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?

The matter density in the Universe today is Pm = -27 kg m-3. What would 2.7 x 10 be the value of the density parameter, 2o, if the Hubble constant had the value Ho = 38 km/s/Mpc? Assume the Universe does not contain dark energy and choose the option below that best matches your answer. Select one: O a. 0.1 O b. 2. О с. 1. O d. 0.7 О е. 0.5

Please answer within 90 minutes.

Consider the following line element, ds^2 = −dt^2 + a^2 (t) (dx^2 + dy^2 ) + b^2 (t) dz^2 , where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.

Pretend that galaxies are spaced evenly, 7.0 Mpc apart, and the average mass of a galaxy is 1.0 ✕ 1011 M. What is the average density (in kg/m3) of matter in the universe? (Note: The volume of a sphere is 4/3pieR^3 and the mass of the sun is 2.0 ✕ 1030 kg.) ______ kg/m^3 Which model universe does this density value support? A: open B: flat C: closed

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

If a galaxy is 9.0 Mpc away from Earth and recedes at 510 km/s, what is H? What is the Hubble time?

Consider the following line element, ds² = -dt² + a² (t) (dx² + dy²) + b²(t) dz², where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.

I understand how we got 1.485*10^19, but where did 1.6*10^-19 come from?  Also what does that symbol before the E mean?

why is it difficult to measure the Hubble constant?