If our Sun (mass = 1.99××103030 kg, radius = 6.96××1088 m) were to collapse into a neutron star (an object composed of tightly packed neutrons with roughly the same density as neutrons within a nucleus, ρnucleusρnucleus = 2.3××101717 kg/m33), what would the new radius of our “neutron-sun” be?

The rest wavelength of the Hα transition of atomic hydrogen is 656.3 nm (recall that 1 nm=10-9 m). If an observer takes a spectrum of a distant galaxy and identifies that line at 920 nm, what is the redshift of the galaxy? (recall that z=(λobs-λem)/λem ) If the value of the Hubble constant is Ho=71 km/s/Mpc, what is the approximate distance to the galaxy in Mpc?

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…

a)Define the term “standard candle” as used in cosmology.  b)The flux is defined asf(Dlum) = L/4πD^2lumwhere L is the absolute luminosity and Dlum is the distance to the radiation source (youmay assume z ≪ 1).Assume that we have measured the flux to be f = 7.234 10^−23 Wm^−2 and the absoluteluminosity is given by L = 3.828 x10^26W. Calculate the luminosity distance D lum to the objectin Mpc.

What is the equation of the sphere with center (1, -2, 5) and radius 9? O (x +1)? + (y – 2)² + (z+5)² = 81 O (r – 1)? + (y + 2)² + (z – 5)² = 81 O x? +y? + z? = 81 O (r – 1)? + (y + 2)² + (z – 5)² = 9 O (r+1)? + (y – 2)² + (z+ 5)² = 9

Astronomers on a planet orbiting 1.500 AU from a star measure the irradiance at the top of their atmosphere as 1700 W/m?. Assume that the irradiance includes all types of radiation produced by the star and that it is emitted isotropically (same in all directions) by the star so that the inverse square law of irradiance can be applied. The current mass of the star is know to be twice the mass of our Sun and that 0.100% of its current mass will be available for hydrogen fusion to helium in the core of the star. What is the current rate of mass conversion in kg/s occurring in the core of the star? Given: 1 AU = 1.495978707 x 10"1 meters, M = 1.989 x 103° kg, c= 2.9979 x 10° m/s aun If the star continues to "burn" mass at this same rate, how long will it be in Earth years until the star runs out of hydrogen fuel in it's core?

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?

The churge deisity asphre of glvn काि hब ऊगर पु pc,@,¢)= Krcos (20) sind pus (oe (Kunstant) of the sphee कdड मिण्र नजय cos 2XSinxdx= Te(-4x+4Sin&x-5h 4x calulute the t p ot dipok manut may need the followilag intyoad you nou b. Find the leading exparsion af the potarial at points r away from term in the multipok the

Suppose you were to try to create a proton-antiproton pair by annihilation of two very high-energy gamma rays of the same wavelength heading toward each other. The proton and the anti-proton have the same masses, but opposite charges. What would be the minimum energy needed for each photon? (e = 1.60 × 10-19 C, m proton = 1.67 × 10-27 kg, c = 3.00 × 108 m/s) 939 MeV O1.022 MeV O 12.2 MeV O 1880 MeV

The photons that make up the cosmic microwave background were emitted about 380,000 years after the Big Bang. Today, 13.8billion years after the Big Bang, the wavelengths of these photons have been stretched by a factor of about 1100 since they were emitted because lengths in the expanding universe have increased by that same factor of about 1100. Consider a cubical region of empty space in today’s universe 1.00 m on a side, with a volume of 1.00 m3. What was the length s0 of each side and the volume V0 of this same cubical region 380,000 years after the Big Bang? s0 = ? m V0 = ? m^3 Today the average density of ordinary matter in the universe is about 2.4×10−27 kg/m3. What was the average density ?(rho)0 of ordinary matter at the time that the photons in the cosmic microwave background radiation were emitted? (rho)0 = ? kg/m^3