astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...

, the nuclear timescale is an estimate of the lifetime of a

star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

based solely on its rate of fuel consumption. Along with the

thermal A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...

and free-fall (aka dynamical) time scales, it is used to estimate the length of time a particular star will remain in a certain phase of its life and its lifespan if hypothetical conditions are met. In reality, the lifespan of a star is greater than what is estimated by the nuclear time scale because as one fuel becomes scarce, another will generally take its place—hydrogen burning gives way to helium burning, etc. However, all the phases after hydrogen burning combined typically add up to less than 10% of the duration of hydrogen burning.

Stellar astrophysics

Hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...

generally determines a star's nuclear lifetime because it is used as the main source of fuel in a

main sequence In astronomy, the main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Her ...

star. Hydrogen becomes helium in the nuclear reaction that takes place within stars; when the hydrogen has been exhausted, the star moves on to another phase of its life and begins burning the helium.

\tau_ = \frac \times \mbox = \frac \times F

where M is the

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

of the star, X is the fraction of the star (by mass) that is composed of the fuel, L is the star's

luminosity Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a st ...

, Q is the energy released per mass of the fuel from

nuclear fusion Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles ( neutrons or protons). The difference in mass between the reactants and products is manifest ...

(the

chemical equation A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas. The reactant entities are given on the left-hand side and the product entities on the right-hand side with a plus sign between t ...

should be examined to get this value), and F is the fraction of the star where the fuel is burned (F is generally equal to .1 or so). As an example, the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

's nuclear time scale is approximately 10 billion years. Time scales {{star-stub