solar mass

The value of the gravitational constant was first derived from measurements that were made by Henry Cavendish in 1798 with a torsion balance.{{cite web |url=http://www.phys.utk.edu/labs/modphys/Pasco%20Cavendish%20Experiment.pdf |title=Universal Gravitational Constant |pages=13 |access-date=11 April 2019 |work=University of Tennessee Physics |first=Geoffrey R. |last=Clarion |publisher=PASCO}} The value he obtained differs by only 1% from the modern value, but was not as precise.{{cite book

|author=Holton, Gerald James |author2=Brush, Stephen G.

| title=Physics, the human adventure: from Copernicus to Einstein and beyond

| date=2001 | page=137 | edition=3rd

| publisher=Rutgers University Press

| isbn=978-0-8135-2908-0}} The diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769,{{cite book

| author=Pecker, Jean Claude| author2=Kaufman, Susan

| title=Understanding the heavens: thirty centuries of astronomical ideas from ancient thinking to modern cosmology | pages=291 | publisher=Springer

| date=2001 | isbn=978-3-540-63198-9| bibcode=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.{{cite book

| first=Cesare | last=Barbieri | date=2007

| title=Fundamentals of astronomy

| pages=132–140 | publisher=CRC Press

| isbn=978-0-7503-0886-1}}{{Cite web|title=How do scientists measure or calculate the weight of a planet?|url=https://www.scientificamerican.com/article/how-do-scientists-measure/|access-date=2020-09-01|website=Scientific American|language=en}}

The first known estimate of the solar mass was by Isaac Newton.{{cite journal |title=Newton's Determination of the Masses and Densities of the Sun, Jupiter, Saturn, and the Earth |first=I. Bernard |last=Cohen |s2cid=122869257 |author-link=I. Bernard Cohen |journal=Archive for History of Exact Sciences |volume=53 |issue=1 |pages=83–95 |date=May 1998 |jstor=41134054 |doi=10.1007/s004070050022 |bibcode=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}}}}.

{{cite book

| first=David | last=Leverington | date=2003

| title=Babylon to Voyager and beyond: a history of planetary astronomy

| page=126 | publisher=Cambridge University Press

| isbn=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.

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.{{Cite web|title=Finding the Mass of the Sun|url=https://imagine.gsfc.nasa.gov/features/yba/CygX1_mass/gravity/sun_mass.html|access-date=2020-09-06|website=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:{{Cite web|last=Woo|first=Marcus|date=6 December 2018|title=What Is Solar Mass?|url=https://www.space.com/42649-solar-mass.html|access-date=2020-09-06|website=Space.com|language=en}}{{Cite web|title=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/20200731060248/http://astro.physics.uiowa.edu/ITU/glossary/keplers-third-law/|url-status=dead}}

$$M\_\backslash odot\; =\; \backslash frac\{4\; \backslash pi^2\; \backslash times\; (1\backslash ,\backslash mathrm\{AU\})^3\}\{G\; \backslash times\; (1\backslash ,\backslash mathrm\{yr\})^2\}$$

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.{{Cite web|title=CODATA Value: Newtonian constant of gravitation|url=https://physics.nist.gov/cgi-bin/cuu/Value?bg|access-date=2020-09-06|website=physics.nist.gov}} As a result, the solar mass is used as the standard mass in the astronomical system of units.

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 10⁻⁵ to 10⁻⁴ {{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=Schröder | 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=155–163 | doi=10.1111/j.1365-2966.2008.13022.x | date=2008 | doi-access=free | 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 p–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.{{cite journal |last1=Genova |first1=Antonio |last2=Mazarico |first2=Erwan |last3=Goossens |first3=Sander |last4=Lemoine |first4=Frank G. |last5=Neumann |first5=Gregory A. |last6=Smith |first6=David E. |last7=Zuber |first7=Maria T. |title=Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission |journal=Nature Communications |date=18 January 2018 |volume=9 |issue=1 |pages=289 |doi=10.1038/s41467-017-02558-1 |language=en |issn=2041-1723 |quote=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 ~ −0.67 × 10⁻¹³ 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 − (2–3) × 10⁻¹⁴{{solar mass}} per year, whereas numerical simulations of coupled corona and solar wind models provided rates between − (4.2–6.9) × 10⁻¹⁴ {{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.{{Cite web|title=Lecture 40: The Once and Future Sun|url=http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit6/futuresun.html|access-date=2020-09-01|website=www.astronomy.ohio-state.edu}} The early Sun had much higher mass-loss rates than at present, and it may have lost anywhere from 1–7% of its natal mass over the course of its main-sequence lifetime.

One solar mass, {{Solar mass|}}, can be converted to related units:{{Cite web|title=Planetary Fact Sheet|url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/|access-date=2020-09-01|website=nssdc.gsfc.nasa.gov}}

• {{math|{{val|27068510}} M_L}} (Lunar mass)
• {{math|{{val|332946}} {{Earth mass}}}} (Earth mass)
• {{math|{{val|1047.35}} {{Jupiter mass}}}} (Jupiter mass)

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

• {{math|{{Solar mass}} G / c² ≈ 1.48 km}} (half the Schwarzschild radius of the Sun)
• {{math|{{Solar mass}} G / c³ ≈ 4.93 μs}}

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

{{cite web

| work=Numerical Standards for Fundamental Astronomy

| publisher=IAU Division I Working Group | year=2012

| title=Astronomical Constants : Current Best Estimates (CBEs)

| url=https://iau-a3.gitlab.io/NSFA/NSFA_cbe.html#GMS2012

| access-date=2021-05-04

}}

• {{val|1.32712442099|(10)|e=20|u=m³s⁻²}} (TCG-compatible)
• {{val|1.32712440041|(10)|e=20|u=m³s⁻²}} (TDB-compatible)

• Chandrasekhar limit
• Gaussian gravitational constant
• Orders of magnitude (mass)
• Stellar mass
• Sun

{{reflist|refs=

{{citation |last1=Sackmann |first1=I.-Juliana |last2=Boothroyd |first2=Arnold I. |s2cid=118904050 |title=Our Sun. V. A Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars |journal=The Astrophysical Journal |volume=583 |issue=2 |pages=1024–1039 |date=February 2003 |doi=10.1086/345408 |bibcode=2003ApJ...583.1024S |arxiv= astro-ph/0210128}}

}}

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Mass

Category:Units of mass

Mass