Stellar Homework #1

Remember to show all your work and to put your final answer for each question in the form of a complete English sentence!

 

 

1.    Look up masses and radii for the following objects and compute their average densities, in grams per cubic centimeter:

  • The Sun
  • A red giant with twice the Sun's mass and 100 times its radius
  • A neutron star with twice the mass of the Sun, but the radius of a city (10 km)

HINT: Problem 1 is a straightforward application of the Density formula. Example 1 on the density handout is especially relevant. You can confirm some of your answers in the text.

Given that one cubic centimeter is about a teaspoon, how many grams would a teaspoon of neutron star material weigh? Given that there are about 900,000 grams in a ton, how many tons does this teaspoon weigh?

Since one cubic centimeter occupies a volume of roughly one teaspoon, you answer for the density of a neutron star tells you exactly how many grams are in one cubic centimeter of neutron star stuff. You should then convert from grams to tons. When deciding whether to multiply or divide, ask yourself; should the number of tons be greater or smaller than the number of grams?

2.    Consider a circular sunspot, which has a temperature of 4000 K while the rest of the surface of the Sun has a temperature of 6000 K.

a) What is the wavelength of maximum emission of the sunspot?

HINT: This is once again an application of Wien's Law. It will tell us the "color" of the sunspot.

b) Compare the luminosity of this sunspot to that of a section of the Sun with the same area

HINT: Here we use the Luminosity formula. Remember to show all your work!

     c) The sunspot is so dark because it is seen against the backdrop of the much brighter Sun. Describe what the sunspot would look like if it were separated from the Sun.

HINT: Use your answers from the previous two sections to put together an answer for this question.

     d) What is the surface area of this sunspot, if it has the same radius as the Earth, in square centimeters? What is the area of a light bulb whose filament is 2 cm in radius? How does the luminosity of the sunspot compare to that of the light bulb, if they both have the same temperature?

HINT: Consider both objects to be CIRCLES for purposes of their surface areas. Again we use the Luminosity formula.

3.    Each of the following objects gives off light, but the majority of their light is given off in a certain part of the spectrum, according to Wien's Law. What is the wavelength of this peak radiation, and what portion of the spectrum does it cover?

  • a star at about 30,000 K
  • the corona of the Sun, at about 2,000,000 K
  • the surface of our skin, at about 297 K
  • the Sun, at about 6000K

HINT: Problem 3 is a straightforward application of Wien's Law. Use the temperature to compute values of lambda-max, and use the electromagnetic spectrum in your book to determine the wavelength region. Remember that 1 Angstrom = 10-10 meters!

 
 
Updated 5/22/02
By James E. Heath
  
 
 
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