Homework 13 Due Friday, April 2, 2004

  1. Kapteyn's star, named after the Dutch astronomer who found it, has a parallax angle of 0.255 arcsec. How far away is the star?

    2.  D = 1/p D = 1/.255 = 3.92 pc

  2. If a red star and a blue star both have the same radius and both are the same distance from the Earth, which one looks brighter in the night sky? Explain why.

    3. The blue star. The blue star is hotter. Because it is hotter and because both stars have the same radius, it is more luminous. The apparent brightness depends on both luminosity and distance. If both stars have the same distance, the more luminous star will be brighter.

  3. What are the most prominent absorption lines you would expect to find in the spectrum of a star with a surface temperature of (a) 35,000 K, (b) 2800 K, and (c) 5800 K (like the Sun)? Briefly describe why these stars have such different spectra even though they have essentially the same chemical composition.

    4. A hot star such as (a) has lines associated with ionized helium in its spectrum. A cool star such as (b) has lines associated with molecules such as TiO in its spectrum. The sun has lines associated with both neutral and ionized metals.

    Helium is a very tightly bound atom. In order for it to let go of an electron, it must be very hot. Hence we won't see ionized helium in a star's spectrum unless it is very hot. Molecules are rather fragile. They can only occur at relatively low temperatures. Hence we only see lines associated with molecules in cooler stars.

  4. Suppose that you want to determine the temperature, diameter, and luminosity of an isolated star (not a member of a binary system). Which of these physical quantities require you to know the distance to the star? Explain.

    You can get the temperature from the spectrum--you don't need the distance here. You need the distance (along with the apparent brightness) to get the luminosity. The radius is calculated from the luminosity--so you need the distance here too.

  5. How much dimmer does the Sun appear from Neptune than from Earth?

    b = L/4pD2
    bfrom Earth/bfrom Neptune = Lsun/4p(1 AU)2 / Lsun/4p(30 AU)2 = 302/12

    The Sun is 900x brighter when viewed from Earth than when viewed from Neptune OR

    The Sun is 1/900 as bright when viewed from Neptune than when viewed from Earth.