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The Cosmological Distance Ladder. Overlapping rungs: Earth Earth-Mars Earth’s orbit Parallax Spectral “Parallax” RR Lyrae variables Cepheid variables Type I Supernovae Type II Supernovae Galaxy brightness. Measuring Earth - Geometry.  = s/r Two wells E-W Measure s Time sun

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Presentation Transcript
slide2

Overlapping rungs:

    • Earth
    • Earth-Mars
    • Earth’s orbit
    • Parallax
    • Spectral “Parallax”
    • RR Lyrae variables
    • Cepheid variables
    • Type I Supernovae
    • Type II Supernovae
    • Galaxy brightness
slide3

Measuring Earth - Geometry

 = s/r

Two wells E-W

Measure s

Time sun

/2 = t/24 hr

slide4

Paris

Ø

Cayenne (in French Guiana)

This angle was measured simultaneously

Measuring Earth-Mars:

In 1672:

slide5

1.5 x 108 km

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.

Calculating Earth’s Orbit:

slide6

Parsecs - Parallax Seconds

You know that Tan(Ø ) = d/D

Today we have accurate parallaxes for about 10,000 stars.

slide7

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…

slide8

Variable Stars:

  • RR Lyrae (cluster variables)
  • Cepheids: (Very Bright)
  • Eclipsing Binary
  • Mira (long period)
  • Eta Carinae
slide11

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
slide12

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
slide13

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…
slide14

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
slide16

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
slide18

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…
slide19

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…