Aitken on double stars

In my opinion Aitken never intended his formula to be more than a
"rule of thumb" tool.

I do not think there is any evidence he intended it to be used for
very faint stars nor for pairs widely differing in magnitude. Indeed
looking at a sample of 20000 catalogued doubles the median difference
in magnitude is only 0.99.

Martin Nicholson wrote:
In my opinion Aitken never intended his formula to be more than a
"rule of thumb" tool.

I do not think there is any evidence he intended it to be used for
very faint stars nor for pairs widely differing in magnitude. Indeed
looking at a sample of 20000 catalogued doubles the median difference
in magnitude is only 0.99.

I think in this you might very well be correct. However, I think it can
be used in that way if one interprets the magnitude m to be that of the
secondary. In any case, one cannot use Aitken's with m being the pair's
magnitude, nor can one use a constant radius either. The radius has to
shrink with increasing secondary magnitude, or else everything will be
called a double (for reasons that have been given too many times to
repeat here).

I've also given my reasons for preferring a coefficient of 0.24 instead
of 0.2. That seems to me a fairly minor quibble, though.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Martin Nicholson wrote:
In my opinion Aitken never intended his formula to be more than a
"rule of thumb" tool.

I do not think there is any evidence he intended it to be used for
very faint stars nor for pairs widely differing in magnitude. Indeed
looking at a sample of 20000 catalogued doubles the median difference
in magnitude is only 0.99.

I think in this you might very well be correct. However, I think it can
be used in that way if one interprets the magnitude m to be that of the
secondary. In any case, one cannot use Aitken's with m being the pair's
magnitude, nor can one use a constant radius either. The radius has to
shrink with increasing secondary magnitude, or else everything will be
called a double (for reasons that have been given too many times to
repeat here).

I've also given my reasons for preferring a coefficient of 0.24 instead
of 0.2. That seems to me a fairly minor quibble, though.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

I am sure you will recall the earlier concerns raised by Mark G
regarding my non-use of the Aitken criteria.

It seems clear that Mark initially misquoted the formula and/or
applied it in a way never intended by Aitken.

Will he now admit the error?

I am sure you will recall the earlier concerns raised by Mark G
regarding my non-use of the Aitken criteria.

It seems clear that Mark initially misquoted the formula and/or
applied it in a way never intended by Aitken.

Will he now admit the error?

Martin Nicholson wrote:

It seems clear that Mark initially misquoted the formula and/or
applied it in a way never intended by Aitken.

In fact, I interpreted the ambiguous wording of Aitken's criterion in
a way that avoids the absurdities of the alternative interpretations,
and in a way that actually gives results closer to S&M's modern
criterion when compared to the alternatives.


Will he now admit the error?

What's erroneous about my employing the interpretation of Aitken that
works better, Martin?

--
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Mark Gingrich San Leandro, California

Martin Nicholson wrote:

It seems clear that Mark initially misquoted the formula and/or
applied it in a way never intended by Aitken.

In fact, I interpreted the ambiguous wording of Aitken's criterion in
a way that avoids the absurdities of the alternative interpretations,
and in a way that actually gives results closer to S&M's modern
criterion when compared to the alternatives.


Will he now admit the error?

What's erroneous about my employing the interpretation of Aitken that
works better, Martin?

--
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Mark Gingrich San Leandro, California

Mark Gingrich wrote:
Will he now admit the error?

What's erroneous about my employing the interpretation of Aitken that
works better, Martin?

soapbox
Nothing, of course. Science is all about taking what we know or what we think
we know, and extending that knowledge to further our understanding of the
universe. Mark's interpretation of Aitken's formula is part of that tradition.

What it's not about, is proving one person right or one person wrong for the
sake of uplifting one at the expense of another. Unless people are allowed to
reach beyond their grasp, and occasionally make mistakes or even fail, humanity
has no hope for the future.

Unfortunately, this thread evolved to become an "I'm right, you're wrong."
thing.
What it should be is a free exchange of ideas with the goal of better
understanding how we identify physical stellar pairings and, with that
knowledge, enhance our enjoyment as observers of the night sky.
/soapbox

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
=============
Email: Remove "ic" from .comic above to respond

Mark Gingrich wrote:
Will he now admit the error?

What's erroneous about my employing the interpretation of Aitken that
works better, Martin?

soapbox
Nothing, of course. Science is all about taking what we know or what we think
we know, and extending that knowledge to further our understanding of the
universe. Mark's interpretation of Aitken's formula is part of that tradition.

What it's not about, is proving one person right or one person wrong for the
sake of uplifting one at the expense of another. Unless people are allowed to
reach beyond their grasp, and occasionally make mistakes or even fail, humanity
has no hope for the future.

Unfortunately, this thread evolved to become an "I'm right, you're wrong."
thing.
What it should be is a free exchange of ideas with the goal of better
understanding how we identify physical stellar pairings and, with that
knowledge, enhance our enjoyment as observers of the night sky.
/soapbox

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
=============
Email: Remove "ic" from .comic above to respond

Mark Gingrich wrote in message ...


What's erroneous about my employing the interpretation of Aitken that
works better, Martin?

Nothing at all providing you make it clear that your interpretation is
exactly that. In an earlier thread you gave me the impression that
your interpretation was what Aitken actually wrote, which was clearly
not the case.

To calculate the linear distance between the components of a double
star
you need to know the angular separation and the distance to the
system.

In many cases the distance is not known so people use apparent
magnitude as a measure of distance (all other factors being equal
fainter stars are further away).

The problem with this "one size fits all" magnitude approach is that
stars vary tremendously. For example if you placed the 50 closest
stars
at a uniform 10 parsec distance they would vary in apparent magnitude
between 1.45 and 17.32. This would have a large effect on the maximum
allowable separation that would qualify as a double.

At the extremes the formula is either too generous (stars with a
particularly high luminosity) or too mean (Red Dwarfs).

Since red dwarfs are the commonest type of star in the sky it seems to
me that Aitken's formula serious under estimates the number of binary
systems. This was not a major problem when only brighter stars were
being surveyed since most red dwarfs are faint but when stars of
magnitude 12 to 16 are being studied the number of red dwarfs being
measured increases rapidly.

We will not know about the candidate doubles I have identified until
we
monitor them - we would not have monitored these stars without
identifying them first - and we would not have identified them without
somebody (in this case me) taking the time to do so.