Celestial Distances

Question 1

What established the relative distances between the planets

Answer 1

• The work of Copernicus and Kepler
• But their work could not establish the absolute distances

Question 2

How were absolute distances established

Answer 2

Astronomers had to measure one distance in the solar system directly

Question 3

Explain distances today

Answer 3

• Radar is used to determine the distances to planets in our solar system
• It provides a distance measure in units of light seconds, minutes, or hours
• Radar can’t be used to measure the distance to the Sun. We use KIII to do that.

Question 4

Explain triangulation in space

Answer 4

• Suppose you are trying to measure the distance to a tree. Suppose also there is a mountain behind that tree. You set up two observing stations some distance apart. That distance is called the baseline
• The position of the tree (in the foreground) relative to the mountain (in the background) is
  different from each end of the baseline.

This apparent change in direction of the remote object due to a change in vantage point of the observer is called parallax

• If the tree were farther away, the whole triangle would be longer and skinnier, and the
  parallax angle would be smaller. The smaller the parallax, the more distant the object we are measuring must be

Question 5

How do we measure the distances to the nearby stars

Answer 5

• We use the Earth’s orbit around the Sun as a
  baseline.
• As Earth travels from one side of its orbit to the other, it provides us with a baseline of 2 AU, or about 300 million kilometres.
• Even still, the stars are far enough away for their parallax shift to be undetected by the naked eye

Question 6

Explain the measurements of stellar parallax

Answer 6

• Measured distances for thousands of stars out to about 300 light years with an accuracy of 10 to 20%.
• Hipparcos could measure parallax angles with milli arcsecond accuracy (corresponding to distances up to +/- 500 pc)

Question 7

Explain HIPPARCOS

Answer 7

High precision parallax collecting satellite

Question 8

Explain Gaia

Answer 8

• Expected to measure the positions and distances to almost one billion stars with an accuracy of a few ten-millionths of an arcsecond.
• Gaia’s distance limit will extend well beyond Hipparcos, studying stars out to 30,000 light years (100 times farther than Hipparcos, covering nearly 1/3 of the galactic disk).

Question 9

Explain HR Diagrams and variable stars

Answer 9

• This allows the star to be placed at a unique location on the HR digram.
• Then, its luminosity can be read off, compared to its flux, and its distance determined.

Question 10

Expalin HR diagram

Answer 10

HR diagram can be used to
determine distances - If we can
observe the spectrum of a star, we
can estimate its distance from our
understanding of the HR diagram.

• By carefully studying the spectral
  features of a star, it’s possible to
  determine its temperature (i.e.,
  spectral class) and its pressure (i.e., size).

Question 11

Explain RR Lyrae variables

Answer 11

• A related group of stars, whose nature was
  understood somewhat later than that of the
  cepheids

Question 12

Explain RR Lyrae variables fully

Answer 12

• Are pulsating horizontal branch aging
  stars of spectral class A or F, with a mass of
  around half the Sun’s
• More common than the cepheids, but less
  luminous, thousands of these pulsating variables are known in our Galaxy
• The periods of RR Lyrae stars are always less
  than 1 day, and their changes in brightness are typically less than about a factor of two

Question 13

Explain Edwin Hubble

Answer 13

• Studied cepheids in nearby galaxies to determine the distances to the galaxies.
• He also measured the radial velocities of the galaxies by measuring the Doppler shifts of
  their spectral features.
• By plotting radial velocity versus distance, he discovered the Universe is expanding

Question 14

Explain Henrietta Leavitt

Answer 14

• Discovered the relation between period and luminosity
• Today, we call the cepheid period-luminosity relationship the Leavitt Law

Question 15

Explain Leavitts findings

Answer 15

• Discovered hundreds of variable stars in the Large Magellanic Cloud and Small
  Magellanic Cloud.
• Found that the brighter-appearing cepheids always have the longer periods of light variation. Thus, she reasoned, the period must be related to the luminosity of the stars.
• To define the period-luminosity relation with actual numbers (to calibrate it), astronomers first had to measure the actual distances to a few nearby cepheids in another way.
• But once the relation was thus defined, it could give us the distance to any cepheid,
  wherever it might be located

Question 16

Explain cepheid variable stars

Answer 16

• Are large, yellow, pulsating stars. Several hundred cepheid variables are known in our Galaxy
• Importance of cepheid variables = the fact that their periods and average
  luminosities turn out to be directly related.
• The longer the period, the greater the luminosity

M= -2.43 log10(P - 1)- 4.05