# Solar luminosity

Evolution of the solar luminosity, radius and effective temperature compared to the present day Sun. After Ribas (2010)[1]

The solar luminosity, L, is a unit of radiant flux (power emitted in the form of photons) conventionally used by astronomers to measure the luminosity of stars. One solar luminosity is equal to the current accepted luminosity of the Sun, which is 3.839×1026 W, or 3.839×1033 erg/s.[2] The value is slightly higher, 3.939×1026 W (equivalent to 4.382×109 kg/s or 1.9×10−16 M/d) if the solar neutrino radiation is included as well as electromagnetic radiation.[3] The Sun is a weakly variable star and its luminosity therefore fluctuates.[4] The major fluctuation is the eleven-year solar cycle (sunspot cycle), which causes a periodic variation of about ±0.1%. Any other variation over the last 200–300 years is thought to be much smaller than this.[3]

## Determination

The solar luminosity is related to the solar irradiance (the solar constant) measured at the Earth or by satellites in Earth orbit. The solar irradiance is responsible for the orbital forcing which causes the Milankovitch cycles, which determine glacial cycles on Earth. The mean irradiance at the top of the Earth's atmosphere is sometimes known as the solar constant, I. Irradiance is defined as power per unit area, so the solar luminosity (total power emitted by the Sun) is the irradiance received at the Earth (solar constant) multiplied by the area of the sphere whose radius is the mean distance between the Earth and the Sun:

$L_\odot = 4\pi kI_\odot A^2\,$

where A is the unit distance (the value of the astronomical unit in metres) and k is a constant (whose value is very close to one) that reflects the fact that the mean distance from the Earth to the Sun is not exactly one astronomical unit.

## References

1. ^ Ribas, Ignasi (February 2010), "The Sun and stars as the primary energy input in planetary atmospheres", Solar and Stellar Variability: Impact on Earth and Planets, Proceedings of the International Astronomical Union, IAU Symposium 264, pp. 3–18, arXiv:0911.4872, Bibcode:2010IAUS..264....3R, doi:10.1017/S1743921309992298
2. ^ Carroll, Bradley W.; Ostlie, Dale A. (2007), An Introduction to Modern Astrophysics, Pearson Addison-Wesley, pp. Appendix A, ISBN 0-8053-0402-9
3. ^ a b Noerdlinger, Peter D. (2008), "Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System", Celest. Mech. Dynam. Astron. 0801: 3807, arXiv:0801.3807, Bibcode:2008arXiv0801.3807N
4. ^ Vieira, L. E. A.; Norton, A.; Dudok De Wit, T.; Kretzschmar, M.; Schmidt, G. A.; Cheung, M. C. M. (2012). "How the inclination of Earth's orbit affects incoming solar irradiance". Geophysical Research Letters 39 (16): n/a. doi:10.1029/2012GL052950. edit