Expert: Tom Whiting - 1/14/2005

Question
I want to thank you for your time and effort in providing this response. I am still attempting to evaluate this information. I'm setting up a spreadsheet to plug in and calculate distances based on the data. This is going to take some time - I'm a 60 year old man who's visually impaired. This is painstaking stuff but I've had some questions in the back of my mind for years and I'm trying to put the pieces together.
If you're still available, when I'm done, I'll have a followup question or two. Thanks again.  

Followup To
Question -
What I seek is a referral to a chart, list, or some such that provides the number of stars by their distances from earth. I have no interest in the names or designations of the stars, but simply in quantity per distance.
Answer -
Hi Stephen,
I don't know how specific you need the information you
asked for, but I will give you what I know.
Most college astronomy textbooks give a listing of the
50 closest stars....all of these start with Proxima Centauri
at 4.23 lightyears and end with Lalande 25372 at about
17 lightyears.  Few inbetween are at the exact same distance,
and these are quite exact distances because one is using
trigonometric parallax for those values, but this calculation
method is only good out to about several hundred lightyears.
Beyond that, we have to resort to spectroscopic parallax
using the H-R diagram mentioned below....not as accurate,
but it's all we have for distance to the stars beyond
several hundred lightyears.

As far as more distant stars, I have not seen that kind of
listing, BUT the book "Olcott's Field Book of the Skies",
by William Tyler Olcott, G.P. Putnam & Sons, 1954
edition, does list numbers of stars by apparent magnitude,
which, as you may know,  there would be a good correllation
between apparent magnitude and distance, except in
the extreme cases, see far below.
In his Appendix in the back of the book, Appendix VI,
he gives the following listing:
Apparent Magnitude          number of stars
0          4
1          15
2          40
3          140
4          530
5          1620
6          4850
7          14,300
8          41,000
9          117,000
10          324,000
11          870,000
12          2,270,000
13          5.7 million
14          13.8 million
15          32 million
16          71 million
17          150 million
18          296 million
19          560 million
20          1,000 million


Perhaps this is the list you were seeking.....
and it would apply to 95% of all stars on the Main Sequence
of the H-R (Hertzsprung-Russell) Diagram, using
spectroscopic parallax as the distance indicator.
The actual  (although not perfectly exact) distance can
be inferred for any particular type of star, say, all solar-type
stars with an Absolute magnitude (M) of about say, +5,
like the sun, using the distance formula, distance in
parsecs is equal to 10 raised to the 1 + 0.2 (times the quantity
m-M)  where m = apparent magnitude and M = absolute
magnitude.  This gives the distance in parsecs, and of course
there are 3.26 ly in a parsec.

So on the apparent magnitude listing above, we see that apparent magnitude 5th mag stars are about  10 raised to the 1st power or 10 parsecs distant or 32.6 lightyears, on average.
(But like I said, this excludes the 5 out of 100 stars that
are not on the Main Sequence, so it does not include
stars like white dwarfs, red giants, red supergiants, red dwarfs, and Blue White supergiants, because they have a completely different Absolute Magnitude value, relative to solar type stars.)

Apparent magnitude 10 would give 10 squared parsecs distance;.
Apparent magnitude 15 would give 10 cubed parsecs
distance.
And apparent magnitude 20 would give 10,000 parsecs
distance.  You can either interpolate for the intermediate
apparent magnitudes, or use the formula above, assuming
you have a logrimithic calculator (which I don't have)
for the decimal powers.

10,000 parsecs is equal to 32,600 lightyears....beyond that
the numbers would become even more unreliable because
of interstellar dust (interstellar dimming) would not give us a true representative value of the apparent magnitude
of a star.....plus, beyond about 500 lightyears, the thickness
of the Milky Way Galaxy, the only directions you are measuring is in the plane of the pancaked-shape Milky Way Galaxy. (Either inward toward the Sco-Sagittarius region, or outward toward the Orion-Taurus-Gemini region.)
And beyond 20,000 lightyears, Milky Way stars only exist
in toward the center of the Galaxy, in the Sco-Sagittarius
region of the sky.  Any other direction would be
virtually empty inter-galactic space.  (Until you get to
another galaxy out there millions of lightyears).

So, hope all this helps.
Clear Skies,
Tom Whiting
Erie, PA


FOLLOW UP...
Stephen,
due to computer wraparound, my listing did not type
out well; the numbers of stars are below the apparent
magnitude number, for instance, there are 4 "0" magnitude
stars, 15 stars of the first  magnitude, 40 of the second
magnitude, 140 are third magnitude, and so on;
like there are 32 million stars with 15th magnitude,
and 71 million of the 16th magnitude.  And BTW, in case
you didn't know, magnitude is a reverse scale, the
higher the whole magnitude number, the dimmer the object.
That's why we have to go negative numbers for the
super-bright objects, like Jupiter is -2nd apparent magnitude,
Venus is -4th, full moon is -13th, and sun is -26.7
apparent magnitude.  There are 2.5 difference in brightness
between whole number magnitudes, and the scale
(increasing difference in whole number magnitudes)
is geometric, not arithematic like 2.5, 5, 7.5, etc) But
rather 2.5, 2.5 squared, 2.5 cubed, 2.5 to the 4th power,
and 2.5 to the 5th power = 100.
 
For instance a five magnitude change is equal to a 100
times change in brightness!
So the difference between say a second magnitude star
(like Polaris) and a 7th magnitude star visible only with
binoculars, is 100 times difference in brightness.
Just in case you didn't know.
Clear Skies,
Tom Whiting
Erie, PA

Answer
Ok Stephen,
I'll be standing by, although not for real long because I
am a 63 year old man with moderate COPD from 45+
years of smoking.

BTW, feel free to contact me directly at
bwhiting@velocity.net if you wish.

Realize too, that those distances to the stars, those ones
in the Milky Way, are continuously changing as we all
revolve around the Milky Way; not much in our short lifetimes, but we've made at least 18 trips around the entire Milky Way since the Solar System formed up about 4.6 billion years ago.  So basically, all the stars we see in the night
sky....their positions and distances....are all "temporary"
as there is no such thing as absolute rest....everything is
moving relative to everything else and nothing is static.

Their current distances and positions are but a snapshot in time on the astronomical scale.  So if you are trying to "read
into the current data" some mystical or religious or
alien life message,  you can disregard that.

Also, a lot of this distance work was already done by,
I believe it was Harlow Shapley back in the 1920's, when he came up with the conclusion that the Solar System was not at the center of the Milky Way (as originally thought), because all the globular clusters showed encompassing a "center" that was 30,000 lightyears toward the Sco-Sagittarius region of the Milky Way, and that turned out to be the correct Galaxy center.  Of course,  he was mostly using Cepheid
variables and RR Lyrae variables for his distance
indicators to the globulars.
Clear Skies,
Tom Whiting
Erie, PA.

Oh, please visit our club website for some great
views of my new 30 inch portable truss-DOB scope at;
http://www.velocity.net/~bwhiting/