# Magnitudes & Other Nonsense, was Re: More #25544 Obs

scribble (scribble@eisa.net.au)
Tue, 8 Dec 1998 00:21:55 +1100

```Greetings SeeSat-L'ers,

This is actually a response to e-mail, although I'm sure some new
subscribers could benefit from the content, so here it is on the list.

Apparent magnitude, the brightness of stars and other celestial
objects, is measured using a logarithmic scale.  It is a function of the
object's luminosity (or intrinsic brightness), it's distance from the
observer and the amount of light absorption occouring between the object and
observer.  The latter being caused via interstellar matter in the case of
stars, and the earth's atmosphere, dust, clouds etc in the case of
artificial satellites.

In ancient times celestial objects were ranked in six classes of apparent
magnitude.  The brightest of these were first magnitude and those just
visible to the naked eye were sixth magnitude.  This system became
inadequate as fainter objects were discovered with the aid of optical
instruments such as the telescope.

In the 1850's it was proposed that the physiological reponse of the eye to
physical stimulus was proportional to the logarithm of that stimulus
(Weber-Fechner law).  A difference in apparent magnitude of two seperate
objects is thus proportional to the difference in the logarithms of their
brightness, i.e. to the logarithm of the ratio of their brightness.

To make the magnitude scale precise, the English Astronomer N.R. Pogson
proposed, in 1956, that a difference of five magnitudes should correspond
exactly to a brightness ratio of 100 to 1.  (W.Herschel had shown this to be
approximately true).  Hence two stars that differ by a single magnitude have
a brightness ratio of:
_____
5 /            : 1   OR  2.512 : 1
\/  100

This ratio is known as the Pogson ratio.

This can now be applied to any magnitude difference as per the following
example.

A magnitude 2 star (X) is 3 magnitudes brighter than a mag 5 star (Y).
i.e.  5 - 2 = 3
the actual brightness difference can now be calculated using the Pogson
ratio.
3
(2.512)   = 15.85

Hence star X is 15.85 times brighter than star Y.

To create an absolute scale, a group of stars near the north celestial pole
where then used as standards to define precise measurement of any other
object.  This group is known as the North Polar Sequence.

As technology developed and more precise measuring techniques were brought
into play (photo electric plates, CCD's etc) it was found that some stars
and indeed other celestial objects were brighter than mag 0.  Hence the
introduction of negative numbers, the greater the absolute value of the
negative number the brighter the object:

_
Object X has mag of -4.  Object Y has mag of 5.  X is 9 Mags brighter
than Y.  i.e. 5 -  4 = 9
9
(2.512)  =  3982.7

Hence object X is 3982.6 times as intense as object Y

To give you an idea of the variation of objects across the scale as found in
the real world, here are a few approximate magnitudes.

Full Moon                                      = -12
The Sun                                        = -27
Venus (at maximum)                      = - 4.7
Sirius (the brightest star)                = - 1.47
Mir (on a good pass)                      = - 2
Bright Iridium Flare                         = - 8
Faintest Naked Eye Object             = + 6
Faintest Object Hubble Can Detect  = +25

If It's the space station you're after it'll be somewhere around mag 2 to
mag -1 on fair to good pass at the moment.  It of course will only get
brighter as it gets bigger.  In fact I would even say that it's probable
that the ISS will become the 3rd brightest object in our skies.

L8r

Jason Gibson
Melbourne Australia
37.9803 S    145.0623 E    40m
-----Original Message-----
From: John Burgess <burgess@ixtel.com>
To: scribble <scribble@eisa.net.au>
Date: Monday, 7 December 1998 22:35
Subject: RE: More #25544 Observation

Dear Jason

I saw your seesat message and I am very new to all of this.

Please could you tell me how magnitude works.

I presume it is literally the brightness, but I don't understand
whether -7 is brighter than 2 or whether 4 is brighter than 5.

If you do not have time to explain I quite understand but maybe you
might know of an explanation on the www.

Thanks alot.

Regards

John Burgess

World Office (44) 700 7111 001
```