Luminosity: distance combined with apparent brightness

Distance: trigonometric parallax

Temperature: either from colors (and blackbody laws) or more detailed spectra

Diameter: Luminosity combined with temperature

Mass: Binary star orbits and Kepler's Laws

Composition: Spectra

Because the distances are so large, we use special units:

light years = 10¹⁶ meters or parsecs = 3.26 light years = 3.086x10¹⁶meters

We will quote distances in parsecs, abbreviated as pc,  for much of the rest of the course; for really large distances we will use a unit of kpc (kiloparsecs - 1000pc) or Mpc (megaparsecs - 1,000,000pc).

The only direct way to measure stellar distances is through parallaxes - the change in direction toward a nearby star due to our change in position as the earth goes around its orbit. See how the parallax is reduced when the distance of the star increases in this animation. Animation by R. Pogge, http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/parallax.html).

After Kepler and Newton, it was obvious that parallax should be observable, but it was still nearly two centuries before a stellar parallax was first measured -- by Bessel in 1838. The problem was that the stars are so distant that parallax is very small and difficult to measure.

Bessel selected a star with a large proper motion because he reasoned that it would be likely to be near the solar system. The stars are all moving rapidly through space. Why is this motion only apparent for nearby ones? Although these two stars are moving at the same speed, notice how the nearer one appears to the astronomer to have gone much further in the same time.(animation by G. Rieke)

See how proper motions change the Big Dipper over 200,000 years! (From R. Pogge, http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/proper.html)

The luminosity of a star is one of its fundamental parameters -- the luminosity is a direct measure of the rate at which nuclear fusion is proceeding in the star's core.

Luminosity, apparent brightness, and distance are linked through the radiation laws, so if we know any two we can compute the third - for example, if we can estimate the luminosity without knowing the distance and can measure the apparent brightness, we can calculate the distance.

Annie Jump Cannon developed the system of stellar classification used today and published the 9 volumes of the "Henry Draper Catalog" classifying 225,000 stars. She managed to maintain uniform criteria for this whole work!

Eclipsing binaries are pairs of stars whose orbits are aligned along our line of sight so that one passes in front of the other: They can provide a check on the computed sizes by measuring the duration of the eclipses and the stellar velocities. (Animation from R. Pogge, http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/eclbin.html)

For nearby, luminous (and hence large) stars, we can measure sizes directly with interferometers -- these cases provide the tests that the other methods are reliable.

are obtained from multiple star systems.

-- more than half of all stars are found in systems of several stars orbiting each other. Binary stars are systems with only two members.

Visual binaries -- both members can be seen and studied, orbits can be measured:

Here are Sirius A and B orbiting each other, from 1900 through 1970 (images from The Essential Cosmic Perspective, Bennett et al., animated by G. Rieke)

In both the examples to the left, the mass of the blue star is 3.6 times greater than of the red one. Animations from R. Pogge, http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/visbin.html)

By plotting the orbit and measuring the period, Kepler's Law can be used to determine the masses of the stars:

-- here P is the period of the orbits of the stars around each other, a is their separation, G is the gravitational constant, and their masses are M₁ and M₂ (technically this gives only the sum of the masses of the two stars but by making a few other measurements such as radial velocities the actual values can be determined).

Spectroscopic binaries are pairs too close together to be seen as separate stars, but whose spectral lines can be seen separately (and which move relative to each other as the stars move around their orbits):   The observer is measuring the system from the direction of the yellow dot to the far left. Animation from R. Pogge, http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.html)   By observing spectroscopic binaries, we have greatly increased the number of stars for which we have information on masses.

Since the stars were all in a nearby galaxy, they were all at very close to the same distance. Also, since they lay close together on the sky, the effects of dust in our galaxy were about the same for all, although there might still be problems with dust in the Magellanic Clouds (but in those days, the effects of dust were not well understood). Thus, apparent brightness was a valid measure of stellar luminosity. Hertzsprung and Leavitt had discovered a behavior of stars relating luminosity and temperature. The temperatures and luminosities are related in a specific way for most stars, as shown in the Hertzsprung-Russell, or H - R, diagram. Most stars lie along the main sequence that extends from the low luminosity, low temperature corner to the high luminosity, high temperature one.

Later, Henry Norris Russell plotted the luminosities and colors for all the stars for which adequate data existed and confirmed these patterns: stars are not found all over this diagram but only in a few regions:

(from http://csep10.phys.utk.edu/astr162/lect/sun/spectrum.html).

"Colors" referred to the differences in brightnesses at two different wavelengths (in this case, blue and visible). The colors provided an indication of stellar temperature. (from http://csep10.phys.utk.edu/astr162/lect/sun/spectrum.html).