Expert: Philip Stahl - 2/28/2005

Question
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Followup To
Question -
Hi Philip,

I have spent many years looking to find out how scientists have come to the conclusion that the universe is so big.

Could you please tell me who, how or what was used to first dictate how far the stars are away from us and who did it.

Who was initially responsible for making the assumption that stars and galaxies are many light years away from us?

And do astronomers use the same system today?

I have asked this question many times and never found an answer. I would appreciate it if you could give me your understanding.

Thank you for your co-operation in this matter.

Kind Regards
David Parkes
Answer -
Hello David.

The methods for measuring distance in astronomy are now so exhaustive and diverse, that it would take a short book to document them all with any degree of completeness. What I can do is give some of the basis for a few of the major methods, used for different distance scales.

The most basic and intuitive method for measuring a star's distance employs elementary trigonometry. It is called the "parallax method" because it uses the phenomenon of "parallax".

You can get a simple idea of this by holding an index finger at arm's length- then looking at it with only the right eye open, then only the left. What you will see as you do this alternatingly - is the visible shift of your index finger against the background. Say from one part of your book shelf to another. A very tiny shift.

The angle subtended between the different background points, with respect to your nose ("vertex" of the resulting triangle), say- is the "parallax angle".

Now, let's generalize this to stars, using the diagram below - which I hope comes out reasonably well in the response:

(E1) x

    -------------------------------------------* (star)

(E2) x
         

Here, the points E1 and E2 represent Earth at two opposite points of its orbit around the Sun. The star indicated is the one whose distance is sought. Using photographs of the star taken at the points E1 and E2, we can measure what is called the angle of parallax p.

The solution for the distance can be obtained from:

D = r/ tan(p)

that is, equal to the radius of the Earth's orbit (equal to 1 A.U. or astronomical unit = 93 million miles = 1.5 x 10^11 meters) 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:

tan(p) = opposite/ adjacent = r/D

that is, the side (radius = r) opposite the angle, divided by the side (D = distance to star) adjacent to the angle (D).

Using algebra, you then make D the subject, which means solving for it.

It can be shown, from the above, that for an angle p = 1" (one second of arc, or 1/3600 of a degree! Bear in mind 60' = 1 deg and 60" = 1' or 1 minute of arc) the resulting D is 206, 265 A.U. or astronomical units (206, 265 x 1.5 x 10^11 m)

The name we use for this particular distance is the *parsec* - and doing the math (tedious, but possible) shows the distance turns out to be:

1 parsec =   3. 26 light years.

Now, given this relation, it follows that any proportionate decrease in the angle p allows one to work out the resulting distance! Thus, if p = 0.5" then D = 2 parsecs or 6.52 Ly, if p = 0.25" then D = 4 parsecs or about 13 Ly and so on, and so forth.

Thus it was found that even the *nearest* stars were light years distant - using the simplest conceptual method available. The first successful parallax measurements - so far as we know - took place around 1838, when Friedrich Bessel (Germany), Thomas Henderson (Cape of Good Hope) and Friedrich Struve (Russia) detected the parallaxes of the stars 61 Cygni, Alpha Centauri and Vega, respectively.

No one knows who "first" used it.

Parallaxes have been measured for thousands of stars. However, for barely 700 are the angles (p) large enough (about p = 0.05" or more) to be measured with a precision of 10% or better. (Which means the resulting distances will have the same order of uncertainty).

Most of these measurable stars are within 20 parsecs or around 66 light years. Clearly, other methods are needed to measure larger distances.

Among these is the method of Cepheid variables. These are a special type of star for which the brightness changes as its surface swells (expands) then contracts.  In 1912, a period-luminosity relationship was discovered for these stars, by Henrietta Leavitt, an astronomer at Harvard College Observatory. Most of these were in the satellite galaxies (to our own) known as "the Small" and "the Large" Magellanic Clouds.

Leavitt's now famous "law" for period-luminosity (relating the time to vary to intrinsic brightness) is found in many astronomy books. You may wish to check the index of several books, when you next go to your local library. Employing this law enables us to use a kind of a "standard candle" to measure distance - based on the principle of the inverse square law for light (e.g. if you have two light sources, say two 100w light bulbs, and place one 5 feet away, the other ten feet away, the more distant one - which is 2x further- will have 1/(2)^2 or 1/4 the apparent brightness of the one closer to your eyes. Thus, it will "appear" as a 25 w bulb by comparison!)

What you will see is the apparent magnitude of the stars plotted against the logarithm of their period (in days). Thus, there is a relation between the apparent magnitude of the star and period of its light curve.

(Note: to save time and preserve continuity I am assuming you are already familiar with a number of concepts, including: "apparent magnitude" and the stellar magnitude scale. If not, you can ask for more details and I will gladly provide these).

Now, since there is a direct relation between apparent and absolute magnitude (the absolute magnitude of a star is just its apparent magnitude from the same standard distance of 10 parsecs or 32.6 light years) there must also be a direct relationship between a (Cepheid) star's *period* and absolute magnitude. Thus, if a given set of Cepheids can have absolute magnitudes assigned to them, the relationship between their periods and absolute magnitudes acts as a distance measuring device.

Entering into this is what is called the "distance modulus" (m - M)  given as the difference between apparent magnitude (m) and absolute magnitude (M):

(m - M) = 5 log_10 (r) - 5

Here, r is the distance to be found.

FOr example, say a star is found to have: m = +4.5, and M = +6.0 (meaning it is actually brighter in apparent magnitude than it really is);

We have:

(4.5 - 6.0) = 5 log_10 (r) - 5

(-1.5) + 5 = 5 log_10 (r)

3.5 =  5 log_10(r)

then:  log_10(r) =   3.5/ 5 = 0.70


taking anti-logs:   r = 5.0 (parsecs)

Which is actually for the star 40 Eridani.

Now, in the case of Cepheids - to employ the P-L relation for any star, we need to first: find a 'zero point' applicable (this is not easy by any means, and I don't intend to go into the technical details!) By choosing the correct "law" appropriate to the type of variable star observed (e.g. 3-day period, 10 -day period, 30-day period etc.) a value can be inserted for the absolute magnitude M.

Then we can again apply the distance modulus equation, as I demonstrated above - since we now have values for both m and M.

Note that the Cepheid method is good for many stars in nearby galaxies (like the Magellanic clouds) or in star clusters. However, one must realize problems can arise - for example many of these Cepheids are in dusty regions of the Milky Way with some light lost by absorption - making them appear less bright than they'd normally be at that distance. Hence - if such anomalous Cepheids are used for finding a distance - they'd give a skewed, erroneous result.

At much larger distances, say for galaxy clusters - we make use of the so-called "Hubble relation" or law. That is, Edwin Hubble first discovered that the galaxies are speeding away from us with velocities proportional to their red shifts. (This is in reference to the shift of observed, known spectral lines toward the *red* or *longer* wavelength region - disclosing movement *away* from an observer. This observation for multiple distant objects has revealed the "expansion" of the universe).

The red shift is given by:

z =  v/c

where c is the velocity of light (300,000 km/s)

For example, if the H-alpha spectral line is found to redshift by 20% from its normal position (at 6563 Angstroms, where 1 A = 10^-8 cm) we have:


0.2 = v/c  or v =  0.2 c

In other words, its velocity of recession is two-tenths the speed of light, or 0.2 (300,000 km/s) = 60,000 km/s

The distance can then be found from the Hubble law:

v  = cz  = HD

where H is Hubble's constant, and D is the distance of the galaxy cluster or other object (e.g. quasar)

We believe that H = 100 km/ sec (Mpc ^-1)according to recent measures, so (using the example of the recessional velocity, v above):

D  =   v/ H   =  60,000 km/s / [100 km/ sec (Mpc ^-1)]

D =  600 Mpc (Mega-parsecs)

That is, 600 x (10^6) parsecs = 6 x 10^8 parsecs (or 6 x 3.26 x 10^8 light years =  1.95 x 10^9 light years

Or, about two billion light years.


The preceding examples, starting with simple parallax- allow you to see that distance measurement (and technique) in astronomy is by no means straightforward. This is also possibly why it is difficult to get satisfactory answers, since there are so many different methods appropriate to differing distance scales. In addition, to understand each method - both mathematics, and a certain amount of physics (e.g. inverse square law for light, spectral line shifts etc.) enter at each point. Therefore, appreciation of the distance methods and their appropriate use, really depends on how much of the physics - and math - one is able to incorporate in order to ascertain for himself how it works.

As far as what astronomers use today, the greatest emphasis is certainly on the last method - since it is the one that provides the key to determining whether the universe will expand forever, or at some point begin to contract. Also, whether the expansion is uniform, e.g. follows a more or less "linear" Hubble relation (v = HD) where v is plotted vs. D as a straight line, and H is effectively the slope or gradient of the linear graph.

Hopefully, even if you may not understand all the details from the different methods presented above, you can see how we came to the conclusion that the stars and galaxies are many light years away from us.  

Thank you Phillip.

Also, I would like to know if an experiment can be done by an observatory if a person off the street requires it. In other words, I have done a lot of research on Unification and I need verification of light measurements on the outer planets of our solar system.

I have a complete understanding of the sub-atomic world and it differs greatly from what the scientific community assumes to be correct.

My understanding can be confirmed if a simple observation of three of the outer planets is undertaken with a light measuring device and a simple formula used for predicting the brightness of light of a fourth planet.

I know this might sound a little strange but it is true.

I live in Australia and if you know of any observatory that might be willing to help me out in this matter I would very much appreciate it.

Thank you for your time.

Kind regards

David Parkes  

Answer
Hello again.

The problem in regard to your request, is the professional Observatories are usually "scheduled to the hilt" - often over-scheduled- for various projects, and the fulfillment of research grants, etc. Not to mention enabling, assisting graduate work.

The best thing that I can advise you to do, is to try to engage the attention of a professional astronomer in Australia - say based at one of its universities- and see if he or she might be willing to sponsor your tests.

Basically, what you would need to do is to prepare a compelling research proposal. Give the objectives, why you think or believe this test is important, how you envisage it would use Observatory facilities, time requirements and so forth.

Also, write a typed cover letter, introducing yourself and summarize in 300 words or less, what the proposal is about.

After that, all you can do is wait, and hope for a response.

The other alternative, of course, is to write one or more of the Observatories directly and see if it is possible to secure time for your tests, even if you have to pay to do so.

Good luck!