Astronomy 1F03 Problem Set 4 Friday Dec 2nd, 2011 Please write your answers on a separate sheet including your working. 1. Escape velocity can be calculated by equating the kinetic energy 1 2 mv 2 esc to the gravitational energy GM m/R and solving for v esc . a) What would be the escape velocity from a 1.8 solar mass Neutron star with a radius of 10 km? b) Calculate the escape velocity from the same object when compressed to a radius of 5.4 km. c) Comment on your answer to part b – what does it imply? 2. Calculate the total mass of the Galaxy foundq within 10 kpc of the Galactic center if the orbital speed at that radius is 210 km/s. Start by recalling that Newton’s Laws imply that body in a stable circular orbit has an orbital velocity v 2 /r = GM/R 2 . (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,
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