} product can also be calculated by observing the motion of the Moon<ref name="moonbounce">{{cite journal |last1=Shuch|first1=H. Paul |title=Measuring the mass of the earth: the ultimate moonbounce experiment|journal=Proceedings, 25th Conference of the Central States VHF Society|date=July 1991|pages=25–30|url=http://www.setileague.org/articles/ham/masserth.pdf|accessdate=28 February 2016|publisher=American Radio Relay League}}</ref> or the period of a pendulum at various elevations. These methods are less precise than observations of artificial satellites. === Using the gravitational constant === Earlier efforts (after 1798) to determine Earth's mass involved measuring G directly as in the [[Cavendish experiment]]. Earth's mass could be then found by combining two equations; [[Newton's laws of motion|Newton's second law]], and [[Newton's law of universal gravitation#Modern form|Newton's law of universal gravitation]]:{{cn|date=August 2016}} :<math> F = mFUCK nca, \quad F = G\frac{mM_\oplus}{r^2}.</math> Substituting earth's gravity, g for the acceleration term, and combining the two equations gives :<math>mg = G\frac{mM_\oplus}{r^2}</math>. The equation can then be solved for {{Earth mass}} :<math>M_\oplus = \frac{gr^2}{G}.</math> With this method, the values for Earth's surface gravity, Earth's radius, and G were measured empirically. === Using the deflection of a pendulum === Before the Cavendish Experiment, attempts to "weigh" Earth involved estimating the mean density of Earth and its volume.{{citation needed|reason=Needs reliable source to back up claim|date=February 2016}} The volume was well understood through surveying techniques, and the density was measured by observing the slight deflection of a pendulum near a mountain, as in the [[Schiehallion experiment]]. The Earth mass could then be calculated as:{{cn|date=August 2016}} :<math> M_\oplus = \rho V</math>. This technique resulted in a mass estimate that is 20% lower than today's accepted value. === Using the period of a pendulum === An expedition from 1737 to 1740 by French scientist [[Pierre Bouguer]] 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's work led to an estimate that is two to three times larger than the true mass of Earth. However, this historical determination showed that the Earth was not hollow nor filled with water, as some had argued at the time.<ref name="Kollerstrom">{{cite journal|url=http://dioi.org/kn/halleyhollow.htm|author=N. Kollerstrom|year= 1992|title=The hollow world of Edmond Halley|journal=Journal for History of Astronomy|volume=23|pages=185–192}} [http://web.archive.org/web/19960101000000-20071107231218/http://www.ucl.ac.uk/sts/nk/halleyhollow.htm archive]</ref> Modern gravitometers are now used for measuring the local gravitational field. They surpass the accuracy limitations of pendulums. === Experiments with pendulums in the nineteenth century === Much later, in 1821, [[Francesco Carlini]] determined a density value of ρ = {{val|4.39|u=g/cm³}} through measurements made with pendulums in the [[Milan]] area. This value was refined in 1827 by [[Edward Sabine]] to {{val|4.77|u=g/cm³}}, and then in 1841 by Carlo Ignazio Giulio to {{val|4.95|u=g/cm³}}. 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 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 {{val|6.6|u=g/cm³}} 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 {{val|6.3|u=g/cm³}}. 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 ρ = {{val|5.77|u=g/cm³}}.{{cn|date=August 2016}} == Variation == {{Example farm|section|date=September 2016}} Earth's mass is constantly changing due to many contributors. Earth primarily gains mass from micrometeorites and cosmic dust, whereas it loses hydrogen and helium gas. The combined effect is a net loss of material, though the annual mass deficit represents an inconsequential fraction of its total mass,{{efn|The total estimated annual loss is {{val|5.5e7|u=kg}},<ref name="IJSRP" /> which constitutes a fraction of {{math|{{sfrac|5.5e7|5.97e24}} ≈ {{sfrac|1|1e17}}}} {{=}} {{sfrac|1|100 Quadrillion}} }} or even the uncertainty in its mass. So its inclusion does not affect total mass calculations. A number of other mechanisms are responsible for mass adjustments, and can be classified into two categories: physical transfer of [[matter]], and mass that is gained or lost through the absorption or release of energy due to the [[mass–energy equivalence]] principle. Several examples are provided for completeness, but their relative contribution is negligible. === Net gains === {{block indent |1= '''In-falling material''' : [[Cosmic dust]], [[Cosmic Rays]], [[meteors]], [[comets]], etc. are the most significant contributor to Earth's increase in mass. The sum of material is estimated to be 37,000 to 78,000 tons annually<ref>"[http://link.springer.com/chapter/10.1007%2F978-1-4419-8694-8_5 Spacecraft Measurements of the Cosmic Dust Flux]", Herbert A. Zook. {{DOI|10.1007/978-1-4419-8694-8_5}}</ref><ref>{{cite web|last1=Carter|first1=Lynn|title=How many meteorites hit Earth each year?|url=http://curious.astro.cornell.edu/about-us/75-our-solar-system/comets-meteors-and-asteroids/meteorites/313-how-many-meteorites-hit-earth-each-year-intermediate|website=Ask an Astronomer|publisher=The Curious Team, Cornell University|accessdate=6 February 2016}}</ref> ; [[Global warming]] : Nasa has calculated that the Earth is gaining energy due to rising temperatures. It has been estimated that this added energy increases the mass of Earth by a tiny amount – 160 tonnes per year.<ref>{{cite web|last1=McDonald|first1=Charlotte|title=Who, What, Why: Is the Earth getting lighter?|url=http://www.bbc.com/news/magazine-16787636|website=BBC Magazine|publisher=BBC News|accessdate=9 February 2016|date=31 January 2012}}</ref> ; [[Solar energy]] conversion (minuscule) : Solar energy is converted to chemical energy by [[photosynthetic pigment]]s as plants construct carbohydrate molecules. This stored chemical energy represents in increase in mass. Most of the chemical energy is reconverted into heat and then lost (radiated) through chemical processes, but some is sequestered and becomes biomass or fossil fuel.{{citation needed|reason=needs reference to back up claim|date=January 2016}} ; [[Artificial photosynthesis]] (minuscule) : Can also theoretically add mass, assumed to be negligible but added for sake of completeness.{{citation needed|reason=Implausible, needs reference to back up claim|date=January 2016}} ; Heat conversion (probably minuscule) : Some outbound radiation is absorbed within the atmosphere by photosynthetic [[bacteria]] and [[archaea]], including from [[chlorophyll f|chlorophyll ''f'']], which bind the energy into matter in the form of chemical bonds.{{citation needed|reason=I estimate this at around 9&nbsp;g/s (89 PW incoming, E=mc^2, m=E/c^2. Very small compared to anything else|date=June 2015}} }} === Net losses === {{block indent |1= '''[[Atmospheric escape]] of gases. ''' : About 3&nbsp;kg/s of hydrogen or 95,000 tons per year<ref>{{cite web|url=https://www.sfsite.com/fsf/2013/pmpd1301.htm|title=Fantasy and Science Fiction: Science by Pat Murphy & Paul Doherty|publisher=}}</ref> and 1,600 tons of helium per year<ref name="techdaily">{{cite web|url=http://scitechdaily.com/earth-loses-50000-tonnes-of-mass-every-year/|title=Earth Loses 50,000 Tonnes of Mass Every Year|work=SciTech Daily}}</ref> are lost through atmospheric escape. ; [[Spacecraft]] on escape trajectories (minuscule) : Spacecraft that are on escape trajectories represent an average mass loss at a rate of {{val|65|u=tons per year}}.<ref name="IJSRP">{{cite journal|last1=Saxena|first1=Shivam|last2=Chandra|first2=Mahesh|title=Loss in Earth Mass due to Extraterrestrial Space Exploration Missions|journal=International Journal of Scientific and Research Publications|date=May 2013|volume=3|issue=5|page=1|url=http://www.ijsrp.org/research-paper-0513.php?rp=P171213|accessdate=9 February 2016}}</ref> Earth lost about 3473 tons in the initial 53 years of the space age, but the trend is currently decreasing. ; Human energy use (minuscule) : Human activities conversely reduce Earth's mass, by liberation of heat that is later radiated into space; [[solar photovoltaics]] generally do not add to the mass of Earth because the energy collected is merely transmitted (as electricity or heat) and subsequently radiated, which is generally not converted into chemical means to be stored on Earth. In 2010, the human world consumed 550 [[exajoule|EJ]] of energy,<ref>{{cite web|url=http://www.resilience.org/stories/2012-02-16/world-energy-consumption-beyond-500-exajoules|title=World energy consumption – beyond 500 exajoules|work=Resilience}}</ref> or 6 tons of matter converted into heat, then almost entirely lost to space.{{Citation needed|reason=needs reference to back up claim|date=February 2016}} ; Deceleration of Earth's core (minuscule) : As the rotation rate of Earth's inner core decelerates, it loses [[Rotational energy|rotational kinetic energy]], which equates to a loss of 16 tons per year.{{citation needed|reason=needs reliable source to back up claim|date=February 2016}} However, this rotation speed has been shown to fluctuate over decades.<ref>{{cite journal |last1=Tkalčić |first1=Hrvoje |last2=Young |first2=Mallory |last3=Bodin |first3=Thomas |last4=Ngo |first4=Silvie |last5=Sambridge |first5=Malcolm |title=The shuffling rotation of the Earth’s inner core revealed by earthquake doublets |journal=Nature Geoscience |volume=6 |pages=497–502 |date=12 May 2013 |doi=10.1038/ngeo1813 |bibcode = 2013NatGe...6..497T }}<!--|accessdate=7 February 2016--></ref> ; Non photosynthesizing life forms consume energy, and radiate as heat.{{citation needed|reason=Implausible, needs reference to back up claim|date=January 2016}} ; Natural processes (probably minuscule) : Events including earthquakes and volcanoes can release energy as well as hydrogen, which may be lost as heat or atmospheric escape.{{citation needed|reason=Implausible, needs reference to back up claim|date=January 2016}} ; Radiation Losses(minuscule) : From radioisotopes either naturally or through human induced reactions such as [[nuclear fusion]] or [[nuclear fission]] amount to 16 tons per year.<ref name="IJSRP" /> ; Additional human impact by induced [[nuclear fission]] : Nuclear fission, both for civilian and military purposes, greatly speeds up natural process of [[Radioactive decay|radiodecay]]. Some 59,000 tons of uranium was supplied by mines in 2013.<ref>{{cite web|url=http://www.world-nuclear.org/info/Nuclear-Fuel-Cycle/Uranium-Resources/Uranium-Markets/|title=Uranium Markets|publisher=}}</ref> The mass of the uranium is reduced as it is converted to energy during the fission reaction. Also, the growing spent fuel stockpiles and environmental releases continues to produce heat (and therefore mass) largely lost to space.{{Citation needed|date=February 2016}} }} == See also == {{Div col|colwidth=24em}} * [[Abundance of elements in Earth's crust]] * [[Cavendish experiment]] * [[Schiehallion experiment]] * [[Earth radius]] * [[Planetary mass]] * [[Orders of magnitude (mass)]] * [[Solar mass]] * [[Structure of the Earth]] * [[Gravitational constant]] * [[Earth Similarity Index]] {{Div col end}} == Notes == {{notelist}} == References == {{reflist}} [[Category:Units of mass]] [[Category:Planetary science]] [[Category:Planetary geology]] [[Category:Units of measurement in astronomy]] [[Category:Earth|Mass]] [[Category:Human-based units of measurement]]'