1. The Cosmological Distance Ladder

2. Overlapping rungs: Earth Earth-Mars Earth’s orbit Parallax
Spectral “Parallax”
RR Lyrae variables
Cepheid variables
Type I Supernovae
Type II Supernovae
Galaxy brightness

3. Measuring Earth - Geometry
 = s/r
Two wells E-W
Measure s
Time sun
/2 = t/24 hr

4. Measuring Earth-Mars:
Paris
This angle was measured simultaneously Ø
Cayenne (in French Guiana)

5. Calculating Earth’s Orbit:
If you know the Earth-Mars distance, Kepler’s law
RE3 = RM3
TE2 TM2
now lets you figure out the radius of Earth’s orbit.
1.5 x 108 km

6. Parsecs - Parallax Seconds
You know that Tan(Ø ) = d/D
Today we have accurate parallaxes for about 10,000 stars.

7. Spectroscopic “parallax”
Since astronomers can
tell by the spectrum of
a star if and where it
falls on the main
sequence, they can get
the absolute magnitude.
If you then measure the
apparent magnitude,
it is a relatively simple process to calculate the
distance to the star: M = m - 5 log10(d/10)
And you know M, and m…

8. RR Lyrae (cluster variables) Cepheids: (Very Bright) Eclipsing Binary
Variable Stars:
RR Lyrae (cluster variables)
Cepheids: (Very Bright)
Eclipsing Binary
Mira (long period)
Eta Carinae

9. Variable Stars:

10. RR Lyrae Variables:

11. RR Lyrae Variables:
How to measure the distance to a galaxy using RR Lyrae variable stars:
Find the RR Lyrae by magnitude curve
Measure its apparent magnitude.
They all have about the same absolute magnitude (0 < M < 1)
Use M = m - 5 log10(d/10) to find d

12. Cepheid Variables: Star contracts, heats up
Singly ionized He gets double ionized
Double ionized is opaque.
Absorbs energy, expands cools
Doubly ionized becomes singly
Goto 1
Polaris 466 Ly = Cepheid

13. Cepheid Variables:
In 1912, Henrietta Leavitt observes Cepheids in the Large and small Magellenic clouds.
These Stars are all the same distance from Earth more or less.
She discovers a period-brightness relationship:
Star is like a gong…

14. Cepheid Variables:
How to measure the distance to a galaxy using Cepheid variable stars:
Find the Cepheid, measure its spectrum
Measure a couple periods, and its apparent magnitude m
Look up its absolute magnitude
Use M = m - 5 log10(d/10) to find d

15. Type I Supernovae:

16. Type I Supernovae: Binary system: A sub-Chandrasekhar white dwarf
A less dense companion star
Gravity strips material off companion star
Dwarf gets more and more massive
Mass exceeds Chandrasekhar limit (1.4 Msun)
Kablooey
Kablooey has a certain absolute magnitude
Kablooey is very very bright.
Use apparent/absolute magnitude to calculate distance
Finding Supernovae…People vs. robots

18. Type II Supernovae: A Huge star Runs out of fuel. Kablooey
Kablooey has a different magnitude each time
Kablooey gives off most of its energy as Neutrinos.
Neutrinos are observable for a long long way
We’re still working on this one…

19. Galaxy Brightness Spiral galaxies 21 cm line width Doppler shift
The wider the line, the faster the rotation
The faster the rotation, the more mass
The more mass, the brighter
Working on this one too…