Finding the Milky Way in the Galaxy

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Slide 28

800 pc

8 kpc

8,000 kpc

8 Mpc

Variable, between 1 and 10 kpc

The distance between the Sun and the Galactic center is closest to:

Slide 29

Mass of the Galaxy

We can use Kepler’s Third Law to estimate the mass of the Milky Way inside the Sun’s orbit

Sun’s distance from center of Milky Way: 8,500 pc = 1.8 x 109 AU

Period of Sun’s orbit around the center of the Milky Way: 230 million years (2.3 x 108 yr)

Slide 30

Simplified form of Kepler’s 3rd law using convenient units

Where M in solar masses

a in AU

P in Earth years

Slide 31

Mass of the Milky Way within the Sun’s orbit

Where M in solar masses, a in AU, P in Earth years

Mass within Sun’s orbit is 1011 M

Total mass of MW Galaxy is ~ 1012 M

Total number of stars in MW Galaxy  2 x 1011

Slide 32

Kepler’s 3rd Law applied to Binary Stars

Where:

G is gravitational constant

G = 6.67·10-11 m3/kg-s2 in SI units

m1, m2 are masses (kg)

P is binary period (sec)

A is semi-major axis (m)

Slide 33

Kepler’s 3rd Law applied to Galaxy

Where M(r) is mass inside r (kg)

Change from P to velocity = v

Slide 34

Rotation curves

Slide 35

Rotation curve of the Milky Way

Slide 36

Rotation curve of Milky Way

Slide 37

Mass of the Milky Way

density  R-2

Slide 38

Dark Matter

Dark – it doesn’t produce light (any kind)

Does have mass, produces gravity

Nature is unknown

Might be normal matter in a form that doesn’t emit much light – very small and dim star, little black holes

More likely it is elementary particles other than normal matter

Slide 39

What properties of the sun could be used to measure the total mass enclosed within the sun's orbit?

mass and orbital speed

mass and distance from the center