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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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 Spring '11
 wadsley
 Astronomy

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