Astronomy 201, Fall’07

 

Problem Set 3 – More Skinny Triangle and Chapter 5 on Light

 

Work out the four problems below and turn in on paper by 5pm Thursday, September 27^th (turn in during class, or to Dr. Dufour’s office 346 HBH, or put in the Astr 201/202 mail slot under the mailboxes near HBH 202…your choice!).  There will be the usual problem solving recitation on these at 7pm Wednesday, 9/26, at HBH 254.

 

Note that we will postpone coverage of Chapter S2 until after the first exam on 10/4 (a revised syllabus will be given out on 10/02).  Instead, we will cover Telescopes (Chapter 6) immediately following Chapter 5 (Light and Matter).  The first exam will be in class on Thursday, October 4^th, as per the syllabus, but will only cover material in Chapters 1-6 and S1 (not including S2!).

 

Since coverage of Chapter 6 material will not be finished until class on 9/27, the due date for the BS/D quiz on MasteringAstronomy.com is extended to 9/28.  A short problem set on Ch. 6 will be assigned on 9/27 due to be handed in during the in-class exam on 10/4.

 

Problems(put answers in scientific notation with three significant digits (e.g., 1.23 X 10⁵):

 

3-1. The skinny triangle says simply that the angular diameter (Ang) in radians (where 1 radian = 57.3 degrees = 206265 arc seconds) subtended by an object of size D at a distance d (both D and d must be in the same length units) is given by the equation:

 

                                     Ang(radians) = D / d.

 

(a) The angular diameter of the sun and moon in the sky is about 0.5 degrees; what is this in radians? 

(b) The average distance of the sun is 1AU (= 1.50 X 10⁸ km); calculate its diameter in km.

(c)The diameter of the moon is about 3500 km; calculate its average distance in km.

 

3-2. KTRU broadcasts in the FM band at a frequency of 91.7 MHz (megahertz) from an antenna (near Humble, TX!) with 50,000 watts power.

(a) Calculate the wavelength in nanometers of waves/photons that KTRU puts out.

(b) Calculate the energy in joules of each of these photons.

(c)  How many of these photons per second are emitted by KTRU’s antenna?

 

3.3. The sun has a surface temperature of about 5800 degrees Kelvin.

(a) At what wavelength (in nanometers) is the peak of its thermal radiation spectrum?

(b) Calculate the total emitted power per square meter of the sun’s surface (in watts).

(c) Given the result above in (b), what is the surface area of the sun (in square meters) that emits the same power as KTRU’s antenna?

 

3-4. Red traffic lights emit at a peak wavelength of about 630 nanometers, yellow peaks around 550 nm, and green about 500 nm.

(a) Calculate the speed in km/s you would have to drive towards a traffic light to shift the colors from (i) red to yellow and (ii) red to green.

(b) Convert these from km/s to miles per hour!

(c) If you were caught running a red light by one of Houston’s famous red-light cameras because you were driving so fast through it that the light’s color was shifted from red to yellow and the fine was $10 per mph over the 30mph speed limit, how much $ would you owe the City of Houston?  (Moral: don’t try to protest this ticket to any judge who knows astronomy!)