Astronomy 201 Fall 2007 Problem Set 5

Due 5pm CST THURSDAY, October 18th

BUT the date/time for the Chs. 14+15 QUIZZES online in MasteringAstronomy.com is 11pm FRIDAY, October 19th

Turn in to the "Astr 201" maildrop to the left of the RSI office (HBH 202) or to the "IN" envelope to the right of Dr. Dufour's office door (HBH 346)

Do the four problems below related to material covered regarding the Sun and stars in Chapters 14 & (first part of )15.

5-1: Lifetime of the sun. Given the total mass of the Sun is about 2 X 10³⁰ kg, of which about 75% was hydrogen(H) when the sun formed, but only 13% of that ever gets fused in the core.

(a) Assuming the above, calculate the total mass of H available for fusion in the Sun.

(b) Using your result in (a) and given that the Sun fuses about 600 billion kg of H each second, calculate how long (in seconds and in years) this supply of H lasts if the fusion rate remains constant over time.

(c) Given the age of the solar system is now 4.6 billion years, how long in the future will the Sun continue to "shine" based on this (over-simplified) model?

5-2: The umbra of a sunspot has a temperature ~4,000 degrees Kelvin, while the surrounding photosphere has a temperature of ~5,800 degrees Kevin.

(a) Using Wien's Law (MI 5.2) calculate the wavelength peak in nanometers of the thermal emission (light) coming from the sunspot and from the surrounding photosphere.

(b) Now, looking at the wavelengths of hydrogen absorption lines on the continuous rainbow color spectrum of Figure 5.15(c), try to note (by interpolating between 486.1 nm and 656.3 nm) the colors corresponding to peak wavelengths found in (a) above. Is the color of sunspots redder or greener than that of the photosphere and do you think this difference would be noticeable to the eye?

(c) Now using the Stefan-Boltzman Law (also given in MI 5.2) calculate the RATIO of the energy per unit area (in watts/m²) given off on the surface of a sunspot compared to that given off by the surrounding photosphere. Given your result, are you surprised that sunspots appear "dark" compared to the photosphere?

5-3: The total energy of sunlight per unit area (which astronomers call the SOLAR FLUX "CONSTANT") at the Earth's surface is about 1,300 watts/m² (ignoring the absorption of light by the Earth's atmosphere!). The average distance of Jupiter from the sun is 5.2 AU. Use the inverse square law of light to calculate what the average solar flux would be on Jupiter's surface.

5-4: Two stars that are solar "clones" (i.e., identical to the Sun in all respects) have parallax angles of 0.250 arc seconds (star1) and 0.100 arc seconds (star2).

(a) Calculate the distances of the two stars in (i) parsecs, (ii) light years, and (iii) AU's.

(b) What would be the RATIO of fluxes (energy received per unit area) at the location of the Sun from the two stars (star1/star2)

(c) How much fainter (in magnitudes) would star2 be than star1 in the nighttime sky?

----------------------end of problem set 5------------------------------

WEB PROJECT AND/OR OBSERVING PROJECT SIGN-UP:

If you plan to do the web project AND/OR the observing project (one, two, or all three parts), indicate such below and turn into Dr. Dufour

during class no later than the Thursday 10/18 class.

NAME: _______________________________________(print please)

1. I plan to do the WEB PROJECT ________________(yes or no) [no maybe's!]

2. I plan to do the OBSERVING PROJECT ______________________(yes or no) [no maybe's!]

Campus Observatory Schedule: Mondays, Tuesdays, Wednesdays, and Thursdays (weather permitting) starting at

8pm in October (must get there before 8:30pm!)

7pm in November until Thanksgiving (must get there before 7:30pm!)

We will also have a few early morning (5AM!) Moon-Venus-Saturn-Mars viewing

sessions during the first week of November (announced in class)

[you likely will have to go on two separate nights to observe all five required objects]