### Assignments:

Unfinished Assignment Study Questions for Lesson 41

### Lesson Objectives:

- Luminosity
- Measuring distance using stellar parallax
- Stellar temperatures
- Stellar masses There are three fundamental properties of a star that astronomers seek to measure: luminosity, temperature, and mass.

The apparent brightness of a star -- how bright it looks in our sky -- is based on its luminosity (the amount of light a star actually emits) and its distance.

The inverse square law for light tells us the relationship between distance, luminosity, and apparent brightness. It states that the apparent brightness of a light source declines according to an inverse square law, so if we look at the Sun from twice the Earth's distance, its apparent brightness would be dimmed by a factor of 4, and if we look at it from three times the distance, its apparent brightness would dim by a factor of 9.

The apparent brightness of a star is determined by measuring the amount of light per square meter we receive from the star. Then if we know its distance, we can use the inverse square law to calculate its luminosity, or if we know its luminosity, we can calculate its distance. We have learned about stellar parallax before. It refers to the small shifts in a star's annual position when we look at it from different positions in Earth's orbit around the Sun.

By measuring the angle of this change when we observe the star, we get its parallax angle. Stars that are further away will appear to shift less, so their parallax angles will be smaller. If we measure this angle in arcseconds, then 1 divided by this angle will give us the distance of the star in parsecs.

For example, if a star has a stellar parallax angle of one-tenths of an arcsecond, then its distance will be 10 parsecs. A parsec is 3.26 light-years, so 10 parsecs would be 32.6 light years. Our Sun falls roughly in the middle when it comes to the luminosities of stars. There are stars that are much dimmer, such as Proxima Centauri, whose luminosity is a tiny fraction of our Sun's. Meanwhile, the brightest stars can be as much as a million times as luminous as our Sun.

Dim stars appear to be more common than bright stars, so even though there are stars that are much brighter than our Sun, the vast majority of stars are dimmer. In addition to luminosity, astronomers seek to determine a star's surface temperature.

As we learned previously, a star's temperature can be determined by looking at its color. A cooler star looks red because it emits a lot more red light than blue light while a hotter star emits more blue light than red light and looks blue.

A star's spectrum can also be used to determine its surface temperature. When using spectral lines to determine temperature, scientists classify a star by spectral type, ranging from hottest to coolest -- O, B, A, F, G, K, and M.

Cool, red stars of spectral type M are much more common than hot, blue stars of spectral type O. The third fundamental property of a star is its mass, and is generally more difficult to measure than its surface temperature or luminosity.

The most dependable method for determining a star's mass is using Newton's version of Kepler's third law. This law requires us to be able to observe one object orbiting another, so for stars, it is generally only used to measure masses in binary star systems -- systems in which two stars orbit each other. Fortunately, about half of all stars appear to be members of binary star systems.