Name: unid: Foundations of Astronomy ASTR/PHYS Final Exam

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1 Name: unid: Physical Constants * Foundations of Astronomy ASTR/PHYS 2500 Final Exam Gravitational constant G x m 3 kg - 1 s - 2 Elementary charge e x C Vacuum permittivity ε x C 2 J - 1 m - 1 Electron Volt ev x J Speed of light in vacuum c x 10 8 m s - 1 Planck constant h x J s Reduced Planck constant h/2π x J s Boltzmann constant k x J K - 1 Stefan- Boltzmann constant σ SB x 10-8 J s - 1 m - 2 K - 4 Proton mass m p x kg Electron mass m e x kg Atomic mass unit u or amu x kg Mass of an iron atom m Fe x kg Astronomical Constants * Mass of Earth x kg Mass of Sun x kg Mass of Moon 7.36 x kg Equatorial radius of Earth 6378 km Mean radius of Earth 6371 km Equatorial radius of Sun x 10 5 km Equatorial radius of Moon 1737 km Mean density of Earth 5515 kg m - 3 Mean density of Sun 1408 kg m - 3 Mean density of Moon 3346 kg m - 3 Jupiter radius Mean Earth radii Jupiter mass Mean Earth masses Luminosity of Sun x W Effective temperature of Sun 5778 K Light- year x km Astronomical Unit x 10 8 km Parsec x km Length of solar day 24 hours = seconds Length of sidereal day 23hours 56 minutes = s Length of a year (Julian) x 10 8 s Possibly useful formulae a = 1/(1+z) V circ2 /r = a (uniform circ. motion) E = 1/2mv 2 GM/r z=(λ obs λ em )/λ em cz = Hd L Eddington ~ 3.3x10 12 L solar M BH /M M = 7.5 σ v 2 R/G

2 Give brief definitions/descriptions of the following: ii 1a. Galaxy type 1b. Eddington luminosity 1c. The distance ladder 1d. Hubble law 1e. Cosmic microwave background 1f. Large scale structure of the Universe 1g. Dark matter

3 iii 2. NASA s New Horizons mission will be arriving at Pluto this July (!). a. Pluto was discovered in 1930 as a dot drifing across the sky in photographs made with a telescope. Suppose that we were able to observe this dot from the location of the Sun, and suppose that the observed drift is the result of Pluto on a circular orbit. Then, if the angular speed of Pluto were 17 arcseconds per day (9.6x10-10 rad/s) as it drifted across the sky, then what is its orbital distance a from the Sun? [Hint: angular speed for a circular orbit is v/r. For the record, Pluto s orbit is modestly eccentric.] a [AU]: b. In 1978, Pluto was found to have a moon, Charon, which orbits on a circular path around Pluto every 6 days. If the distance between Pluto and Charon is 17,000 km, what is Pluto s mass as compared to the Earth? (you may neglect the mass of Charon in your calculation.) [Note: the size of the binary is a tiny fraction of the semimajor axis Pluto- Charon is a tiny target for a satellite!] Mass [M Earth ]: c. New Horizons is careening through the Solar System, after having a close encounter with Jupiter (gravity assist) to take it out to Pluto. Assuming that it is on a zero- energy (marginally [un]bound) orbit, how fast is the satellite traveling relative to the Sun as it nears Pluto if it is headed radially outward? v [km/s]: [Definitely do not run into anything during the drive- through!]

4 3. Below is a color- magnitude diagram of Globular Cluster M15, with apparent visual band magnitude V and B- V colors of its individual stars (Sandage 1970, ApJ, 162, 841). All magnitudes have been corrected for extinction and reddening using the values of E(B- V) and A V as indicated in the diagram (e.g., V 0 = V observed + A V [e.g., Ryden & Petereson, Ch. 16]). iv RR a. Time series data from RR Lyrae stars in M15 (stars nearest the symbol RR ) suggest that their absolute magnitudes in the V band are M V = Find the distance d to M15. d [kpc]: b. The dashed line shows the location of bright main sequence (MS) stars. Using the table on the right, estimate a minimum age for this cluster. age [Gyr]: c. A characteristic radius of M15 is R ~ 4.5 pc and the line- of- sight velocity dispersion of stars is σ v ~ 10.2 km/s (Dull et al ApJ 481, 281). Estimate the mass of M15 in solar units. [Hint: treat M15 as you would an elliptical galaxy] M [M ]: type B- V MS age (Gyr) <0.01 B5V A2V F2V F5V G5V K0V

5 v 4. The spectrum of quasar Q is shown above (Ellison 2000) a. From the observed Lyman- alpha emission line, what is the redshift z of this object? (The rest- frame wavelength of the Ly- α line is 1216 Angstroms [Å].) z: b. Find the value of the scale factor a at that redshift (in units where the present- day expansion factor is a = 1). a: c. Approximately how old was the universe when the light we receive was emitted from this object? [Hint: You may suppose that the Universe was matter- dominated since the big bang and that the scale factor a(t) = (t / 14 Gyr) 2/3, assuming as before that a = 1 today.] T (Gyr): d. What are the myriad absorption lines on the blue- shifted side of the broad Ly- α line?