Physics Problem Set 2

Problem sex 2 (1) Siring a) if Flax = 1.2 x 10^-4 erg/cm² sec From inverse square law F = L / 4πR² we solve R = √(L/4πF) = √(3.83 x 10^33 erg/sec / 4π x 1.2 x 10^-4 erg/cm² sec) R = 1.57 x 10^18 cm = 1.68 light years b) since 1 parsec = 3.26 light years This value for R is 0.515 parsec so parallax p = 1/p = 1 / 0.515 parsec = 1.94 sec c) actual parallax p = 0.38 sec D = 1/p = 1 / 0.38 = 2.63 pc = 8.12 x 10^18 cm = 8.58 light years From Inverse square Law d) now that we know how far away Sirius is we can find its Luminosity From the inverse square law F = L / 4πR² L = 4πR²F = 9.94 x 10^34 erg/sec ~ 1.2 x 10^-4 g/cm² sec 8.12 x 10^18 cm Lsirius / Lsun is 9.94 x 10^34 / 3.83 x 10^33 = 26 (2) Small angle Formulae 3 θ (degrees) θ (radians) Tan (θ) Sin (θ) Cos (θ) 2 3.491102 3.47E-2 3.49E-2 0.997 15 0.262 0.268 0.259 0.766 40 0.678 0.839 0.643 0.766 89 1.55 57.3 1.75x12 - degrees 57.3 Calculator clearly cos(θ) does not equal 1 when θ = 15 042 on the other hand, both sin θ and tan θ do. As θ gets bigger, both sin θ = tan θ = θ become more and more accurate (3) Faint lights <=> 8 miles is 1.29 x 10^6 cm = R at this distance bulb has 2 100 w Flux = L/4πR² = 4.80 x 10^-5 erg/cm²-sec: this is my minimum. MINIMM still -14二 6) with 7= 44 R2 4 Calculate R= 8.92 x 10 10 R= 47 12-14 cm = 554 thousand miles -S the Moon is 384 thousand tm [237 thousand miles) quay - which is closer than this limiting disYZACE yes the telescape could detay light bulb the (4) Estimations There is no "right answer" to these questions. Here are one way to approach them. (A) I estimate that I walk about 4 miles per hour, and that I can keep this up for 8 hours per day. I also estimate that I could do this more or less steadily, except for one day of rest each week. In this case I can walk 32 miles per day, or (6)(32)=192 miles per week. The end of the semester is about 9 weeks away right now (depending on exactly when "now" is) so this means I could walk about (192)(9)=1728 miles before the end of the semester. I am not sure of the details of this result, but it is not wildly inaccurate. In particular, I am sure that there is no way I could walk to Los Angeles before the end of the semester. Google says that the distance from Boston (that's pretty close to Amherst) to Los Angeles is 2605 miles. In order for me to get across the country before the end of the semester I would have to walk (2605)/(1728)=1.5 times faster, which is too much for me! But maybe you could do it. (B) The distance to the Sun is 1 A. U. = 1.5 X 10 13 cm = 93 million miles. Suppose you drove at a good speed, say 80 miles per hour (no traffic cops in space). If you kept this up for 8 hours per day, six days per week you would travel (80)(8)(6)=3840 miles each week = (3840)(52) = 2.0 X 105 miles per year. If you are about 20 years old now and will live to an age of 90, you have 70 years left of driving. In this time you will cover (70) (2.0 X 105)=14 million miles, which is a lot less than the distance to the sun. Here, too, I am not sure of the precise numbers. On the other hand, in order to reach the sun before you die you would have to travel 93 million/14 million = 6.6 times farther per week that my estimates: this means driving at (6.6)(80)=528 miles per hour! So I am sure of this conclusion. (C) The distance to alpha centauri is D-1/P=1/(3/4) = 1.33 parsecs, or 4.10 X 10 18 cm. Let's find the speed of the spacecraft. This speed is the distance it travels divided by the time it takes to travel that distance. Distance: The Earth is 1 A.U. from the Sun. Pluto (Google or Appendix F of the textbook) is 39.4 Au from the sun. So to get to Pluto New Horizons will travel 38.4 A. U. 5.74 X 10 14 cm. Time: the spacecraft requires 2015-2006 = 9 years = (9)(365)(24)(60)(60) = 2.84 X 108 seconds to get there. So the spacecraft's speed is (5.74 X 10 14 cm)/(2.84 X 108 seconds) = 2.02 X 10 cm/sec. So the time required for it to get to alpha centauri would be Time (4.1 X 10 18 cm)/(2.02 X 106 cm/sec) = 2.03 X 10 12 seconds = 64,400 years. NO: it won't get there before we all die.