URL-STATUS=DEAD, {{failed verification|date=April 2024}}}}The solar mass ({{solar mass}}) is a standard unit of mass in astronomy, equal to approximately {{val|2|e=30|ul=kg}}. It is approximately equal to the mass of the Sun. It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. This equates to about two nonillion (short scale), two quintillion (long scale) kilograms or 2000 quettagrams:{{block indent|{{math|{{solar mass}} {{=}} {{val|1.98847|0.00007|e=30|u=kilogram}}}}}}The solar mass is about {{val|333000}} times the mass of Earth ({{Earth mass}}), or {{val|1047}} times the mass of Jupiter ({{Jupiter mass}}).

History of measurement

The value of the gravitational constant was first derived from measurements that were made by Henry Cavendish in 1798 with a torsion balance.WEB,weblink Universal Gravitational Constant, 13, 11 April 2019, University of Tennessee Physics, Geoffrey R., Clarion, PASCO, The value he obtained differs by only 1% from the modern value, but was not as precise.HOLTON, GERALD JAMES >AUTHOR2=BRUSH, STEPHEN G., Physics, the human adventure: from Copernicus to Einstein and beyond

page=137, 3rd, Rutgers University Press

parallax#Diurnal parallax>diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769,PECKER, JEAN CLAUDE> AUTHOR2=KAUFMAN, SUSAN

PAGES=291, Springer

isbn=978-3-540-63198-9, 2001uhtc.book.....P, yielding a value of {{val|9|u=arcsecond}} (9 arcseconds, compared to the present value of {{val|8.794148|u=arcsecond}}). From the value of the diurnal parallax, one can determine the distance to the Sun from the geometry of Earth.CESARE > LAST=BARBIERI, 2007, Fundamentals of astronomy

publisher=CRC Press

ACCESS-DATE=2020-09-01

LANGUAGE=EN, The first known estimate of the solar mass was by Isaac Newton.JOURNAL, Newton's Determination of the Masses and Densities of the Sun, Jupiter, Saturn, and the Earth, I. Bernard, Cohen, 122869257, I. Bernard Cohen, Archive for History of Exact Sciences, 53, 1, 83â€“95, May 1998, 41134054, 10.1007/s004070050022, 1998AHES...53...83C, In his work Principia (1687), he estimated that the ratio of the mass of Earth to the Sun was about {{frac|{{val|28700}}}}. Later he determined that his value was based upon a faulty value for the solar parallax, which he had used to estimate the distance to the Sun. He corrected his estimated ratio to {{frac|{{val|169282}}}} in the third edition of the Principia. The current value for the solar parallax is smaller still, yielding an estimated mass ratio of {{frac|{{val|332946}}}}.DAVID > LAST=LEVERINGTON, 2003, Babylon to Voyager and beyond: a history of planetary astronomy

publisher=Cambridge University Press, 978-0-521-80840-8, As a unit of measurement, the solar mass came into use before the AU and the gravitational constant were precisely measured. This is because the relative mass of another planet in the Solar System or the combined mass of two binary stars can be calculated in units of Solar mass directly from the orbital radius and orbital period of the planet or stars using Kepler's third law.

Calculation

The mass of the Sun cannot be measured directly, and is instead calculated from other measurable factors, using the equation for the orbital period of a small body orbiting a central mass.WEB, Finding the Mass of the Sun,weblink 2020-09-06, imagine.gsfc.nasa.gov, Based on the length of the year, the distance from Earth to the Sun (an astronomical unit or AU), and the gravitational constant ({{math|G}}), the mass of the Sun is given by solving Kepler's third law:WEB, Woo, Marcus, 6 December 2018, What Is Solar Mass?,weblink 2020-09-06, Space.com, en, WEB, Kepler's Third Law {{!, Imaging the Universe|url=http://astro.physics.uiowa.edu/ITU/glossary/keplers-third-law/|access-date=2020-09-06|website=astro.physics.uiowa.edu|archive-date=2020-07-31|archive-url=https://web.archive.org/web/20200731060248weblink|url-status=dead}}M_odot = frac{4 pi^2 times (1,mathrm{AU})^3}{G times (1,mathrm{yr})^2}The value of G is difficult to measure and is only known with limited accuracy (see Cavendish experiment). The value of G times the mass of an object, called the standard gravitational parameter, is known for the Sun and several planets to a much higher accuracy than G alone.WEB, CODATA Value: Newtonian constant of gravitation,weblink 2020-09-06, physics.nist.gov, As a result, the solar mass is used as the standard mass in the astronomical system of units.

Variation

The Sun is losing mass because of fusion reactions occurring within its core, leading to the emission of electromagnetic energy, neutrinos and by the ejection of matter with the solar wind. It is expelling about {{Solar mass|{{val|2|-|3|e=-14}}}}/year.{{citation | first1=Bradley W. | last1=Carroll | last2=Ostlie | first2=Dale A. | date=1995 | title=An Introduction to Modern Astrophysics | edition=revised 2nd | publisher=Benjamin Cummings | isbn=0201547309 | page=409 | postscript=. }} The mass loss rate will increase when the Sun enters the red giant stage, climbing to {{Solar mass|{{val|7|-|9|e=-14}}}}/year when it reaches the tip of the red-giant branch. This will rise to {{Solar mass|{{10^|-6}}}}/year on the asymptotic giant branch, before peaking at a rate of 10âˆ’5 to 10âˆ’4 {{Solar mass}}/year as the Sun generates a planetary nebula. By the time the Sun becomes a degenerate white dwarf, it will have lost 46% of its starting mass.{{citation | last1=SchrÃ¶der | first1=K.-P. | last2=Connon Smith | first2=Robert | s2cid=10073988 | title=Distant future of the Sun and Earth revisited | journal=Monthly Notices of the Royal Astronomical Society | volume=386 | issue=1 | pages=155â€“163 | doi=10.1111/j.1365-2966.2008.13022.x | date=2008 | bibcode=2008MNRAS.386..155S|arxiv = 0801.4031 }}The mass of the Sun has been decreasing since the time it formed. This occurs through two processes in nearly equal amounts. First, in the Sun's core, hydrogen is converted into helium through nuclear fusion, in particular the pâ€“p chain, and this reaction converts some mass into energy in the form of gamma ray photons. Most of this energy eventually radiates away from the Sun. Second, high-energy protons and electrons in the atmosphere of the Sun are ejected directly into outer space as the solar wind and coronal mass ejections.JOURNAL, Genova, Antonio, Mazarico, Erwan, Goossens, Sander, Lemoine, Frank G., Neumann, Gregory A., Smith, David E., Zuber, Maria T., Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission, Nature Communications, 18 January 2018, 9, 1, 289, 10.1038/s41467-017-02558-1, en, 2041-1723, The fusion cycle that generates energy into the Sun relies on the conversion of hydrogen into helium, which is responsible for a solar mass reduction with a rate of ~ âˆ’0.67 Ã— 10âˆ’13 per year. On the other hand, the solar wind contribution is more uncertain. The solar cycle significantly influences the solar mass loss rate due to solar wind. Estimates of the mass carried away with the solar wind showed rates between âˆ’ (2â€“3) Ã— 10âˆ’14{{solar mass, per year, whereas numerical simulations of coupled corona and solar wind models provided rates between âˆ’ (4.2â€“6.9) Ã— 10âˆ’14 {{solar mass}} per year.|doi-access=free |pmid=29348613 |pmc=5773540 |bibcode=2018NatCo...9..289G }}The original mass of the Sun at the time it reached the main sequence remains uncertain.WEB, Lecture 40: The Once and Future Sun,weblink 2020-09-01, www.astronomy.ohio-state.edu, The early Sun had much higher mass-loss rates than at present, and it may have lost anywhere from 1â€“7% of its natal mass over the course of its main-sequence lifetime. The Sun gains a very small amount of mass through the impact of asteroids and comets. However, as the Sun already contains 99.86% of the Solar System's total mass, these impacts cannot offset the mass lost by radiation and ejection.{{Citation needed|date=September 2020}}

Related units

One solar mass, {{Solar mass|}}, can be converted to related units:WEB, Planetary Fact Sheet,weblink 2020-09-01, nssdc.gsfc.nasa.gov,

{{math|{{val|27068510}} ML}} (Lunar mass)
{{math|{{val|332946}} {{Earth mass}}}} (Earth mass)
{{math|{{val|1047.35}} {{Jupiter mass}}}} (Jupiter mass)
{{math|{{val|1988.55}} quetta grams}} ({{math|{{val|1.98855}} ronna tonnes}})

It is also frequently useful in general relativity to express mass in units of length or time.

{{math|{{Solar mass}} G / c2 â‰ˆ 1.48 km}} (half the Schwarzschild radius of the Sun)
{{math|{{Solar mass}} G / c3 â‰ˆ 4.93 Î¼s}}

The solar mass parameter (GÂ·{{Solar mass|}}), as listed by the IAU Division I Working Group, has the following estimates:WEB

, Numerical Standards for Fundamental Astronomy
, IAU Division I Working Group, 2012
, Astronomical Constants : Current Best Estimates (CBEs)
,weblink
, 2021-05-04

{{val|1.32712442099|(10)|e=20|u=m3sâˆ’2}} (TCG-compatible)
{{val|1.32712440041|(10)|e=20|u=m3sâˆ’2}} (TDB-compatible)

References

}}

- content above as imported from Wikipedia
- "Solar mass" does not exist on GetWiki (yet)
- time: 12:34am EDT - Sat, May 18 2024

[ this remote article is provided by Wikipedia ]

CONNECT

GetWiki

Solar mass

History of measurement

Calculation

Variation

Related units

See also

References