1 ASTRONOMY 2290 Problem Set #4 September 29, 2009 due: October 7, 2009 Name 1. What does the term spectral signature mean? And why is it important? 2. Star A has a magnitude mA = 11 and star B has magnitude mB = 18.5. Which star is appears brighter in the sky and by what factor? 3. Suppose a star has 40 times the radius of the Sun but is 1/2 as hot (lower temperature). What is its luminosity compared to the Sun? 4. A star has a temperature of 2000 K. At what wavelength is it brightest (the peak flux)? Can you see photons at this wavelength with your eye?September 30, 2009 Problem Set #4 2 25. A star is located at a distance of 900 parsecs. Would it appear brighter or fainter if it were moved to a distance of 100 parsecs? By what factor? 6. Consider the energy level diagram at right (note – this is not the hydrogen atom). The numbers on the right represent the energy above the ground state for that level. List what will happen to each of the photons (listed below by their energy) that encounter the atom. The electron starts out in the ground state for each photon. 45 eV photon _____________ 30 eV photon _____________ 20 eV photon _____________ 12 eV photon _____________ Briefly explain your reasoning Now suppose two atoms have the energy levels as shown above. In atom A an electron goes from n = 4 to n = 3 while in atom B an electron goes from n = 3 to n = 2. Which atom emits the highest energy photon? 7. Suppose a star is known to have an absolute magnitude of -1. The apparent magnitude of the star is found to be 14. How far away is the star? 12340 eV12 eV20 eV24 eV40 eVSeptember 30, 2009 Problem Set #4 3 38. A type I Cepheid variable is found in the galaxy M100. It has a period of 10 days and the observed flux from the star is 3.2x10-13 ergs/cm2. a) What is the approximate luminosity of the star? b) How far away is the star in Mpc (Megaparsecs)? (Note that: 1 pc = 3x1018 cm, 1 Mpc = 106 pc, Lsun = 4x1033 ergs/sec) c) Suppose there was dust between us and the Cepheid which caused the flux we measured (as quoted above) to be dimmer by a factor of 4 than the real (undimmed) flux. Is the galaxy closer or further than you have calculated and by what factor? Briefly explain why. 102103104Luminosity (Lsun)0.3131030100Period (days)Type ICepheidsType IICepheidsRR Lyrae Stars CepheiSeptember 30, 2009 Problem Set #4 4 49. Two stars are observed to have an orbital period of 2 years. If their separation is 4 AU, what is the mass of the system? 10. Below is a sketch of the H-R diagram. Answer the questions appropriately. List the stars in order of hottest to coolest ________________ Which star is largest? _______ Which star(s) are on the main-sequence ________________ Which star is smallest? _______ Which star has the highest luminosity? ________________ Is star 4 or 5 larger _______ What kind of star is star 5? ________________ Is star 7 or 4 larger? _______ What kind of star is star 1? ________________ LuminosityO B A F G K M62 53 1