Homework 3
Due June 22
1. A graph of the “velocity of recession” of distant galaxies as a function of distance
looks like this.
What does the graph tell us? What are the units for the slope?
Important points
~ distant galaxies have a greater redshift (a “velocity of recession”)
... the greater the distance, the greater the velocity
! km $
The units of the slope would be # s & , i.e., units of y divided by units
#" Mpc &%
of x
~NOTE: the “velocity of recession” is not really a velocity but a
measure of how long light has been travelling through an
expanding space-time
2. We believe the Big Bang occurred 13.7 billion years ago. How many seconds was
that? If a step represents a power of 10, how many steps would we need to “walk back”
to t=0?
! 365.25 days $! 24 hrs $! 3600 s $
17
13.7x10 9 years #
&#
&#
& = 4.32x10 s
" 1 year %" 1 day %" 1 hr %
Each step is a power of 10 ... we would need more than 17 but less
that 18 steps.
3. At its brightest an RR Lyrae variable star has a luminosity 50 Lsun but it is only 1.69 x
10-14 times as bright as our sun. What is its distance?
b∝
L
L
2
2 ⇒ D ∝
D
b
D2 =
€
50
distance to sun 2 = 2.98x1015 AU 2
−14
1.69x10
D = 5.46 x 10 7 AU ≈ 862 light years
4. Given a thousand stars on you would most likely have
850
84
37
21
7
1
M stars
K stars
G stars
F stars
A stars
B star
You would only get an O star about once every 100 million stars.
a) If the Milky Way has 200 billion stars how many of these would be G stars? b) How
many would be M stars?
We find the total number of stars
850+84+37+21+7+1=1,000
a) number of G stars
37
200x10 9 ) = 7.4x10 9
(
1000
b) number of M stars
850
200x10 9 ) = 170x10 9
(
1000
5. You are observing a star near the center of the galaxy. It moves around the center in
about 290,000 years at about 10 light years from the very center. What is the mass of
the center of the galaxy? (63,240 AU = 1 light year)
First convert distance to AU
! 63, 240 Au $
5
10 light years #
& = 6.32x10 AU
" 1 light year %
Now use Kepler’s third law
3
5
a 3 ( 6.32x10 )
=
= 3.00x10 6 solar masses
P 2 ( 2.90x10 5 )2