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**Stellar parameters** such as their mass,
luminosity, radius, temperature,
metallicity, age, rotation period,
and distance can occasionally be determined directly,
but more values can be determined using models,
varying from simple equations to charts reflecting many observed stars,
and to simulations of stellar processes.
Through a chain of such determinations, many parameters
can be determined or approximated.

In some cases even when a parameter cannot be fully determined, a probability distribution of its values can be, which has value in studies of entire populations. For example, if the viewing angle of a binary system's orbit is undetermined, the distribution of viewing angles is known so data from a population of such binary systems still reveals information about the distribution of parameters that the viewing angle would have revealed.

The most direct methods:

- parallax - triangulation to measure the distance to nearby stars.
- astrometry - to measure the radius of nearby giants.
- spectroscopy - effective temperature (black-body radiation) curve and qualitative indication of their makeup.

Less direct methods:

- luminosity is apparent magnitude "times" distance (with any two, you have the third).
- luminosity, radius and temperature are related (with any two, you have the third).
- H-R diagram and spectrum shows temperature, and approximate radius, mass, and luminosity.
- photometry gives an approximate temperature, which relates radius to luminosity.

Binary stars observed over time reveal much:

- visual binary - allows the orbital period to be determined.
- visual binary and astrometry give the orbit size if the distance is known.
- spectroscopic binary - shows the orbital period and ratio of masses.
- double-line spectroscopic binary - reveals the ratio of orbital velocities.
- eclipsing binary reveals viewing angle.
- orbital velocity over time reveals the orbit size.
- ratio of orbital velocities reveals ratio of masses.
- ratio of orbital velocities and viewing angle reveals actual orbital velocities.
- orbital size and period determine sum of masses (with any two, you have the third).
- period and distance determine orbital size (with any two, you have the third).
- eclipsing binary reveals individual spectra.

See "stellar distance determination", "stellar mass determination", "stellar radius determination", "stellar luminosity determination", "stellar temperature determination", "stellar age determination", "stellar rotation", and "gyrochronology".

ATLAS Stellar Model

binary star

mass-radius relation