Solar mass: Difference between revisions
Mass by diameter? Not really. Just an imprecise graphic. |
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The '''solar mass''' ('''{{solar mass}}''') is a | The '''solar mass''' ('''{{solar mass}}''') is a frequently used [[mass#Units of mass|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 [[star]]s, as well as [[star cluster|stellar cluster]]s, [[nebula]]e, [[galaxy|galaxies]] and [[Black hole|black holes]]. More precisely, the mass of the Sun is | ||
{{block indent|nominal solar mass {{math|{{solar mass}} {{=}} {{val|1.988416|e=30|u=kilogram}}}} or a best estimate of {{solar mass}} {{=}} {{val|1.988475|0.000092|e=30|u=kilogram}}.<ref name="Quantities"/>}} | {{block indent|nominal solar mass {{math|{{solar mass}} {{=}} {{val|1.988416|e=30|u=kilogram}}}} or a best estimate of {{solar mass}} {{=}} {{val|1.988475|0.000092|e=30|u=kilogram}}.<ref name="Quantities"/>}} | ||
The solar mass is about {{val|333000}} times the [[Earth mass|mass of Earth]] ({{Earth mass}}), or {{val|1047}} times the [[Jupiter mass|mass of Jupiter]] ({{Jupiter mass}}). | The solar mass is about {{val|333000}} times the [[Earth mass|mass of Earth]] ({{Earth mass|sym=y}}), or {{val|1047}} times the [[Jupiter mass|mass of Jupiter]] ({{Jupiter mass}}). | ||
== History of measurement == | == 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]].<ref>{{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}}</ref> The value he obtained differs by only 1% from the modern value, but was not as precise.<ref>{{cite book | The value of the gravitational constant was first derived from measurements that were made by [[Henry Cavendish]] in 1798 with a [[torsion balance]].<ref>{{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}}</ref> The value he obtained differs by only 1% from the modern value, but was not as precise.<ref>{{cite book | ||
| | |author1=Holton, Gerald James |author2=Brush, Stephen G. | ||
| title=Physics, the human adventure: from Copernicus to Einstein and beyond | | title=Physics, the human adventure: from Copernicus to Einstein and beyond | ||
| date=2001 | page=137 | edition=3rd | | date=2001 | page=137 | edition=3rd | ||
| publisher=[[Rutgers University Press]] | | publisher=[[Rutgers University Press]] | ||
| isbn=978-0-8135-2908-0}}</ref> The [[parallax#Diurnal parallax|diurnal parallax]] of the Sun was accurately measured during the transits of Venus in 1761 and 1769,<ref>{{cite book | | isbn=978-0-8135-2908-0}}</ref> The [[parallax#Diurnal parallax|diurnal parallax]] of the Sun was accurately measured during the transits of Venus in 1761 and 1769,<ref>{{cite book | ||
| | | author1=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 | | 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 | | date=2001 | isbn=978-3-540-63198-9| bibcode=2001uhtc.book.....P | ||
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| isbn=978-0-7503-0886-1}}</ref><ref>{{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}}</ref> | | isbn=978-0-7503-0886-1}}</ref><ref>{{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}}</ref> | ||
The first known estimate of the solar mass was by [[Isaac Newton]].<ref>{{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 }}</ref> In his work ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'' (1687), he estimated that the ratio of the mass of Earth to the Sun was about | The first known estimate of the solar mass was by [[Isaac Newton]].<ref>{{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 }}</ref> In his work ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'' (1687), he estimated that the ratio of the mass of Earth to the Sun was about 1:{{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 1:{{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 1:{{val|332946}}.<ref> | ||
{{cite book | {{cite book | ||
| first=David | last=Leverington | date=2003 | | first=David | last=Leverington | date=2003 | ||
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}}</ref> | }}</ref> | ||
As a unit of measurement, the solar mass came into use before the | As a unit of measurement, the solar mass came into use before the astronomical unit 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 star#Use in astrophysics|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 == | == 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.<ref>{{ | 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.<ref>{{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}}</ref> 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 laws of planetary motion|Kepler's third law]]:<ref>{{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}}</ref><ref>{{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}}</ref> | ||
<math display="block">M_\odot = \frac{4 \pi^2 \times (1\,\mathrm{ | <math display="block">M_\odot = \frac{4 \pi^2 \times (1\,\mathrm{au})^3}{G \times (1\,\mathrm{yr})^2}</math> | ||
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.<ref>{{ | 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.<ref>{{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}}</ref> As a result, the solar mass is used as the standard mass in the [[astronomical system of units]]. | ||
== Variation == | == Variation == | ||
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== Related units == | == Related units == | ||
One solar mass, {{Solar mass|}}, can be converted to related units:<ref>{{Cite web|title=Planetary Fact Sheet|url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/|access-date=2020-09-01|website=nssdc.gsfc.nasa.gov}}</ref> | One solar mass, {{Solar mass|}}, can be converted to related units:<ref>{{Cite web|title=Planetary Fact Sheet|url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/|access-date=2020-09-01|website=nssdc.gsfc.nasa.gov}}</ref> | ||
* {{math|{{val|27068510}} | * {{math|{{val|27068510}} {{lunar mass|sym=y}}}} ([[Lunar mass]]) | ||
* {{math|{{val|332946}} {{Earth mass}}}} ([[Earth mass]]) | * {{math|{{val|332946}} {{Earth mass|sym=y}}}} ([[Earth mass]]) | ||
* {{math|{{val|1047.35}} {{Jupiter mass}}}} ([[Jupiter 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. | It is also frequently useful in [[general relativity]] to express mass in units of length or time. | ||
* | * {{Solar mass}}''G''/''c''<sup>2</sup> ≈ 1.48 km (half the [[Schwarzschild radius]] of the Sun) | ||
* | * {{Solar mass}}''G''/''c''<sup>3</sup> ≈ 4.93 μs | ||
The solar mass parameter (''G'' | The solar mass parameter (''G''{{Solar mass|}}), as listed by the IAU Division I Working Group, has the following estimates:<ref> | ||
{{cite web | {{cite web | ||
| work=Numerical Standards for Fundamental Astronomy | | work=Numerical Standards for Fundamental Astronomy | ||
Revision as of 02:06, 20 June 2025
Template:Short description Template:Infobox unit
The solar mass (Template:Solar mass) is a frequently used unit of mass in astronomy, equal to approximately Template:Val. 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. More precisely, the mass of the Sun is Template:Block indent
The solar mass is about Template:Val times the mass of Earth (Template:Earth mass), or Template:Val times the mass of Jupiter (Template: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.[1] The value he obtained differs by only 1% from the modern value, but was not as precise.[2] The diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769,[3] yielding a value of Template:Val (9 arcseconds, compared to the present value of Template:Val). From the value of the diurnal parallax, one can determine the distance to the Sun from the geometry of Earth.[4][5]
The first known estimate of the solar mass was by Isaac Newton.[6] In his work Principia (1687), he estimated that the ratio of the mass of Earth to the Sun was about 1:Template:Val. 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 1:Template:Val in the third edition of the Principia. The current value for the solar parallax is smaller still, yielding an estimated mass ratio of 1:Template:Val.[7]
As a unit of measurement, the solar mass came into use before the astronomical unit 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.[8] Based on the length of the year, the distance from Earth to the Sun (an astronomical unit or au), and the gravitational constant (Template:Math), the mass of the Sun is given by solving Kepler's third law:[9][10]
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.[11] 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 Template:Solar mass/year.[12] The mass loss rate will increase when the Sun enters the red giant stage, climbing to Template:Solar mass/year when it reaches the tip of the red-giant branch. This will rise to Template:Solar mass/year on the asymptotic giant branch, before peaking at a rate of 10−5 to 10−4 Template: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.[13]
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.[14]
The original mass of the Sun at the time it reached the main sequence remains uncertain.[15] 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.[16]
Related units
One solar mass, Template:Solar mass, can be converted to related units:[17]
It is also frequently useful in general relativity to express mass in units of length or time.
- Template:Solar massG/c2 ≈ 1.48 km (half the Schwarzschild radius of the Sun)
- Template:Solar massG/c3 ≈ 4.93 μs
The solar mass parameter (GTemplate:Solar mass), as listed by the IAU Division I Working Group, has the following estimates:[18]
- Template:Val (TCG-compatible)
- Template:Val (TDB-compatible)
See also
References
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