Title: Week 5 At Play in the Cosmos Assignment
Course: ASTRON103: The Evolving Universe: Stars, Galaxies, and Cosmology (001) DHH SU18 > Section: Week 5

Measuring Stellar Radii

This weeek, you're going to use Exploration Mode* in At Play in the Cosmos to measure the radii of selected stars. First, read the background info; then, undertake the tasks listed. Unlike previous weeks, your progress won't automatically be transmitted to the game servers (and thence to my grade book); instead, you'll have to make a file submission, as described below in the write-up section.

* Exploration Mode can be found at the bottom of the mission list in the main menu.

Background

At Play in the Cosmos provides the Small Angle tool for measuring the radii of stars. However, astronomers typically can't use this approach, because the stars are so distant that their angular sizes are too small to be measurable. Instead, astronomers calculate the radii of stars by using the Stefan-Boltzmann law for the relationship between energy radiated and temperature.

As discussed in Section 18.3 of the Astronomy textbook, the luminosity (L), surface area (A) and energy flux (F) of a star are related by

\(L = F \times A.\)

Since stars are spherical in shape, the surface area is related to the radius (R) via

\(A= 4\pi R^{2}.\)

Likewise, the temperature (T) and energy flux are related by the Stefan-Boltzmann law,

\(F= (5.67 \times10^{-8}) \, T^{4}\)

(see Section 5.2 of Astronomy).

Using these equations, the radius of the star can be measured in At Play in the Cosmos using the following steps:

- measure L using the Luminosity tool
- measure T using the Blackbody tool
- calculate F from T using the third equation above
- calculate A from L and F using the first equation above
- calculate R from A using the second equation above

Tasks

Apply the procedure outlined above to determine the radius of the following stars:

- Merope
- Polaris
- Kepler 62
- Canopus
- Zeta Ophiuci
- Wolf 359
- Bellatrix

By comparing the radius of the stars against the radius of the Sun, classify each of them as a main-sequence star or a giant/supergiant. (1pt each)

Which do you think is likely to be the youngest? And the oldest? Be sure to justify your answers. (3 pts)

Write-Up

Your final write-up should be as long as necessary (but typically 1 page or less), providing your answers to the questions given above. You don't have to show your working, but if you do it's easier to award partial credit for incorrect answers. Your write-up should be uploaded as a Microsoft Word (.doc, .docx) or Portable Document Format (.pdf) file.