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Various Techniques for Measuring Astronomical Distances

Various Techniques for Measuring Astronomical Distances. Alex Blanton. Introduction. A very common tool for knowing the distance to a star is the distance modulus. Through knowing of the Galaxies motion, a celestial body can be determined by calculating its galactic position.

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Various Techniques for Measuring Astronomical Distances

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  1. Various Techniques for Measuring Astronomical Distances Alex Blanton

  2. Introduction • A very common tool for knowing the distance to a star is the distance modulus. • Through knowing of the Galaxies motion, a celestial body can be determined by calculating its galactic position. • Through the expansion of the Universe, Edwin Hubble was able to find a relationship through velocity and distance on inter galactic scales.

  3. A star’s magnitude • The magnitude of a star is the value of the star’s brightness. • The first scale of magnitudes went from 6 to 0, with 0 being the brightest. Future astronomers chose to use this convention, but discovered magnitudes beyond 0 and 6.

  4. Absolute Magnitude • Absolute magnitude is the apparent magnitude a star would have if it were located 10 parsecs away. • The inverse law of radiation is used to find the luminosity if the flux is measured.

  5. Apparent Magnitude • Apparent magnitude is how bright a star appears to the naked eye. • Astronomers can measure this by flux.

  6. The Equations

  7. The Distance Modulus • If the apparent and absolute magnitude of a star is known, the distance modulus can be employed.

  8. Errors with the Distance Modulus • One very big problem with the distance modulus is that it does not take into account the dust between Earth and the star!

  9. Optical depth and the Extinction Coefficient • An extra coefficient, , must be added to account for a change in magnitude.

  10. Interstellar Reddening • As light passes through dust, high frequency and low frequency waves get filtered since longer wavelengths pass through the dust easier.

  11. Radial Distance and Radial Velocity • As an object moves through the Milky Way, it has it’s own “peculiar” velocity and a radial velocity around the galactic center. • Based on observations, a “rotation curve” has been fitted for the galactic curve. Where a1 = 1.00767 , a2 = 0.0394, and a3 = 0.00712

  12. Kinematic Distance Now there is a function for α!

  13. Kinematic Distance The star is either behind the tangent point, or in front of the tangent point. To solve for this, spectral lines of a cloud at the tangent point are used. Absorption lines = close Emission lines = far

  14. Drawbacks to Kinematic Distances • There must be a cloud around the tangent point! No cloud means you have two distances with no way of knowing which one is the real value. • If not careful, it is easy to choose the wrong distance when looking at the “Radio Recombination Line”.

  15. Early Concepts of Expansion • Using Doppler shifted spectral lines to uncover the radial velocities of objects in our Milky Way. • V.M. Slipher recorded many Doppler shifted spectral lines, and found that most were red shifted.

  16. A Universe Bigger than the Milky Way • During the time V. M. Slipher was working, Edwin Hubble was able to prove that M31 was “extragalactic”. • By using Cepheid variable stars, he showed that the distance to M31, as well as 18 other galaxies, was beyond the reach of the Milky Way

  17. A Happy Coincidence • After Hubble was able to determine the distance to several galaxies, he found that the distance away from a star is proportional to it’s recessional velocity. This became known as Hubble’s Law

  18. Hubble Flow and Peculiar Velocities • A galaxy can move through space at it’s own peculiar velocity, but an extra “recessional velocity” is added because space is expanding.

  19. Cosmological Redshift • As space expands, light leaving a galaxy is stretched out because space is expanding. Although the Doppler shift equations cannot account for curved space, they still prove useful.

  20. Ambiguity of the Hubble Constant • Ambiguity of the Hubble constant arose since remote galaxies were used to calibrate Hubble’s Law. • After the Wilkinson Microwave Anisotropy Probe (WMAP) was launched to explore the CMB, the Hubble constant so that

  21. In Summary • Knowing distances to stars can give us a 3D map of the Milky Way. • Having more than one tool to measure the distance will lead to more accurate results. • By using these methods on a cosmological scale, astronomers can determine the in workings of the Universe.

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