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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 with the help of models,
which may be simple equations,
charts reflecting many observed stars,
or elaborate simulations of stellar processes.
Through chains of such determinations,
many such parameters can often
be determined or approximated.

In some cases even when a parameter cannot be fully determined, a probability distribution of its values can be through statistically-based 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.
- interferometry and parallax, to measure the radius of nearby giant stars.
- spectroscopy - effective temperature (black-body radiation) curve and qualitative indication of their makeup.

Less direct methods:

- luminosity, apparent magnitude, and distance are interrelated such that with any two, you have the third.
- luminosity, radius and temperature are similarly interrelated.
- 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 speeds.
- eclipsing binary reveals viewing angle.
- orbital speed over time reveals the orbit size.
- ratio of orbital speeds reveals ratio of masses.
- ratio of orbital speeds and viewing angle reveals actual orbital velocities.
- orbital size and period determine sum of masses, such that with any two, you have the third.
- period and distance determine orbital size, such that 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".

https://www.astro.up.pt/investigacao/conferencias/toe2014/files/bsmalley.pdf

ATLAS Stellar Model

binary star

H3 Survey (H3)

mass-radius relation

stellar kinematics