Problem

$1$

$.$

a$)$

$(2$ pts$)$

In a spiral galaxy far far away,

a star system

$2$

$4$

$,$

$000$ light years away from the

center of that

galaxy is

orbiting a

round

the center

a

t a

speed of about

$30$

$0$ km$/$s

$.$ Assuming

the orbit is perfectly

circular, what is the total mass

in that galaxy

enclosed within th

at star system$$s

orbit $($in solar masses$)?$

b$)$

If

you know

the distribution of stars

and gas

in

that

galaxy taper

s

off

at distances beyond the star

system mentioned in a$),$

but

the orbital speed

stays the same

at large distances

$,$ what would you

conclude about the following questions.

i$)(1$ pts$)$ Does this mean the total mass enclosed at larger and larger radius increases, decreases or stays

the same

$($assuming Newtonian dynamics is correct$)$

$?$

ii$)(1$ pt$)$

What does this result mean?

Problem

$2$

$($

$4$

pts$).$

In class we discussed how to measure distance on different scales.

On very large scales, there is a

Hubble flow due to the expansion of the Universe governed by Hubble$$s law:

v $=$ H

$0$

d

$.$ For low redshift,

v $=$ cz$,$

where

c is speed of light in vacuum, z is redshift

$.$ Remember redshift z is

defined as

$!$

$!$

$"$

#$$\%$

$"$

$!$

&$\text{'}!\%$

$!$

&$\text{'}!\%$

$.$

If

a spectral line that$$s supposed to be at $656$ nm in the rest frame is observed to be at $774\mathrm{.}08$ nm

in

a

galax

y

$.$ H

ow far away is

this

galaxy

$($in Mpc$)$

$?$

$($Use Ho$=70$ km$/$s$/$Mpc$.)$