1)
Estimate the mass distribution of the galaxy with rotation as given in the plot
(below) of rotation speed
v
versus
R,
the
distance from the centre of the galaxy.
(a)
Compute the mass at 6 points, R=2, 5, 10, 15, 20, and 25 kpc from estimates of the
rotation speed in the given plot.
(b)
Make a plot of log
10
(mass), on the yaxis, versus
log
10
(R) from the centre of this galaxy.
In class it was shown that the circular rotation velocity
v
for material in orbit around the
centre of the galaxy is
v
2
GM
R
R
where
G
is the gravitational constant and
M
R
is the mass interior to a point a distance
R
from the center. The textbook has a similar equation in an example.
If the mass in the galaxy is distributed in a spherically symmetric fashion with a density
distribution that goes like
1
R
then the mass distribution will look like
M
R
R
3
The average slope of your plot will be 3 –
.
might be for this galaxy. (Marks: 4)
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 Spring '06
 Kines
 Mass, Parsec

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