Short description: Unit of measurement
1 R = Units
6.95700×108 metres
695,700 kilometres
0.00465047 astronomical unit
432,288 miles
7.35355×10−8 light-year
2.25461×10−8 parsec
2.32061 light-seconds

Solar radius is a unit of distance used to express the size of stars in astronomy relative to the Sun. The solar radius is usually defined as the radius to the layer in the Sun's photosphere where the optical depth equals 2/3:[1]

$\displaystyle{ 1\,R_{\odot} = 6.957\times 10^8 \hbox{ m} }$

695,700 kilometres (432,300 miles) is approximately 10 times the average radius of Jupiter, 109 times the radius of the Earth, and 1/215th of an astronomical unit, the approximate distance between Earth and the Sun. The solar radius to either pole and that to the equator differ slightly due to the Sun's rotation, which induces an oblateness in the order of 10 parts per million.[2]

## Measurements

Evolution of the solar luminosity, radius and effective temperature compared to the present-day Sun. After Ribas (2009)[3]

The uncrewed SOHO spacecraft was used to measure the radius of the Sun by timing transits of Mercury across the surface during 2003 and 2006. The result was a measured radius of 696,342 ± 65 kilometres (432,687 ± 40 miles).[4]

Haberreiter, Schmutz & Kosovichev (2008)[1] determined the radius corresponding to the solar photosphere to be 695,660 ± 140 kilometres (432,263 ± 87 miles). This new value is consistent with helioseismic estimates; the same study showed that previous estimates using inflection point methods had been overestimated by approximately 300 km (190 mi).

In 2015, the International Astronomical Union passed Resolution B3, which defined a set of nominal conversion constants for stellar and planetary astronomy. Resolution B3 defined the nominal solar radius (symbol $\displaystyle{ R^{N}_{\odot} }$) to be equal to exactly 695700 km.[5] The nominal value, which is the rounded value, within the uncertainty, given by Haberreiter, Schmutz & Kosovichev (2008), was adopted to help astronomers avoid confusion when quoting stellar radii in units of the Sun's radius, even when future observations will likely refine the Sun's actual photospheric radius (which is currently[6] only known to about an accuracy of ±100–200 km).

## Examples

Solar radii as a unit are common when describing spacecraft moving close to the sun. Two spacecraft in the 2010s include:

WOH G64 (largest known star) 1540[7] 1,071,378,000
Betelgeuse 764[8] 531,500,000
Antares A 680[9] 473,076,000
Rigel A 78.9[10] 54,980,000
Aldebaran 45.1[11] 31,375,000
Arcturus 25.4[12] 17,670,000
Pollux 9.06[13] 6,300,000
Sirius A 1.711[14] 1,190,350
Sun 1 695,700
Proxima Centauri 0.1542[15] 107,275
Jupiter 0.1028 71,492[16]
Saturn 0.0866 60,268[16]
Uranus 0.03673 25,559[16]
Neptune 0.03559 24,764[16]
Earth 0.009168 6,378[16]
Venus 0.00869 6,051.8[16]
Mars 0.00488 3,396.19[16]
Mercury 0.0035 2,440.53[16]
Moon 0.0025 1,738.1[17]
Pluto 0.0017 1,188.3[16]

## References

1. Haberreiter, M; Schmutz, W; Kosovichev, A.G. (2008), "Solving the Discrepancy between the Seismic and Photospheric Solar Radius", Astrophysical Journal 675 (1): L53–L56, doi:10.1086/529492, Bibcode2008ApJ...675L..53H
2. NASA RHESSI oblateness measurements 2012
3. Ribas, Ignasi (August 2009). "The Sun and Stars as the Primary Energy Input in Planetary Atmospheres". Proceedings of the International Astronomical Union 5 (S264 [Solar and Stellar Variability: Impact on Earth and Planets]): 3–18. doi:10.1017/S1743921309992298. Bibcode2010IAUS..264....3R.
4. Emilio, Marcelo; Kuhn, Jeff R.; Bush, Rock I.; Scholl, Isabelle F. (2012), "Measuring the Solar Radius from Space during the 2003 and 2006 Mercury Transits", The Astrophysical Journal 750 (2): 135, doi:10.1088/0004-637X/750/2/135, Bibcode2012ApJ...750..135E
5. Mamajek, E.E.; Prsa, A.; Torres, G.; et, al. (2015), IAU 2015 Resolution B3 on Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties, Bibcode2015arXiv151007674M
6. Meftah, M; Corbard, T; Hauchecorne, A.; Morand, F.; Ikhlef, R.; Chauvineau, B.; Renaud, C.; Sarkissian, A. et al. (2018), "Solar radius determined from PICARD/SODISM observationsand extremely weak wavelength dependence in the visibleand the near-infrared", Astronomy & Astrophysics 616: A64, doi:10.1051/0004-6361/201732159, Bibcode2018A&A...616A..64M
7. Levesque, Emily M.; Massey, Philip; Plez, Bertrand; Olsen, Knut A. G. (2009-06-01). "The Physical Properties of the Red Supergiant WOH G64: The Largest Star Known?". The Astronomical Journal 137 (6): 4744–4752. doi:10.1088/0004-6256/137/6/4744. ISSN 0004-6256. Bibcode2009AJ....137.4744L.
8. Joyce, Meridith; Leung, Shing-Chi; Molnár, László; Ireland, Michael; Kobayashi, Chiaki; Nomoto, Ken'ichi (2020-10-01). "Standing on the Shoulders of Giants: New Mass and Distance Estimates for Betelgeuse through Combined Evolutionary, Asteroseismic, and Hydrodynamic Simulations with MESA". The Astrophysical Journal 902 (1): 63. doi:10.3847/1538-4357/abb8db. ISSN 0004-637X. Bibcode2020ApJ...902...63J.
9. Ohnaka, K.; Hofmann, K. -H.; Schertl, D.; Weigelt, G.; Baffa, C.; Chelli, A.; Petrov, R.; Robbe-Dubois, S. (2013-07-01). "High spectral resolution imaging of the dynamical atmosphere of the red supergiant Antares in the CO first overtone lines with VLTI/AMBER". Astronomy and Astrophysics 555: A24. doi:10.1051/0004-6361/201321063. ISSN 0004-6361. Bibcode2013A&A...555A..24O.
10. Moravveji, Ehsan; Guinan, Edward F.; Shultz, Matt; Williamson, Michael H.; Moya, Andres (2012-03-01). "Asteroseismology of the nearby SN-II Progenitor: Rigel. I. The MOST High-precision Photometry and Radial Velocity Monitoring". The Astrophysical Journal 747 (2): 108. doi:10.1088/0004-637X/747/2/108. ISSN 0004-637X. Bibcode2012ApJ...747..108M.
11. Hatzes, A. P.; Cochran, W. D.; Endl, M.; Guenther, E. W.; MacQueen, P.; Hartmann, M.; Zechmeister, M.; Han, I. et al. (2015-08-01). "Long-lived, long-period radial velocity variations in Aldebaran: A planetary companion and stellar activity". Astronomy and Astrophysics 580: A31. doi:10.1051/0004-6361/201425519. ISSN 0004-6361. Bibcode2015A&A...580A..31H.
12. Ramírez, I.; Allende Prieto, C. (2011-12-01). "Fundamental Parameters and Chemical Composition of Arcturus". The Astrophysical Journal 743 (2): 135. doi:10.1088/0004-637X/743/2/135. ISSN 0004-637X. Bibcode2011ApJ...743..135R.
13. Baines, Ellyn K.; Armstrong, J. Thomas; Schmitt, Henrique R.; Zavala, R. T.; Benson, James A.; Hutter, Donald J.; Tycner, Christopher; Belle, Gerard T. van (2017-12-21). "Fundamental Parameters of 87 Stars from the Navy Precision Optical Interferometer". The Astronomical Journal 155 (1): 30. doi:10.3847/1538-3881/aa9d8b. ISSN 0004-6256.
14. Liebert, James; Young, Patrick A.; Arnett, David; Holberg, J. B.; Williams, Kurtis A. (2005-09-01). "The Age and Progenitor Mass of Sirius B". The Astrophysical Journal 630 (1): L69–L72. doi:10.1086/462419. ISSN 0004-637X. Bibcode2005ApJ...630L..69L.
15. Kervella, P.; Thévenin, F.; Lovis, C. (February 2017). "Proxima's orbit around Alpha Centauri". Astronomy & Astrophysics 598: L7. doi:10.1051/0004-6361/201629930. ISSN 0004-6361. Bibcode2017A&A...598L...7K.