Astronomy 201  Fall'07  Problem Set 7

The four problems below cover material in Chapter 17.  These should be worked out and turned in on Thursday -- in class (preferably) but not later than 5pm.

(They are based on Probs 49, 50, 52, & 54, respectively, in Ch. 17 of the text)

The basic skills and definitions quiz for Chapter 17 is posted on MasteringAstronomy.com and should be taken (as assignment 7) no later than 11pm on the evening of the 1st.

7-1: Roasting the Earth.  During its final days as a red giant, the Sun will reach a peak luminosity of about 3,000L(Sun).  Then the Earth will absorb ~3000 more times more energy than now and therefore will have to radiate ~3000 times more energy per unit surface area than now.  So calculate the estimated surface temperature of the Earth necessary to do this (assume the Earth's size does not change and look at MI15.5)

7-2:  Supernova Betelgeuse.  The red supergiant star Betelgeuse (in the constellation of Orion) is 427 light year distant.  Currently the brightest star in the sky is Sirius, which has a luminosity of 26L(Sun) and a distance of 26 light years. 

(a) How much brighter than Sirius (i.e. by what factor or ratio) would the SN Betelgeuse appear in the sky if its luminosity increases to 10¹⁰L(Sun) at the peak of the supernova?

(b) If the apparent magnitude of Sirius is m = -1.6, what would be the apparent magnitude of SN Betelgeuse at maximum brightness?

(c) Would SN Betelgeuse be brighter than Venus at max brightness (m = -3.3)?  …brighter than the full moon (m = -13.6)?

7-3:  Expansion of the Crab Nebula.  Astrometric measurements of the Crab Nebula filaments show that the fartherest are now 100 arc seconds from the center of the nebula and are moving away from the center at about 0.11 arcseconds per year. 

(a) Use this info to estimate the year that the supernova ejected the filaments (traceback time) assuming constant motion over time.

(b) Compare this with the known date of the Crab supernova.

(c ) Based on (a) and (b), are the filaments accelerating or decelerating since being ejected?

7-4:  Speed of Supernova Debris.  In February 2001 (14.0 years after the event) the radius of the inner ring of SN1987A was measured to be 0.7 light year.

(a) Compute the speed of the debris that was seen hitting the inner ring around SN 1987A measured in February 2001.

(b) How does this speed compare with the speed of light?  Are you surprised?

ANNOUNCEMENT!

For you observing project fans, this is the week to observe.  The observatory will be open starting at 8pm local Mon-Fri nights and the brightest comet in two decades has flared up in the sky near the constellation Perseus, so c'mon over!  Also, Tuesday we will take a vote in class if there is interest in doing a 5AM morning session Thursday morning to view Saturn, Venus, Mars, the moon, and the comet as well (almost circumpolar) -- comet fans should check out: http://www.skyandtelescope.com/observing/home/10775326.html