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Distances Near objects appear to move more than far objects against a distant horizon. Trigonometric parallax is used to measure distance to near stars. Parallax time A r y Earth’s orbit d distant stars time B near stars

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Near objects appear to move more than far objects against a distant horizon.

Trigonometric parallax is used to measure distance to near stars.


time A



Earth’s orbit


distant stars

time B

near stars

Stellar distances are inversely proportional to the parallax angle.

Earth’s radius fixed

Define distance by angle

The parsec (pc) is the distance that would result in one arc second of parallax.

1 pc = 3.086  1016 m

1 pc = 2.06  105 AU

near stars
Near Stars
  • The Hipparcos satellite measured parallax of 118,000 stars.
    • Resolution: 0.001 arc-second and 0.2% luminosity.
  • Gaia launches in 2011 to measure 109 stars in the galaxy

Arcturus 11.3 pc (ESA)

spectroscopic parallax
The Hipparcos data provides very precise distances.

Use for absolute magnitudes

Precise HR diagram

Distant stars can be fit on the main sequence.

Measure luminosity and apparent magnitude

Spectroscopic Parallax
star clusters
Spectroscopic parallax assumes stars on the main sequence.

Better to average stars at the same distance

Globular clusters are dense with 100,000 stars in a 20-100 pc region with less than 0.3 pc separating the stars.

Open clusters tend to be smaller and younger.

Star Clusters
cluster types
Type I Clusters

Hot young stars

Lots of gas and dust

Abundant in heavy elements

Active star formation

Type II Clusters

Old red stars

No gas and dust

Few heavy elements

No star formation, just old stars

Cluster Types
standard candle
Standard Candle
  • Up to 30 pc distance is measured with parallax.
    • Less certainty to 300 pc
    • Longer distances by spectroscopic parallax
  • The best measure of large distances are variable stars.
    • Luminosity directly related to the period.
vibrational modes
Thermal motion in a star relates the speed to potential energy.

Radial pressure waves move at the speed of sound.

The period of vibration is inversely proportional to the square root of the density.

Vibrational Modes
cepheid variables
Cepheid variables are massive relatively cool stars.

~ 4 to 15 M

Color classification F to K

The period and apparent luminosity determine the distance.

Density ~ 10-3 kg/m3

Vibrational period ~ 106 s

Cepheid Variables
rr lyrae variables
RR Lyrae variables are short period white variables.

~ 1 M

Color classification A

These are type I stars.

Found in globular clusters

Useful for galactic distances

Density ~ 10 kg/m3

Vibrational period ~ 4  104 s

RR Lyrae Variables
variables in m3
Variables in M3

RR Lyrae stars in one night time lapse

instability strip
Cepheid and RR Lyrae stars fall in a narrow band on the HR diagram.

Instability strip

Not on main sequence

As stars pass through band they oscillate.

Instability Strip
band of stars
The sun is in a galaxy called the Milky Way.

Observed as a diffuse band

Millions of stars in a telescope

The Milky Way is thicker in some directions.

Appears as a band across the sky

Band of Stars
  • The band of the Milky Way is the same view a viewer would have sitting inside a disk of stars.
  • This disk has type I stars with gas and dust.



top view

side view

  • Astronomers measure the distance to globular clusters.
  • Type II globular clusters are in a sphere around one point.
  • This sphere is the galactic halo.
  • The center of the sphere is the center of the galaxy.


globular clusters

size and shape
Size and Shape
  • To view the galaxy from inside, we
    • measure the distance to globular clusters
    • measure distributions of hydrogen gas in the disk.
  • The Milky Way is 50,000 pc across with a central bulge.
  • The stars group in arms.
galactic structure
Galactic Structure
  • The galactic nucleus is bright and massive.
  • It is obscured by the dust of the galactic disk.
  • The Milky Way is probably similar to M83.