YOUR NAME: SHOW YOUR CALCULATION AND MOTIVATE YOUR ANSWERS EVERYWHERE EVEN WHERE IT DOES NOT EXPLICITLY SAYS TO.

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Abner Green
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1 Observational Astronomy / NYU, Fall 2013 FINAL YOUR NAME: SHOW YOUR CALCULATION AND MOTIVATE YOUR ANSWERS EVERYWHERE EVEN WHERE IT DOES NOT EXPLICITLY SAYS TO. FEEL FREE TO USE ANY PAPER SOURCE YOU HAVE WITH YOU AND ASK FOR CLARIFICATIONS IF ANYTHING IS CONFUSING. DO NOT USE THE INTERNET. IF WE SEE YOU BROWSING THE INTERNET YOU WILL HAVE 10 POINTS DEDUCTED FROM YOUR FINAL SCORE. EACH TIME WE CATCH YOU (there are only 70 points available. so ). YOU CAN USE YOUR PHONE AS A CALCULATOR, BUT IT WILL BE OBVIOUS IF YOU LINGER ON IT. BY DESIGN THERE ARE VERY FEW CALCULATIONS THAT REQUIRE A CALCULATOR. Write your name on each sheet. Read the exam through before starting. Label your final answer clearly. To obtain the maximum score you have to answer 14 out of the first 20 questions, and all of the last 5, multipart questions. Partial credit can be awarded for questions, so even if you cannot answer every part do answer whatever possible. On the last page are several useful constants and formulae. Look at them! you won t need

2 them all, but all those that you will need should be there. NAME: ANSWER 14 OF THE FIRST 20 QUESTIONS (2.5 points for each correct): 1) You are in NYC at a geographical latitude of 40 degrees. What is the altitude of the Celestial Equator? How do you know it? 2) What are the Equatorial coordinates of the North pole the Polar circles, both the Tropic of Cancer the Tropic of Capricorn What is the definition of polar caps and tropics? 3) What is the rotation period of the Moon, and what is its (sidereal) orbital period? What does the relationship between these two periods mean for an observer on the Earth? 4) The Cat s eye Nebula is a planetary nebula with apparent magnitude m=9.8. Its

6) The Crab nebula is a Supernova remnant from a Core Collapse supernova is it the one above left or above right?

3 absolute magnitude is M= 0.2. What is its distance? NAME: 5) The Snowball nebula is a protoplanetary nebula. Which one do you think it is: below left or below right? What created it, and what is the bright object in its center? 6) The Crab nebula is a Supernova remnant from a Core Collapse supernova is it the one above left or above right? It has a bright object in the center, but you cannot see it in visible wavelengths. Spaces telescopes such as Chandra can though. Why? What is it? 7) The center of our Galaxy is located on the sky at a right ascension of about 18h. On what night of the year does it transit at midnight? On what night at 11:30PM?

4 8) On March 15 at about 2am you notice an interesting star rising. Because of bad weather you don t get a chance to see the star again until June 15. Within 20 minutes, at what time does the star rise that night? 9) The angular size of the moon change throughout the moon s orbit from 29.3 arcmin to 34.1 arcmin. Derive the ellipticity of the moon s orbit. 10) Io is the most volcanic solar system object we know. What causes its tremendous volcanic activity?

5 11) Epsylon Lira is known as the Double Double star: a system of two pairs of visual binary stars. The separation between the two main components, Epsilon 1 and Epsilon 2 is 208. Each of those is itself a binary system: Epsilon 1 s components have a separation of 2.3 and Epsilon 2 s of 2.6. What size telescope do you need to observe both pair and resolve the components on the roof Gallatin? Would it be easier or harder to resolve them if you were observing in Infrared light? 12) What parameters of a planet can be derived from a transit, knowing the characteristics of the host star? What parameters can be derived from a radial velocity survey? What do we need to know in each case about the star and what technique is most helpful to find out the star characteristics? 13) What element will the core of an old M=12M sun star be made of? What happens in the final stages of its life?

14) A star has a mass of 0.54 Msun. How long will its main sequence life be? What will the main activity in its interior be during this time? Say that its color is observed to be blue.

6 14) A star has a mass of 0.54 Msun. How long will its main sequence life be? What will the main activity in its interior be during this time? Say that its color is observed to be blue. Draw where it is in the HR diagram below? What phase of its stellar life? (Put axis labels, and possibly ranges on the plot). 15) Two observations were enabled by the use of large (100 inch) telescopes in roughly the 1930 which change dramatically our ideas about cosmology and lead to the Big Bang theory (and are now two of the 4 observational pillars of Lambda CDM theory). Which are they?

7 16) In the course of the semester we got quite familiar with Vega, because early in the semester it was close to zenith at the beginning of the labs. Given this information, what, roughly, is its Declination? Explain how you know it. 17) Explain how a prism creates a rainbow. What acts as a prism in the sky to cause the meteorological rainbows? 18) What is the difference between a reflector and a refractor telescope? What are the pros of refractors? Sketch each one including lenses, objective and eyepiece, and showing the path of an incoming beam of light (coming at you from infinity).

8 19) During meteor showers we see a dramatic increase in the event rate of meteors ( shooting stars ). Explain briefly why. 20) What is the modern requirement for a theory to be a scientific theory? Give an example of a theory that satisfies this condition, and how, and of one that does not.

9 ANSWER ALL QUESTIONS BELOW (Up to 7 points each): 1) You are looking at the moon. You are using a telescope similar to those we used in the class, with an aperture of about 8 inches and a 1m focal length. With a 20mm eye piece you can fit in your field of view in the same pointing the Mare Imbrum and the Mare serenitatis, and no other lunar seas. What focal length eyepiece do you need to fit the entire face of the moon in your field of view? Now you want to observe a faint object. In your light conditions you can see stars as faint as Riegel B. You are really interested though in observing GK Orion s. GK Orion s variability has a 236 days period and you know tonight it is at its intermediate magnitude 10.2, and that it varies by 1.5 magnitudes. What size telescope should you buy to see GK through its variability cycle on the site from which you observe?

10 2) The mass of the luminous matter in the Milky Way is about 1 trillion Solar masses: M sun (which roughly means there are a trillion stars in it!). Assuming, although not true, that the milky is spherically symmetric. The escape velocity in this case is: for M = M sun. This is the velocity such that if you were at a distance r from the center, and were able to throw something, say an apple, at that speed away from the center of the galaxy, your apple would escape the Galaxy s gravity and be lost in Outer space. a) calculate the escape velocity for the Galaxy. b) If you were able to do this experiment, would you expect to in fact to see your apple escape the galaxy or not? Why or why not? If not, what other than luminous matter could keep it from getting lost in outer space?

11 3) What is the axial tilt of a planet that has no seasons? What are the declination of its polar circles and its tropics? There is one almost such planet in the solar system, which is it? Despite the lack of seasons its temperature is far from uniform. Why? Now describe, qualitatively, the seasonal and diurnal cycles of an exoplanets that is in the habitable zone of its star, which is a solar type star, and that is roughly earth size and mass, but that has an 89 degree axial tilt, like Uranus.

12 Would you expect this planet to be Habitable? NAME: 4) Orion is one of the most spectacular, amateur observer friendly views in the sky. It hosts Betelgeuse, a naked eye star, and the Orion nebula is possibly the only nebula that should be visible from Gallatin with a small telescope. The coordinates of Betelgeuse are 5h 55m 10.3s and 7deg 24m 25.4s. When should you have taken this class to maximize your probability of being able to observe it? Calculate its visibility window altogether, between the hours of 7pm and 6am. What is the earliest date at which Betelgeuse will rise within those hours? What is the latest?

13 5) You are servicing the Hubble space telescope with George Clooney (or Sandra Bullock if you prefer). A large field of debris is expanding from a point where a Chinese satellite is supposed to be. Using a Doppler radar, you measure the pieces farthest from the center of the debris field are moving the fastest. You can describe this with the "Rubble Law", and find that the value of the "Rubble Constant" is 3 x 10 3 km s 1 /lighthour. How long ago was the planet destroyed? (hint: help yourself by thinking about the units of the variables that you have, and of the variable you want to obtain!) How is this problem similar to the determination of the age of the Universe from the Hubble constant? How is it different? What would you get if you measured the speed of a piece of debris 2 light hours away

14 from the center? USEFUL CONSTANTS & FORMULAE: G=6.7x10 11 m 3 kg 1 s 2 c = 3.0x10 8 m s 2 H0 = 70 km s 1 /Mpc M sun = 2x10 30 kg radians to degree conversion: 180/π ~ 60 small angle approximation: θ = s/d (radians) F = G m1+m2 r 2 orbital period: T= 4π 2 /(G(M1+M2)) Keplerian orbit relation: T 2 /a 3 = constant constant motion: t = d x v (time = distance * velocity) orbital eccentricity: e = d/a Magnification: Fobjective/Feyepiece Resolution: θ = 1.22 λ D Power ~ πd 2 (proportional to) Surface of a sphere: 4πr 2 magnitudes: m1 m2 = 2.5 log 10 (F1/F2) (adding 2.5 magnitude for a 10 fold decrease in flux) Flux F ~ (D/r) 2 wave relations ν = c/λ Black Body: F ~ T 4 (proportional to) λ max ~ T 1 (proportional to)

15 distances: d = *D+1 z = ν/c z = λ obs λ emit. λ emit Main sequence life time: t=10gyr(msun/m) 2.5 > note that this was a power 2 in the notes. 2.5 is mode correct!

Now on to scales in the. Let s change scale by TWO orders of magnitude at a time and see what happens.

Now on to scales in the. Let s change scale by TWO orders of magnitude at a time and see what happens. Announcements Read 2.1 (Magnitude & Flux), 3.1, 3.2, 3.3 In-class Quiz #1 on Tuesday, January 29. Homework #2 due in class on Thursday, January 31. Disability Services is in need of a note taker for this