Earth mass

Earth mass (ME or M, where ⊕ is the standard astronomical symbol for planet Earth) is the unit of mass equal to that of Earth. The current best estimate for Earth mass is M = 5.9722×1024 kg, with a standard uncertainty of 6×1020 kg (relative uncertainty 10−4).[2] It is equivalent to an average density of 5515 kg⋅m−3.

The Earth mass is a standard unit of mass in astronomy that is used to indicate the masses of other planets, including rocky terrestrial planets and exoplanets. One Solar mass is close to 333,000 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 6.0456×1024 kg.

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.

Earth Mass
Archimedes lever
19th-century illustration of Archimedes' quip of "give me a place to stand on, and I will move the earth"[1]
General information
Unit systemastronomy
Unit ofmass
1 M in ...... is equal to ...
   SI base unit   (5.9722±0.0006)×1024 kg
   U.S. customary   1.3166×1025 pounds

Unit of mass in astronomy

The mass of Earth is estimated to be:


which can be expressed in terms of solar mass as:


The ratio of Earth mass to lunar mass has been measured to great accuracy. The current best estimate is:[3][4]

Masses of noteworthy astronomical objects relative to the mass of Earth
Object Earth mass M Ref
Moon 0.0123000371(4) [3]
Sun 332946.0487±0.0007 [2]
Mercury 0.0553 [5]
Venus 0.815 [5]
Earth 1 By definition
Mars 0.107 [5]
Jupiter 317.8 [5]
Saturn 95.2 [5]
Uranus 14.5 [5]
Neptune 17.1 [5]
Gliese 667 Cc 3.8 [6]
Kepler-442b 1.0 – 8.2 [7]
The LAGEOS satellite was used to precisely measure Earth's gravity, and therefore, its mass.

The GM product for the Earth is called the geocentric gravitational constant and equals (398600441.8±0.8)×106 m3 s−2. It is determined using laser ranging data from Earth-orbiting satellites, such as LAGEOS-1.[8][9] The GM product can also be calculated by observing the motion of the Moon[10] or the period of a pendulum at various elevations. These methods are less precise than observations of artificial satellites.

The relative uncertainty of the geocentric gravitational constant is just 2×10−9, i.e. 50000 times smaller than the relative uncertainty for M itself. M can be found out only by dividing the GM product by G, and G is known only to a relative uncertainty of 4.6×10−5 (2014 NIST recommended value), so M will have the same uncertainty at best. For this reason and others, astronomers prefer to use the un-reduced GM product, or mass ratios (masses expressed in units of Earth mass or Solar mass) rather than mass in kilograms when referencing and comparing planetary objects.


Earth's density varies considerably, between less than 2700 kg⋅m−3 in the upper crust to as much as 13000 kg⋅m−3 in the inner core.[11] The Earth's core 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.[11] About 90% of the mass of the Earth is composed of the iron–nickel alloy (95% iron) in the core (30%), and the silicon dioxides (c. 33%) and magnesium oxide (c. 27%) in the mantle and crust. Minor contributions are from iron(II) oxide (5%), aluminium oxide (3%) and calcium oxide (2%),[12] besides numerous trace elements (in elementary terms: iron and oxygen c. 32% each, magnesium and silicon c. 15% each, calcium, aluminium and nickel c. 1.5% each). Carbon accounts for 0.03%, water for 0.02%, and the atmosphere for about one part per million.[13]

History of measurement

Mendenhall gravimeter pendulums
Pendulums used in Mendenhall gravimeter 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,[14] to 0.1% by 1930.[15]

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,[16] and at 0.01% (10−4) by the 2000s. The current relative uncertainty of 10−4 amounts to 6×1020 kg 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 60 miles (97 km) to the degree of latitude, corresponding to a radius of 5,500 km (86% of the Earth's actual radius of about 6,371 km), resulting in an estimated volume of about one third smaller than the correct value.[17]

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 1024 kg. 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,[18] 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 (4.2±0.5)×1024 kg.

In the 18th century, knowledge of Newton's law of 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.[19] 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.[14]

Schiehallion experiment

That a further attempt should be made on the experiment was proposed to the Royal Society in 1772 by Nevil Maskelyne, Astronomer Royal.[20] 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.[21] 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.[21] 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.[22] This corresponds to a mean density about 4​12 higher than that of water (i.e., about 4.5 g/cm3), 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 ​2031 (or 65%) of the diameter of the Earth (modern value 55%).[23] 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.[22]

Cavendish experiment

The 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, and Newton's law of universal gravitation.

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

Where "little g":


Cavendish found a mean density of 5.45 g/cm3, about 1% below the modern value.

19th century

Room in Which Mr. Baily Weighed the Earth
Experimental setup by Francis Baily and Henry Foster to determine the density of Earth using the Cavendish method.

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 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 as "11,456,688,186,392,473,000 lbs." (1.1×1019 lb = 5.0×1018 kg, modern value is 5.15×1018 kg) and states that "compared with the weight of the globe this mighty sum dwindles to insignificance".[24]

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 quadrillion pounds" (14 Quadrillionen Pfund) [6.5×1024 kg] in Masius (1859). [25] Beckett (1871) cites the "weight of the earth" as "5842 quintillion tons" [5.936×1024 kg].[26] 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" [3.98586×1014]. This is the gravitational parameter in m3·s−2 (modern value 3.98600×1014) 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 G (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 ρ = 4.39 g/cm3 through measurements made with pendulums in the Milan area. This value was refined in 1827 by Edward Sabine to 4.77 g/cm3, and then in 1841 by Carlo Ignazio Giulio to 4.95 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.[27] 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 6.6 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 6.3 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 = 5.77 g/cm3.

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.[28] G is notoriously difficult to measure, and some high-precision measurements during the 1980s to 2010s have yielded mutually exclusive results.[29] Sagitov (1969) based on the measurement of G by Heyl and Chrzanowski (1942) cited a value of M = 5.973(3)×1024 kg (relative uncertainty 5×10−4).

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 6.676 ×10−11  m3 kg−1 s−2 (relative uncertainty 3×10−4) in results reported since the 1980s, although the 2014 NIST recommended value is close to 6.674×10−11  m3 kg−1 s−2 with a relative uncertainty below 10−4. The Astronomical Almanach Online as of 2016 recommends a standard uncertainty of 1×10−4 for Earth mass, M 5.9722(6)×1024 kg[2]


Earth's mass is variable, subject to both gain and loss due to the accretion of micrometeorites and cosmic dust and the loss of hydrogen and helium gas, respectively. The combined effect is a net loss of material, estimated at 5.5×107 kg (54,000 tons) per year. This amount is 10−17 of the total earth mass.[30] 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 within the mass uncertainty of 0.01% (6×1020 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 1,600 tons of helium per year[32] 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 37,000 to 78,000 tons annually.[33][34]

Additional changes in mass are due to the mass–energy equivalence principal, although these changes are relatively negligible. An increase in mass has been ascribed to rising temperatures (global warming), estimated at 160 tonnes per years as of 2016.[35] Another 16 tons per year are lost in the form of rotational kinetic energy due to the deceleration of the rotation of Earth's inner core. This energy is transferred to the rotational energy of the Solar System, and the trend might also be reversible, as rotation speed has been shown to fluctuate over decades.[36] Mass loss due to nuclear fission is estimated to amount to 16 tons per year.[30]

An additional loss due to spacecraft on escape trajectories has been estimated at 65 tons per year 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.[30]

See also


  1. ^ Δοσ μοι που στω και κινω την γην (attributed by Pappus of Alexandria, Synagoge VIII). Engraving from ^^Mechanic’s Magazine^^ (cover of bound Volume II, Knight & Lacey, London, 1824).
  2. ^ a b c The cited value is the recommended value published by the International Astronomical Union in 2009 (see 2016 "Selected Astronomical Constants" in The Astronomical Almanac Online, USNOUKHO). The recommended value in 1976 was (5.9742±0.0036)×1024 kg, see IAU (1976) System of Astronomical Constants.
  3. ^ a b Pitjeva, E.V.; Standish, E.M. (2009-04-01). "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit". Celestial Mechanics and Dynamical Astronomy. 103 (4): 365–372. Bibcode:2009CeMDA.103..365P. doi:10.1007/s10569-009-9203-8.
  4. ^ Luzum, Brian; Capitaine, Nicole; Fienga, Agnès; et al. (10 July 2011). "The IAU 2009 system 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/s10569-011-9352-4.
  5. ^ a b c d e f g "Planetary Fact Sheet – Ratio to Earth". Retrieved 2016-02-12.
  6. ^ "The Habitable Exoplanets Catalog – Planetary Habitability Laboratory @ UPR Arecibo".
  7. ^ "HEC: Data of Potential Habitable Worlds".
  8. ^ Ries, J.C.; Eanes, R.J.; Shum, C.K.; Watkins, M.M. (20 March 1992). "Progress in the determination of the gravitational coefficient of the Earth". Geophysical Research Letters. 19 (6): 529. Bibcode:1992GeoRL..19..529R. doi:10.1029/92GL00259.
  9. ^ Lerch, Francis J.; Laubscher, Roy E.; Klosko, Steven M.; Smith, David E.; Kolenkiewicz, Ronald; Putney, Barbara H.; Marsh, James G.; Brownd, Joseph E. (December 1978). "Determination of the geocentric gravitational constant from laser ranging on near-Earth satellites". Geophysical Research Letters. 5 (12): 1031–1034. Bibcode:1978GeoRL...5.1031L. doi:10.1029/GL005i012p01031.
  10. ^ Shuch, H. Paul (July 1991). "Measuring the mass of the earth: the ultimate moonbounce experiment" (PDF). Proceedings, 25th Conference of the Central States VHF Society: 25–30. Retrieved 28 February 2016.
  11. ^ a b See structure of the Earth: inner core volume 0.7%, density 12,600–13,000, mass c. 1.6%; outer core 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.
  12. ^ Jackson, Ian (1998). The Earth's Mantle - Composition, Structure, and Evolution. Cambridge University Press. pp. 311–378.
  13. ^ The hydrosphere (Earth's oceans) account for about 0.02% 2.3×10−4 of total mass, Carbon for about 0.03% of the crust, or 3×10−6 of total mass, Earth's atmosphere for about 8.6×10−7 of total mass. Biomass is estimated at 10−10 (5.5×1014 kg, see Bar-On, Yinon M.; Phillips, Rob; Milo, Ron. "The biomass distribution on Earth" Proc. Natl. Acad. Sci. USA., 2018).
  14. ^ a b Poynting, J.H. (1913). The Earth: its shape, size, weight and spin. Cambridge. pp. 50–56.
  15. ^ P. R. Heyl, A redetermination of the constant of gravitation, National Bureau of Standards Journal of Research 5 (1930), 1243–1290.
  16. ^ IAU (1976) System of Astronomical Constants
  17. ^ Mackenzie, A. Stanley, The laws of gravitation; memoirs by Newton, Bouguer and Cavendish, together with abstracts of other important memoirs, American Book Company (1900 [1899]), p. 2.
  18. ^ "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
  19. ^ Ferreiro, Larrie (2011). Measure of the Earth: The Enlightenment Expedition that Reshaped Our World. New York: Basic Books. ISBN 978-0-465-01723-2.
  20. ^ Maskelyne, N. (1772). "A proposal for measuring the attraction of some hill in this Kingdom". Philosophical Transactions of the Royal Society. 65: 495–499. Bibcode:1775RSPT...65..495M. doi:10.1098/rstl.1775.0049.
  21. ^ a b Danson, Edwin (2006). Weighing the World. Oxford University Press. pp. 115–116. ISBN 978-0-19-518169-2.
  22. ^ a b Hutton, C. (1778). "An Account of the Calculations Made from the Survey and Measures Taken at Schehallien". Philosophical Transactions of the Royal Society. 68: 689–788. doi:10.1098/rstl.1778.0034.
  23. ^ Hutton (1778), p. 783.
  24. ^ Archibald Tucker Ritchie, The Dynamical Theory of the Formation of the Earth vol. 2 (1850), Longman, Brown, Green and Longmans, 1850, p. 280.
  25. ^ J.G.Mädler in: Masius, Hermann, Die gesammten Naturwissenschaften, vol. 3 (1859), p. 562.
  26. ^ 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".
  27. ^ Poynting, John Henry (1894). The Mean Density of the Earth. London: Charles Griffin. pp. 22–24.
  28. ^ "Since the geocentric gravitational constant [...] is now determined to a relative accuracy of 10−6, our knowledge of the mass of the earth is entirely limited by the low accuracy of our knowledge of the Cavendish gravitational constant." Sagitov (1970 [1969]), p. 718.
  29. ^ 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.
  30. ^ a b c Saxena, Shivam; Chandra, Mahesh (May 2013). "Loss in Earth Mass due to Extraterrestrial Space Exploration Missions". International Journal of Scientific and Research Publications. 3 (5): 1. Retrieved 9 February 2016.
  31. ^ "Fantasy and Science Fiction: Science by Pat Murphy & Paul Doherty".
  32. ^ "Earth Loses 50,000 Tonnes of Mass Every Year". SciTech Daily. 2012-02-05.
  33. ^ "Spacecraft Measurements of the Cosmic Dust Flux", Herbert A. Zook. doi:10.1007/978-1-4419-8694-8_5
  34. ^ Carter, Lynn. "How many meteorites hit Earth each year?". Ask an Astronomer. The Curious Team, Cornell University. Retrieved 6 February 2016.
  35. ^ McDonald, Charlotte (31 January 2012). "Who, What, Why: Is the Earth getting lighter?". BBC Magazine. BBC News. Retrieved 9 February 2016.
  36. ^ Tkalčić, Hrvoje; Young, Mallory; Bodin, Thomas; Ngo, Silvie; Sambridge, Malcolm (12 May 2013). "The shuffling rotation of the Earth's inner core revealed by earthquake doublets". Nature Geoscience. 6 (6): 497–502. Bibcode:2013NatGe...6..497T. doi:10.1038/ngeo1813.
Alpha Centauri Bb

Alpha Centauri Bb (α Cen B b) was a proposed exoplanet orbiting the K-type main-sequence star Alpha Centauri B, located 4.37 light-years from Earth in the southern constellation of Centaurus, now shown not to exist.The claimed discovery of the planet was announced in October 2012 by a team of European observers, and the finding received widespread media attention. However, the announcement was met with scepticism by some astronomers, who thought that the European team was over-interpreting its data.In October 2015, astronomers from the University of Oxford published a scientific paper disproving the existence of the planet. They observed that an identical statistical analysis of randomly-generated synthetic data gave the same results as the actual astronomical data. This led Xavier Dumusque, the lead author of the original paper, to concede "We are not 100 percent sure, but probably the planet is not there."

Annualized geo solar

Annualized geo-solar (AGS) enables passive solar heating in even cold, foggy north temperate areas. It uses the ground under or around a building as thermal mass to heat and cool the building. After a designed, conductive thermal lag of 6 months the heat is returned to, or removed from, the inhabited spaces of the building. In hot climates, exposing the collector to the frigid night sky in winter can cool the building in summer.

The six-month thermal lag is provided by about three meters (ten feet) of dirt. A six-meter-wide (20 ft) buried skirt of insulation around the building keeps rain and snow melt out of the dirt, which is usually under the building. The dirt does radiant heating and cooling through the floor or walls. A thermal siphon moves the heat between the dirt and the solar collector. The solar collector may be a sheet-metal compartment in the roof, or a wide flat box on the side of a building or hill. The siphons may be made from plastic pipe and carry air. Using air prevents water leaks and water-caused corrosion. Plastic pipe doesn't corrode in damp earth, as metal ducts can.

AGS heating systems typically consist of:

A very well-insulated, energy efficient, eco-friendly living space;

Heat captured in the summer months from a sun-warmed sub-roof or attic space, a sunspace or greenhouse, a ground-based, flat-plate, thermosyphon collector, or other solar-heat collection device;

Heat transported from the collection source into (typically) the earth mass under the living space (for storage), this mass surrounded by a sub-surface perimeter "cape" or "umbrella" providing both insulation from easy heat-loss back up to the outdoors air and a barrier against moisture migration through that heat-storage mass;

A high-density floor whose thermal properties are designed to radiate heat back into the living space, but only after the proper sub-floor-insulation-regulated time-lag;

A control-scheme or system which activates (often PV-powered) fans and dampers, when the warm-season air is sensed to be hotter in the collection area(s) than in the storage mass, or allows the heat to be moved into the storage-zone by passive convection (often using a solar chimney and thermally activated dampers.)Usually it requires several years for the storage earth-mass to fully preheat from the local at-depth soil temperature (which varies widely by region and site-orientation) to an optimum Fall level at which it can provide up to 100% of the heating requirements of the living space through the winter. This technology continues to evolve, with a range of variations (including active-return devices) being explored. The listserve where this innovation is most often discussed is "Organic Architecture" at Yahoo.

This system is almost exclusively deployed in northern Europe. One system has been built at Drake Landing in North America. A more recent system is a Do-it-yourself energy-neutral home in progress in Collinsville, IL that will rely solely on Annualized Solar for conditioning.

Astronomical system of units

The astronomical system of units, formally called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976, and has been significantly updated in 1994 and 2009 (see astronomical constant).

The system was developed because of the difficulties in measuring and expressing astronomical data in International System of Units (SI units). In particular, there is a huge quantity of very precise data relating to the positions of objects within the Solar System which cannot conveniently be expressed or processed in SI units. Through a number of modifications, the astronomical system of units now explicitly recognizes the consequences of general relativity, which is a necessary addition to the International System of Units in order to accurately treat astronomical data.

The astronomical system of units is a tridimensional system, in that it defines units of length, mass and time. The associated astronomical constants also fix the different frames of reference that are needed to report observations. The system is a conventional system, in that neither the unit of length nor the unit of mass are true physical constants, and there are at least three different measures of time.

Elena V. Pitjeva

Elena Vladimirovna Pitjeva is a Russian astronomer working at the Institute of Applied Astronomy, Russian Academy of Sciences, St. Petersburg. She has published over 100 articles, as listed in Google Scholar and the Astrophysics Data System in the field of solar system dynamics and celestial mechanics


She began employment activity as an engineer-observer at the Astrophysical observation station of the Astronomical Observatory of Leningrad State University in Byurakan (Armenia). Then Pitjeva worked at the Institute of Theoretical Astronomy of the USSA Academy of Science and the Institute Applied Astronomy RAS since the date of its foundation in 1988 as researcher and senior researcher. At present she is head of the Laboratory of Ephemeris Astronomy of this institute.

Major research interests of Dr. Pitjeva include the construction of numerical ephemerides of the planets, the determination of the planets' and asteroids' masses, the parameters of planet rotation and planetary topography, the solar corona and oblateness and general relativity testing. She is one of creators of the numerical Ephemerides of Planets and the Moon (EPM) of IAA RAS that originated in the seventies of the past century and have been developed since that time. The version of the EPM2004 ephemeris has been adopted as the ephemeris basis of Russian Astronomical Yearbook since 2006. The updated EPM2008 ephemerides are available to outside users via ftp.

The works of Pitjeva have recently been used by several scientists to test several models of modified gravity in the Solar System.

Dr. Pitjeva has also contributed to a better understanding an influence of asteroids and Trans-Neptunian Objects on the planets' motion. Recently Dr. Pitjeva collaborated with Dr. Standish and proposed to the IAU Working Group on Numerical Standards for Fundamental Astronomy (NSFA) the values of the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit in meters, mainly obtained while fitting the constructed DE (JPL) and EPM (IAA RAS) planet ephemerides. These values have been adopted by the 27 General Assembly of International Astronomical Union as Current Best Estimates as the IAU (2009) System of Astronomical Constants.

Pitjeva is a member of the International Astronomical Union: OC of Commission 4 “Ephemerides”,

Commission 52 “Relativity in Fundamental Astronomy”


Eris (dwarf planet)

Eris (minor-planet designation 136199 Eris) is the most massive and second-largest (by volume) dwarf planet (and plutoid) in the known Solar System. Eris was discovered in January 2005 by a Palomar Observatory-based team led by Mike Brown, and its discovery was verified later that year. In September 2006 it was named after Eris, the Greek goddess of strife and discord. Eris is the ninth most massive object directly orbiting the Sun, and the 16th most massive overall, because seven moons are more massive than all known dwarf planets. It is also the largest which has not yet been visited by a spacecraft. Eris was measured to be 2,326 ± 12 kilometers (1,445.3 ± 7.5 mi) in diameter. Eris's mass is about 0.27% of the Earth mass, about 27% more than dwarf planet Pluto, although Pluto is slightly larger by volume.Eris is a trans-Neptunian object (TNO) and a member of a high-eccentricity population known as the scattered disk. It has one known moon, Dysnomia. As of February 2016, its distance from the Sun was 96.3 astronomical units (1.441×1010 km; 8.95×109 mi), roughly three times that of Pluto. With the exception of some long-period comets, until 2018 VG18 was discovered on December 17, 2018, Eris and Dysnomia were the most distant known natural objects in the Solar System.Because Eris appeared to be larger than Pluto, NASA initially described it as the Solar System's tenth planet. This, along with the prospect of other objects of similar size being discovered in the future, motivated the International Astronomical Union (IAU) to define the term planet for the first time. Under the IAU definition approved on August 24, 2006, Eris is a "dwarf planet", along with objects such as Pluto, Ceres, Haumea and Makemake, thereby reducing the number of known planets in the Solar System to eight, the same as before Pluto's discovery in 1930. Observations of a stellar occultation by Eris in 2010 showed that its diameter was 2,326 ± 12 kilometers (1,445.3 ± 7.5 mi), very slightly less than Pluto, which was measured by New Horizons as 2,372 ± 4 kilometers (1,473.9 ± 2.5 mi) in July 2015.

Gas dwarf

A gas dwarf is a gas planet with a rocky core that has accumulated a thick envelope of hydrogen, helium, and other volatiles, having as result a total radius between 1.7 and 3.9 Earth radii (1.7–3.9 R⊕). The term is used in a three-tier, metallicity-based classification regime for short-period exoplanets, which also includes the rocky, terrestrial-like planets with less than 1.7 R⊕ and planets greater than 3.9 R⊕, namely ice giants and gas giants.Smaller gas planets and planets closer to their star will lose atmospheric mass more quickly via hydrodynamic escape than larger planets and planets farther out.The smallest known extrasolar planet that might be a gas dwarf is Kepler-138d, which is less massive than Earth but has a 60% larger volume and therefore has a density (2.1(+2.2/-1.2) grams per cubic centimetre) that indicates either a substantial water content or possibly a thick gas envelope.A low-mass gas planet can still have a radius resembling that of a gas giant if it has the right temperature.

Gliese 176 b

Gliese 176 b is a super-Earth exoplanet approximately 31 light years away in the constellation of Taurus. This planet orbits very close to its parent red dwarf star Gliese 176 (also called "HD 285968").

The initial announcement confused the planetary periodicity with the stellar periodicity of 40 days, thus giving a 10.24 day period for a 25 Earth-mass planet. Subsequent readings filtered out the star's rotation, giving a more accurate reading of the planet's orbit and minimum mass.

The planet orbits inside the inner magnetosphere of its star. The quoted temperature of 450 K is a "thermal equilibrium" temperature.It is projected to be dominated by a rocky core, but the true mass is unknown. If the orbit is oriented such that we are viewing it at a nearly face-on angle, the planet may be significantly more massive than the lower limit. If so, it may have attracted a gas envelope like Uranus or Gliese 436 b.

Gliese 832

Gliese 832 (Gl 832 or GJ 832) is a red dwarf of spectral type M2V in the southern constellation Grus. The apparent visual magnitude of 8.66 means that it is too faint to be seen with the naked eye. It is located relatively close to the Sun, at a distance of 16.2 light years and has a high proper motion of 818.93 milliarcseconds per year. Gliese 832 has just under half the mass and radius of the Sun. Its estimated rotation period is a relatively leisurely 46 days. The star is roughly 9.5 billion years old.In 2014, Gliese 832 was announced to be hosting the closest potentially habitable Earth-mass-range exoplanet to the Solar System. This star achieved perihelion some 52,920 years ago when it came within an estimated 15.71 ly (4.817 pc) of the Sun.

HD 69830 b

HD 69830 b is a Neptune-mass or super-Earth-mass exoplanet orbiting the star HD 69830. It is 10 times more massive than Earth. It also orbits very close to its parent star and takes 82/3 days to complete an orbit.

This is likely to be a rocky planet, not a gas giant. If it had formed as a gas giant, it would have stayed that way.If HD 69830 b is a terrestrial planet, models predict that tidal heating would produce a heat flux at the surface of about 55 W/m2. This is 20 times that of Io.


Kepler-1520 (initially published as KIC 12557548) is a K-type main-sequence star located in the constellation Cygnus. The star is particularly important, as measurements taken by the Kepler spacecraft indicate that the variations in the star's light curve cover a range from about 0.2% to 1.3% of the star's light being blocked. This indicates that there may be a rapidly disintegrating planet, a prediction not yet conclusively confirmed, in orbit around the star, losing mass at a rate of 1 Earth mass every billion years. The planet itself is about 0.1 Earth masses, or just twice the mass of Mercury, and is expected to disintegrate in about 100-200 million years. The planet orbits its star in just 15.7 hours, at a distance only two stellar diameters away from the star's surface, and has an estimated effective temperature of about 2255 K. The orbital period of the planet is one of the shortest ever detected in the history of the extrasolar planet search. In 2016, the planet was confirmed as part of a data release by the Kepler spacecraft.

Lunar distance (astronomy)

Lunar distance (LD or



{\textstyle \Delta _{\oplus L}}

), also called Earth–Moon distance, Earth–Moon characteristic distance, or distance to the Moon, is a unit of measure in astronomy. It is the average distance from the center of Earth to the center of the Moon. More technically, it is the mean semi-major axis of the geocentric lunar orbit. It may also refer to the time-averaged distance between the centers of the Earth and the Moon, or less commonly, the instantaneous Earth–Moon distance. The lunar distance is approximately a quarter of a million miles (400000 km).The mean semi-major axis has a value of 384,402 km (238,856 mi). The time-averaged distance between Earth and Moon centers is 385,000.6 km (239,228.3 mi). The actual distance varies over the course of the orbit of the Moon, from 356,500 km (221,500 mi) at the perigee to 406,700 km (252,700 mi) at apogee, resulting in a differential range of 50,200 km (31,200 mi).Lunar distance is commonly used to express the distance to near-Earth object encounters. Lunar distance is also an important astronomical datum; the precision of this measurement to a few parts in a trillion has useful implications for testing gravitational theories such as general relativity, and for refining other astronomical values such as Earth mass, Earth radius, and Earth's rotation. The measurement is also useful in characterizing the lunar radius, the mass of the Sun and the distance to the Sun.

Millimeter-precision measurements of the lunar distance are made by measuring the time taken for light to travel between LIDAR stations on the Earth and retroreflectors placed on the Moon. The Moon is spiraling away from the Earth at an average rate of 3.8 cm (1.5 in) per year, as detected by the Lunar Laser Ranging Experiment. By coincidence, the diameter of corner cubes in retroreflectors on the Moon is also 3.8 cm.

Millisecond pulsar

A millisecond pulsar (MSP) is a pulsar with a rotational period in the range of about 1–10 milliseconds. Millisecond pulsars have been detected in the radio, X-ray, and gamma ray portions of the electromagnetic spectrum. The leading theory for the origin of millisecond pulsars is that they are old, rapidly rotating neutron stars which have been spun up or "recycled" through accretion of matter from a companion star in a close binary system. For this reason, millisecond pulsars are sometimes called recycled pulsars.

Millisecond pulsars are thought to be related to low-mass X-ray binary systems. It is thought that the X-rays in these systems are emitted by the accretion disk of a neutron star produced by the outer layers of a companion star that has overflowed its Roche lobe. The transfer of angular momentum from this accretion event can theoretically increase the rotation rate of the pulsar to hundreds of times a second, as is observed in millisecond pulsars.

However, there has been recent evidence that the standard evolutionary model fails to explain the evolution of all millisecond pulsars, especially young millisecond pulsars with relatively high magnetic fields, e.g. PSR B1937+21. Bülent Kiziltan and S. E. Thorsett showed that different millisecond pulsars must form by at least two distinct processes. But the nature of the other process remains a mystery.

Many millisecond pulsars are found in globular clusters. This is consistent with the spin-up theory of their formation, as the extremely high stellar density of these clusters implies a much higher likelihood of a pulsar having (or capturing) a giant companion star. Currently there are approximately 130 millisecond pulsars known in globular clusters. The globular cluster Terzan 5 alone contains 33 of these, followed by 47 Tucanae with 22 and M28 and M15 with 8 pulsars each.

Millisecond pulsars, which can be timed with high precision, are better clocks than the best atomic clocks of 1997. This also makes them very sensitive probes of their environments. For example, anything placed in orbit around them causes periodic Doppler shifts in their pulses' arrival times on Earth, which can then be analyzed to reveal the presence of the companion and, with enough data, provide precise measurements of the orbit and the object's mass. The technique is so sensitive that even objects as small as asteroids can be detected if they happen to orbit a millisecond pulsar. The first confirmed exoplanets, discovered several years before the first detections of exoplanets around "normal" solar-like stars, were found in orbit around a millisecond pulsar, PSR B1257+12. These planets remained for many years the only Earth-mass objects known outside the Solar System. One of them, PSR B1257+12 D, has an even smaller mass, comparable to that of our Moon, and is still today the smallest-mass object known beyond the Solar System.

Missa Gaia/Earth Mass

Missa Gaia/Earth Mass is an album released by Paul Winter in 1982 for Living Music. He co-wrote the mass with Paul Halley, Jim Scott, Oscar Castro-Neves, and Kim Oler. The title stems from two languages, Latin (missa = mass) and Greek (gaia = mother nature). The Earth Mass was one of the first contributions made by Paul Winter when he and his Paul Winter Consort became the artists in residence at the Cathedral of St. John the Divine in New York City. The mass includes the usual text, such as the Kyrie and the Agnus Dei, and also other text, hymns, and instrumental pieces. The mass is an environmental liturgy of contemporary music. It features the instrumentation of the Paul Winter Consort along with a choir, vocal soloists, and the calls of wolves, whales, and many other animals that are woven into the pieces, sometimes used as the melody.

Since it was first written, the mass is performed annually at the Cathedral of St. John the Divine at The Feast of St. Francis which is the blessing of the animals.

Ocean planet

An ocean planet, ocean world, water world, aquaplanet or panthalassic planet is a type of terrestrial planet that contains a substantial amount of water either at its surface or subsurface. The term ocean world is also used sometimes for astronomical bodies with an ocean composed of a different fluid, such as lava (the case of Io), ammonia (the case of Titan's inner ocean) or ethane (which could be the most abundant kind of exosea).Earth is the only known astronomical object to have bodies of liquid water on its surface, although several exoplanets have been found with the right conditions to support liquid water. For exoplanets, current technology cannot directly observe liquid surface water, so atmospheric water vapor

may be used as a proxy. The characteristics of ocean worlds—or ocean planets—provide clues to their history, and the formation and evolution of the Solar System as a whole. Of additional interest is their potential to originate and host life.

Planet Nine

Planet Nine is a hypothetical planet in the outer region of the Solar System. Its gravitational effects could explain the unlikely clustering of orbits for a group of extreme trans-Neptunian objects (eTNOs), bodies beyond Neptune that orbit the Sun at distances averaging more than 250 times that of the Earth. These eTNOs tend to make their closest approaches to the Sun in one sector, and their orbits are similarly tilted. These improbable alignments suggest that an undiscovered planet may be shepherding the orbits of the most distant known Solar System objects.This undiscovered super-Earth-sized planet would have a predicted mass of five to ten times the Earth, and an elongated orbit 400 to 800 times as far from the Sun as the Earth. Konstantin Batygin and Michael E. Brown suggest that Planet Nine could be the core of a giant planet that was ejected from its original orbit by Jupiter during the genesis of the Solar System. Others propose that the planet was captured from another star, was once a rogue planet, or that it formed on a distant orbit and was pulled into an eccentric orbit by a passing star.As of 2018, no observation of Planet Nine had been announced. While sky surveys such as Wide-field Infrared Survey Explorer (WISE) and Pan-STARRS did not detect Planet Nine, they have not ruled out the existence of a Neptune-diameter object in the outer Solar System. The ability of these past sky surveys to detect Planet Nine were dependent on its location and characteristics. Further surveys of the remaining regions are ongoing using NEOWISE and the 8-meter Subaru Telescope. Until Planet Nine is observed, it remains a hypothetical object. Several alternative theories have been proposed to explain the observed clustering of TNOs.

Planetary mass

Planetary mass is a measure of the mass of a planet-like object. Within the Solar System, planets are usually measured in the astronomical system of units, where the unit of mass is the solar mass (M☉), the mass of the Sun. In the study of extrasolar planets, the unit of measure is typically the mass of Jupiter (MJ) for large gas giant planets, and the mass of Earth (M⊕) for smaller rocky terrestrial planets.

The mass of a planet within the Solar System is an adjusted parameter in the preparation of ephemerides. There are three variations of how planetary mass can be calculated:

If the planet has natural satellites, its mass can be calculated using Newton's law of universal gravitation to derive a generalization of Kepler's third law that includes the mass of the planet and its moon. This permitted an early measurement of Jupiter's mass, as measured in units of the solar mass.

The mass of a planet can be inferred from its effect on the orbits of other planets. In 1931-1948 flawed applications of this method led to incorrect calculations of the mass of Pluto.

Data from influence collected from the orbits of space probes can be used. Examples include Voyager probes to the outer planets and the MESSENGER spacecraft to Mercury.

Also, numerous other methods can give reasonable approximations. For instance, Varuna, a potential dwarf planet, rotates very quickly upon its axis, as does the dwarf planet Haumea. Haumea has to have a very high density in order not to be ripped apart by centrifugal forces. Through some calculations, one can place a limit on the object's density. Thus, if the object's size is known, a limit on the mass can be determined. See the links in the aforementioned articles for more details on this.

Terrestrial planet

A terrestrial 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 are the inner planets closest to the Sun, i.e. Mercury, Venus, Earth, and Mars. The terms "terrestrial planet" and "telluric planet" are derived from Latin words for Earth (Terra and Tellus), as these planets are, in terms of structure, "Earth-like". These planets are located between the Sun and the Asteroid Belt.

Terrestrial planets have a solid planetary surface, making them substantially different from the larger giant planets, which are composed mostly of some combination of hydrogen, helium, and water existing in various physical states.

Ömerli Dam

Ömerli Dam (Turkish: Ömerli Barajı) is a rock-fill dam in Istanbul Province, Turkey.Ömerli Dam is located in Çekmeköy district of Istanbul Province. The rock-fill dam was built by the Turkish State Hydraulic Works on the Riva Creek to provide tap water for the city. Construction started in 1968, and the dam went in service in 1973.The volume of the earth mass used in the dam is 2,200 dam3 (78,000,000 cu ft). The dam has a thalweg height of 52 m (171 ft). It forms the reservoir Lake Ömerli (Turkish: Ömerli Gölü), which has a surface of 23 km2 (8.9 sq mi) and water capacity of 386 nm3 (1.36×10−23 cu ft).In 1999, a sanitation project was launched to protect the reservoir from waste water pollution. In the time span of the last twenty years after the construction of the dam, the surrounding area saw a rapid urbanization that brought the risk of pollution of the reservoir. The project foresaw the collection of waste water by collectors and treatment in sewage plants before emptying into the sea.

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