Expert: Philip Stahl - 11/30/2006

Question
As I am still working on my understanding of Astronomy I wanted to ask what proof do we have of the distance of stars and of their size? How is this determined and how is this determination verified scientifically? Thanks.  

Answer
Hello, Fred

The comprehensive answer to your questions involves a lot more math and physics than can easily be given here.  However - I will try to highlight at least the basics, in the hope you will be interested in maybe learning much more about it, say by 'googling' various hitherto unseen terms.

Anyway, the most direct and straightforward way to obtain an idea of the distance of a star is by what we call 'triangulation'. A rough diagram is attached below to show this.

E1  x


    --------------------------D-----------------------O S


E2   x  



In the diagram you see the Sun and the orbit of the Earth, with the Earth's opposition positions (180 degrees apart) identified 'E1' and 'E2'. We know that the radius of the orbit is 93 million miles. We want to find the distance D to some star, S, as shown.

We also know that when we view the star from position E1 it will be slightly displaced from when we view it at E2. You can get the same sense of how this works by holding your index finger at arm's length and looking at it only with your right eye- then your left. Note the background your finger is against, and note how the finger appears to shift when you shift from left to right eye and back again.

The angle made by this is known as the *parallax angle* p.

In practice, we use photographs of a star taken at the opposite (E1, E2) points in the Earth's orbit, and can measure what is called the angle of parallax p. This is shown as the narrow angle (E1-S-E2) in the diagram. The solution of the distance can be obtained from:

D = r/ tan(p)

that is, equal to the radius of the Earth's orbit divided by the tangent of the angle p. (which will be a very, very small angle).

The tangent is a function which denotes a ratio of lengths for a right triangle. In this case, the tangent of the angle p is defined:tangent p = tan(p) = opposite/ adjacent = r/D

that is, the side opposite the angle(r), divided by the side adjacent to the angle (D). Using algebra, you then make D the subject, and solve for it.

The same applies to how the size of a star is found. The instrument that does this is called an interferometer- which is usually attached to the upper end of a telescope. The instrument is used to produce what we call interference fringes of light, from two different parts of the star observed.

From a comparison of the light and dark fringes in interference, e.g.

XXXXXXXX
--------
XXXXXXXX
________
XXXXXXXX
________
XXXXXXXX



the star's angular diameter (in arc seconds or fractions thereof) can be found, which can then be converted into a linear diameter. (in kilometers, or miles)

The point again, is that the basis for this phenomenon (interference) cannot be understood unless one has studied advanced physics courses, usually in Electromagnetic theory and optics. In those courses you will actually be given equipment that can produce alternating dark and light fringes and you will be able to see this first hand.

It should be noted that parallax (for distance) and interferometer method (for size0 methods work optimally only for those stars at relatively close range. Beyond say about 50 light years, we use many other methods which depend on the intrinsic brightness of stars as compared with "standard candles" that are known to fluctuate over defined periods.

We call these "Cepheid variable stars". I would prefer not to get into them unless you specifically ask about them - as that is a whole other area that requires some background in astrophysics.

As for verification, scientifically, this is usually done when the standards, distances etc. are employed for many other lines of research. For example, most recently it was done in terms of the type Ia supernovae and the plots of their brightness vs. their red shifts, in a graph similar to:

Corrected Apparent magnitude
^
!
!
!  
!
!
!
!-14
!0--------------!---Redshift Z (1.0)


The "red shift" means the shift in the spectral lines toward the red or longer wavelength end of the spectrum - to find the distance.

We denote the shift z = v/ c

where v is the recessional velocity - or speed with which it is moving away, and c is the speed of light

Now, in the type Ia plots, which were used by a number of specialist teams to work out the dark matter-dark energy component (a whole separate issue, but again - if you ask - we can discuss) a consistent data pattern emerged. The points trending almost uniformly from the convergence of the plot axes to the right at a roughly 45 deg. slope.

If there were major errors in the recorded brightnesses, or distances - this would have shown up - and the research teams would have called attention to it. For example, in the plots made they'd have seen various points *way* off the plot lines!

This did not occur - nor has it in other associated work - so we are confident that the scientific determinations of stellar distances etc. are fairly accurate. Certainly to within the standard errors of the instruments.

Hope this helps.

Again, if anything is unclear - please ask for clarification and we can go over it. I prefer this approach rather than (as one recent questioner has done) giving me a '6' rating in clarity when they never indicated they were having problems grasping what was stated, in multiple exchanges.