1F03 Astronomy Problem Set 4
Friday Nov 26th, 2010 Please write your answers on a separate sheet including your working. 1. Escape velocity can be calculated by equating the kinetic energy G M m/R and solving for vesc .
1 2 2 m vesc
to the gravitational energy
a) What would be the escape velocity from a 1.6 solar mass Neutron star with a radius of 10 km? b) Calculate the escape velocity from an object that weighs 1 solar mass with a radius of 3 km. Comment on your answer what does it imply?
2. Calculate the total mass of the Galaxy lying within 20 kpc of the Galactic center if the rotational speed at that radius is 220 km/s. (Note: Be careful to convert to SI units before doing your calculation). Give the nal answer in solar masses.
3. Redshift, z , measures how much light has moved from its true wavlength to a longer observed wavelength due to motion away from the observer, z = (observed true )/true = v/c. As long as the redshift is not too high, you can directly convert velocity distance to using Hubbles law: v = H0 d. H0 is Hubbles constant and you can assume it has a value of 70 km/s/Mpc. Mpc is mega-parsec. a) Consider a distant Quasar with an absorption feature at 160 nm. If we think this is due to the Lyman alpha absorption line that is normally at 122 nm what is the redshift of the gas cloud that is producing the absorption line? b) Assuming Hubbles expansion law holds, how far away from the Milky Way is the gas cloud?
4. a) The Virgo cluster is observed to have a recessional velocity of 1250 km/s. Estimate the distance to the Virgo cluster using Hubbles Law, v = H0 d, with H0 = 70 km/s/Mpc. b) For H0 = 70 km/s/Mpc, the critical density of the universe is crit = 9 1027 kg/m3 . Assuming that the density of the universe is the critical density, calculate the mass contained in a sphere centred on the Virgo cluster and extending out to the Milky Way using the distance you just estimated. c) Calculate the escape velocity from the surface of this sphere.