Wk08-Scaling_Relations_Activity_avaiceman

Student Name: Lab TA: Group Members: Astronomy 1101 Scaling Relations Activity Part 1: Remembering Parallax and the Inverse Square Law of Light As we get deeper into stars it is useful to remember the concepts we have used to get here. These ideas help us to go deeper into the Universe building on themselves. It’s been a while since we have done Parallax but let’s review it and also see how Parallax and the Apparent Brightness of light are different. Parallax Formula : D = 1 / P where P is the parallax angle and D is the distance. If P is measured in arcseconds, the distance D has units of parsecs (pc). Inverse Square Law : Brightness = Luminosity / ( 4 π d 2 ) The star Betelgeuse is 3 times more distant than the star Achernar, but has about the same apparent brightness. 1. Based on the information above, how does the parallax angle of Betelgeuse compare to that of Achernar? Start by figuring out which one should be larger, then figure out by how much. D=1/p Parallax angel of Betelgeuse is 3 times smaller than that of Achernar. 2. How does the luminosity of Betelgeuse compare to the Luminosity of Achernar? (Always show your work or explain your answer!) B=L/ ( 4 π d 2 ) Luminosity of Betelgeuse is 9 times less than Achernar. For the next question you do not have to show your work, but you should still set up the problem and have an answer that makes sense. These are directly related to the idea of having a habitable zone which needs a certain amount of energy from the host star for water to be liquid. 1

3. Compared to its current appearance on Earth, how bright would the Sun appear when viewed from… a. half of Earth’s current distance from the Sun? The sun would be 2 times as bright. b. 5 times Earth’s current distance from the Sun (close to Jupiter’s orbit)? The sun would be 25 times dimmer. c. the (average) orbital distance of Pluto at 40 AU? The sun would be 1600 times dimmer. Part 2: Luminosity, Temperature, and Area Breaking down the Luminosity Equation into its parts, L = 4 π R 2 σ T 4 , We can write in words what each of the following terms are. Look at the term as a whole, not as individual values. When we compare objects relative to the Sun then σ , 4, and  divide out. a. 4 π R 2 – Surface Area (m 2 ) of a sphere b. L – Luminosity (Watts) c. T – Temperature (Kelvin) d. σ – Stefan-Boltzmann constant . A physical constant like G in the gravity equation. 4. Using the Luminosity Equation above, we are going to take the ratio of L star to L sun . Write down the complete equation for the star’s luminosity below and simplify by dividing out all of the common terms (like  ) to get a relation that involves only those quantities that can change, such as L, R, and T. Make sure that subscript labels indicate the object to which a quantity belongs (i.e. R star is the radius of a star, as you can see R sun is the radius of the Sun). Because we’ve made a formula that takes out all of the constants, we can more clearly see how luminosity changes when we change those quantities that can change. We call such formulae scaling relations . DO NOT use numerical values to answer this question. 2