The relationship between the average luminosity and pulsation period for Cepheid variable stars can be written L = L⊙P3.7, where the period P is measured in days. A cepheid variable is observed in a distant galaxy, and is determined to have a pulsation period of 50 days. The average flux received from this star is measured to be 2.14×10−16Wm−2. Determine the distance to the galaxy and express your answer in units of Mpc.

A cloud of gas has a temperature of 5,000 K. Estimate the width of the hydrogen H-alpha line with an intrinsic wavelength λ = 656 nm. (Note: the typical velocity of hydrogen atoms in a gas with temperature T is about (kT/mH)1/2, where k is Boltzmann constant and mH is the mass of a hydrogen atom, which is approximately the mass of a proton).

Show work. For the following: A parsec is a distance equal to 3.26 light years. The speed of light is 2.998 x 10°m/s. A nght year is a unit of distance equal to the distance light travels in one year. The brightest star in the night sky is Sirius, (Not the radio station) is 2.63 parsecs away. (1km30.621miles, 365d-1yr) How many miles away is this star?

An object was discovered on Feb. 24.37 UT (position R.A. = 5h35m.8, Decl. = -69 18'), obtained m = 4.8 on Feb. 24.454 UT. This object proved to be the most famous supernova (SN) in the 20th Century and the brightest visible from Earth since 1604. It is classified as a SN of the type Il in the Large Magellanic Cloud (SN1987A). Its brightness peaked in May 1987, with an apparent magnitude of m = 2.8. a) Find the absolute magnitude M of the SN1987A at maximum. Distance of the LMC is 51,400 pc. b) The progenitor (before SN explosion) star was a blue supergiant of the apparent magnitude m = 12.8. How much brighter (in terms of flux density) this SN was at maximum compared to the progenitor star. Find the ratio FSN/ Ebetore

What is the lifetime on the main sequence of a star whose surface temperature is 6500° K and whose radius is 2 X 109 m ? ( LS=3.826 X 1026 J/s)

a) b) Electron degeneracy pressure in a white dwarf star, of uniform density p, in the nonrela- tivistic case is given by Pwd ħ² 3memp 25/305/3 where symbols have their usual meanings. Using the result that the central pressure in a star, of radius R and uniform density, under gravitational attraction is given by Pc = Gp² R², derive an expression for the radius Rwd of a white dwarf in terms of its mass M, in the case of nonrelativistic electron degeneracy. Using your result, briefly discuss the limitations of your expression for the radius, in the context of white dwarfs of increasing mass. Consider a white dwarf, mass M, radius Rwd and temperature T, consisting entirely of helium nuclei and electrons. Show that the internal thermal energy of the ions alone is given by 3 M Eth= -kT, 8 mp where mp is the proton mass. White dwarfs initially have a very high temperature when they form, and then cool by radi- ation. Derive a differential equation for the rate of change of the temperature…

The typical core-collapse supernova has an energy budget of about 1046 J. This energy comes from the gravitational potential energy of an inner core with mass Mic, which collapses from an initial radius of 5 x 106 m down to the final radius of 50 km. Estimate Mic, in solar masses, for this to be a realistic energy source of the core-collapse supernova. You may assume that the density before the collapse is uniform. Discuss briefly how a Type la supernova is different from a core-collapse supernova from a massive star?

If a binary star system has a 0.1M⊙ star and a 10.0M⊙ star with a measured periastron and apastron of 40 and 80 AUs, respectively, calculate the orbital period in years of the binary star system. Be sure to show all work!

Which of the following is a true statement? A smaller diameter star can never have a smaller number for its apparent magnitude than a larger star. Two stars with the same diameter and effective surface temperature will necessarily have the same absolute magnitude as well. Aristotle was the first person to detect stellar parallax. All G2 stars necessarily have the same absolute magnitude.

Approximate values of length (in meters) 107 Diameter of Earth 1011 Distance from Earth to Sun 1016 Distance traveled by light in one year 1021 Diameter of the Milky Way Galaxy 1022 Distance from Earth to the nearest galaxy 1025 Distance from Earth to the edge of the known universe