6.2

Question 1

Star Motion in a Gravitational Potential

Answer 1

• Circular orbits are possible for rotational symmetry
• planar orbits for motions in a symmetry plane
• random orbits for other cases

Question 2

Milky Way Characteristics

Answer 2

• Predominant circular rotation in the galactic disk
• globular clusters have random orbits
• average radial velocity of globular clusters approximates systemic velocity of Milky Way
• Average position and distance of globular clusters approximates galactic center

truly i do not understand the last bullet point, maybe because im tired hahaha

like does he mean that the distance form us to the galactic center is the same as from us to globular clusters?!?

hahahahahha Ill have to think about it too. No idea

ohhhhh, see i didnt really know what globular clusters are, but once you know it, and you know that they are mostly not in the disk but spherically around the center, then their average is obviously the center that they are orbiting around i guess, altough their orbits are random so it doesnt make suuuper much sense, but better then nothing hahaha

Question 3

Sun’s Distance to Galactic Center

Answer 3

R₀ ≈ 8 kpc

Question 4

Sun’s Tangential (Rotation) Velocity

Answer 4

Theta₀ ≈ 220 km/s

Question 5

Sun’s Orbital Period Around Galactic Center

Answer 5

P₀ ≈ 2 · 10⁸ years

Question 6

Age of Sun and Its Galactic Circuits

Answer 6

• 𝛕_⊙ ≈ 4.6 · 10⁹ years
• Sun circled galactic center about 23 times

Question 7

Estimate of Milky Way Mass Inside Sun’s Orbit

Answer 7

M_gal(R < R₀) ≈ 10¹¹ M_⊙

Question 8

Local Standard of Rest (LSR)

Answer 8

LSR is mean galactic motion of stars in solar neighbourhood.

Question 9

Peculiar Motion of Sun

Answer 9

≈ (-10, +5, 7) km/s
(radial, tangential, vertical)

v_LSR = (0, Theta, 0)

sun: (π, theta_O - theta, Z)

• motion through space relative to the average motion of other stars in the Milky Way galaxy.
• The Sun, along with the entire solar system, is not stationary but rather moves through space.
• This motion is influenced by the gravitational interactions with other stars, galaxies, and even dark matter in the Milky Way.
• The peculiar motion of the Sun is typically measured in terms of its velocity with respect to the local standard of rest, which is the average motion of stars in the solar neighborhood.

Question 10

Typical Velocity Dispersion for Old Stars

Answer 10

Of the same order as Sun’s peculiar motion.

(so of order 10 km/s)

Question 11

Radial Dependence of Rotation Velocity Near Sun

from what can it be determined and where well known

not sure if radial dependence is the best way of putting it

Answer 11

• v_r (radial) from Doppler shifts
• v_t (tangential) from proper motion μ and distance d or annual parallax π
• Both well known for stars within d < 1 kpc

Question 12

Interpretation of Radial and Tangential Velocities

Answer 12

v_r shows a quadrant pattern.
Thus: Omega = Theta / R larger, or P shorter for small R (differential rotation)

im not sure what is meant by this, i guess the velocities have different sign depending on the quadrant

Question 13

Radial Dependence of Θ(R)

Answer 13

For l = 0° (-) and l = 180° (+):

• R = R₀ ± d
• Θ(R) ≈ constant near the Sun

l is longitude (i think)