Absolute magnitude is related to period:
$$\begin{equation}
\bar{M}_v = -2.76 \log \left( \frac{P}{10 \; \textrm{days}}\right)-4.16
\end{equation}$$
where $\bar{M}_V$ is the absolute magnitude in the $V$ band, measured over one complete period.
With this relation, if we know $M$ and $m$, then we can get distance, $d$.
$$\begin{equation}
M = m - 5 \log\left(\frac{d}{10 \; \textrm{pc}} \right)
\end{equation}$$
Shapley's Map
Globular Clusters - more near the center.
Milky Way Structure
Thin & Thick disks
Thin disk:
M: 6 × 1010 M☉
form: $e^{-z/h}$
$h \sim 0.350 \; \textrm{kpc}$
[Fe/H]: -0.5 to +0.3
Thick disk:
M: 0.2-0.4 × 1010 M☉
form: $e^{-z/h}$
$h \sim 1 \; \textrm{kpc}$
[Fe/H]: -2.2 to -0.5
Metallicity
The ratio of Fe to H in the spectra of stars can be used to quantify a star.
This is called the metallicity. ($N_{Fe}$ and $N_{H}$ are the number of Iron and Hydrogen atoms atoms.) Stars with the same proportion as the sun, will have values of [Fe/H] = 0. More metal rich stars have higher positive values. Less metal rich stars have negative values.
In general, younger stars will have higher metallicity than older stars.
Milky way stats
200 Billion Stars
Type: Barred spiral galaxy
Diameter: 100–180 kly (31–55 kpc)
Thickness of thin stellar disk: 2 kly (0.6 kpc)
Oldest known star ≥ 13.7 Gyr
Whole thing is moving at 600 km per second w.r.t the extragalactic frame of reference
Radial velocity: $v_r$. Measured using doppler shift of the star's absorption lines.
Tangential velocity: $v_t$. Measured using proper motion, $\mu$ and distance $d$.
$$\begin{equation}
\mu = \frac{v_t}{d}
\end{equation}$$
(in the small angle limit)
Space motion is the resultant of the radial and tangential velocities:
$$\begin{equation}
v = \sqrt{ v_r^2 + v_t^2}
\end{equation}$$
Two stars (sun = orange, Kapteyn's Star = white)
Measuring the rotation curve
We would like to know the distance $R$. Let's say we can't measure $d$, but we know $R_0$ and $l$.
Dark Matter
There's more stuff there that we just can't see, so it's called dark...
Astrophycisists and Cosmology folks are still figuring out what it is.
The leading candidate is WIMPS: Weakly Interacting Massive Particle. These are hypothetical particles that don't follow the same rules as the others in the standard model of particles physics.
The Galactic Center
Can't see it too well
If we were closer...
Let's move the solar system to half a parsec away from the galactic center.
The nearest star would be ~ 1000 AU away
The night sky would have 106 stars brighter than Sirius
The total starlight would be ~ 200 times brighter than the moon
Stars might collide!
Based on the orbital parameters, we can get the semi-major axis of S2:
$$\begin{equation}
a_{S2} = \frac{r_p}{1-e} = 1.4 \times 10^{14} \; \textrm{m}
\end{equation}$$
Based on Kepler's Third law, and a period of 15.24 ± 0.36 yr:
$$\begin{equation}
M = \frac{4 \pi^2 a_{S2}^3}{G P^2} \\
\simeq 7 \times 10^{36} \; \textrm{kg}
\\
\simeq 3.5 \times 10^{6} M_{\textrm{Sun}}
\end{equation}$$
Image of Black Hole at the center of the Milky Way