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Ways to determine Distances


Distances in the Universe

Lengths and Distances

km, miles; AUs; light seconds, light minutes, light days, etc; light years (ly), kilo light years (kly), etc; parsec (pc), kpc, Mpc, Gpc

absolute vs. apparent magnitude/brightness/luminosity; distanc module m-M 

    m-M = 5 lg(D/10 pc) = 5 lg(D/pc) - 5 = 5 lg(D/ly) - 7.

    D = 10 pc * 10^((m-M)/5)

linear vs. angular (apparent) diameter 
    d/D = 2 tan (Dim/2) ~ arc Dim

    D = d [cot(Dim/2)/2] ~ d / arc Dim

radial velocity/proper motion

Distances in the Solar System

.. to be determined later :) ..

Distance determinations in the Solar System have been performed in the past by parallax measurements from different points on Earth (in former centuries, risky and expensive sea journeys were done for this purpose).

Nowadays, distances in the solar system are very acurately determined by radar methods, often involving spacecraft.

Trigonometric Parallax

Moving Clusters

Hyades: about 200 stars, 151 ly distant. Crucial because used for virtually all cluster distance determinations by CMD fitting, and thus for almost all greater distance determinations, including zero point gauges for other methods. Hyades distcance was believed to amount 40 pc (130 ly) since the 1920s and got corrected to 46 pc (150 ly) by the 1960s when Hodge and Wallerstein noted inconsistency with nearby star HRD. Hipparcos' parallax measurement found a very close value of 151 ly for the Hyades distance.

Ursa Major Moving Cluster: about 60 stars at 78 ly
Scorpius-Centaurus cluster: about 100 stars at 560 ly; includes a number of B and A stars
(Pleiades estimated by Van Leeuwen at 126 pc, 410 ly)

Secular and Statistical Parallaxes

Similar to Moving Cluster method but for objects of one type (i.e., stars of one spectral type); solar motion, mean parallax and distance

Important if other distance values not available for certain object type (B stars, RR Lyrae, Cepheids)

Binaries: Dynamical and Spectroscopic-Visual Parallaxes

Color Magnitude Diagram Fitting

Compare CMD obtained for a cluster with theoretical or empirical HRD (practically, almost always the Hyades)

References

Hartmut Frommert [contact]
[SEDS]