The geometry of spacetime in the Universe on large scales is determined by the mean energy density of the matter in the Universe, ρ. The critical density of the Universe is denoted by ρ0 and can be used to define the parameter Ω0 = ρ/ρ0. Describe the geometry of space when: (i) Ω0 < 1; (ii) Ω0 = 1; (iii) Ω0 > 1. Explain how measurements of the angular sizes of the hot- and cold-spots in the CMB projected on the sky can inform us about the geometry of spacetime in our Universe. What do measurements of these angular sizes by the WMAP and PLANCK satellites tell us about the value of Ω0?

Is the Maxwell - Boltzmann distribution consistent with the following statements? Explain it briefly. a) The most populated quantum levels are always those with the lowest energy. b) Among all energy levels, the particles are distributed equally. c) All microstates are equally probable.

Use Wien's Law to calculate the peak wavelength of light coming from the Sun. Assume T=5800 K for the surface temperature of the Sun. Wein's displacement law says that the blackbody temperature and peak wavelength multiplied together give a constant of 0.29 cm-K. (K is degrees Kelvin).   Convert the wavelength from part A into a frequency. The product of wavelength and frequency for electromagnetic radiation is a constant, the speed of light (c), 3 x 10^10 cm/s.

The radio galaxy Cygnus A possesses a lobe of plasma that is detected by both radio and X-ray observatories. The temperature of the X-ray-emitting plasma is 4 keV and the number density of the particles in the plasma is 4x103 m-3. Assume that the plasma is composed solely of completely ionized hydrogen, so the number densities of protons and electrons per cubic meter are identical. * the given number density of particles corresponds to the number density of hydrogen nuclei, so you can safely assume that the number density of electrons is equivalent to this number density a) Compute the collision frequency in Hertz between electrons and ions in the plasma. b) Compute the Debye wavelength in meters of the plasma. c) Compute the plasma parameter of the plasma.

What is the rate of thermal radiation Emitted from a star with a radius of 2.310 x 10⁹m and a surface temperature of 8,420k? Assume that the spherical surface behaves as blackbody radiator .

In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5 km, and it has an average density of 1.4x10^3 kg/m^3. The diameter of the moon is 2.16x10^3 miles.

4. A binary system is composed of two identical stars orbiting each other with some period To. a) Now imagine scaling all lengths (separation between the stars and the radius of the stars) by a factor k, but keeping the density of the stars the same. By what factor does the period change? b) Now instead of scaling the lengths, scale the density by k (i.e. p → kx p). By what factor does the period change?

The Planck time is the unique interval of time that can be built out of G, c, and h.  Some physicists think that time intervals shorter than the Planck time have no meaning.  Using G = 6.7 x 10-11 kg-1 m3 s-2, c = 3 x 108 m s-1, and h = 6.6 x 10-34 kg m2 s-1, calculate the Planck time, in units of 10-43 s.

The radio galaxy Cygnus A possesses a lobe of plasma that is detected by both radio and X-ray observatories. The temperature of the X-ray-emitting plasma is 4 keV and the number density of the particles in the plasma is 4x103 m-3. Assume that the plasma is composed solely of completely ionized hydrogen, so the number densities of protons and electrons per cubic meter are identical. * the given number density of particles corresponds to the number density of hydrogen nuclei, so you can safely assume that the number density of electrons is equivalent to this number density a) Compute the temperature of the plasma in Kelvin. b) Using the calculated temperature for the plasma, compute the mean velocity in meters per second of an electron within the plasma. c) Compute the Coulomb cross section in square meters for a collision between an electron and a proton in the plasma.

For a circular velocity profile of the type Θ(r)=αr3/10Θ(�)=��3/10, where α� is a constant and r� is the radial distance from the centre of a spiral galaxy, find the ratio κ(r)/Ω(r)�(�)/Ω(�), where κ(r)�(�) is the epicyclic frequency and Ω(r)Ω(�) is the angular velocity. Enter your answer to 2 decimal places.