[AZ-Observing] Re: Some Mars Figuring (while waiting for clear sk ies!)...

Hmm.

First of all,

  (d/2)^2*pi is equivalent to (d^2/4)*pi by association (or pi*r^2 for that
matter)

But I think it's misleading to calculate areas as you have, since arcseconds
are not a linear dimension but an angular one. In a way, the size of Mars in
arcseconds is already an "area". This angle can be calculated from:

theta = (180/pi)*3600*2*Arctan(d/(2r))

where:

 theta = angular size (in arcseconds) 
 180/pi = degrees per radian conversion
 3600 = arcseconds/degree conversion
 d = diameter of mars = 6794 kilometers
 r = distance from Earth to Mars (if you use the table at the EVAC web site,
you have to convert from Astronomical Units to kilometers, so multiply the
AU by 149.6X10^6 to get km)

I tried this for a couple days on the EVAC site listing, and the sizes I
calculated compared favorably.

r is the important number here as it will begin to change very rapidly as
Earth passes mars on the inside lane of the "racetrack" around the Sun.

Solid angles (measured in steradians) are calculated in a different way.

On the other hand, I agree with your conclusion. Get thee to a telescope!!!





-----Original Message-----
From: Tejera, Rick [mailto:rtejera@xxxxxxxxxxx]
Sent: Wednesday, August 27, 2003 6:25 AM
To: 'az-observing@xxxxxxxxxxxxx'; EVAC@xxxxxxxxxxxxxxxxx
Subject: [AZ-Observing] Re: Some Mars Figuring (while waiting for clear
sk ies!)...


Greg,
Just to point out the area of a circle is defined as PI*r^2 or pi*(d^2)/4.
Looks like you used the diameter in the formula calling for radius.

I had to look it up myself, been a while for me, too.

Rick 

-----Original Message-----
From: Greg Askins [mailto:gregaskins@xxxxxxx]
Sent: Tuesday, August 26, 2003 6:43 PM
To: EVAC@xxxxxxxxxxxxxxxxx; az-observing@xxxxxxxxxxxxx
Subject: [AZ-Observing] Some Mars Figuring (while waiting for clear
skies!)...


While waiting for the skies to get dark (and hopefully get/stay clear) 
to view Mars this week, I started wondering just how much larger Mars 
is this week than it will be over the next few weeks (as our weather 
here in Phoenix should start to get better). Looking through my recent 
Sky&Telescopes and Astronomy magazines, I was surprised how much 
smaller Mars was depicted by the end of September (even though its 
diamater measurement was still almost 85% of maximum).
With some time on my hands (since the observing here has been difficult 
and doesn't look great tonight during the evening hours), I decided to 
calculate the total viewable size of Mars (its total area) including 
the effect of its upcoming phase. Using the data supplied here by EVAC:
http://www.eastvalleyastronomy.org/EVAC/mars-ephem03.htm
I get a total size of Mars at maximum of 494.214 square arc-seconds (I 
think this is the proper notation). I used this equation: 
(25.11/2)squared X 3.1416 X .998 phase.


Now for the comparisons (% of Max. Size and Total Size -- including 
phase effect):

Maximum (8/27/03):                      (100%)   494.214 sq.arc-secs

One month later 9/27/03:                (69.7%)  344.537 sq.arc-secs

Star party on 10/01/03:         (64.1%)  316.910 sq.arc-secs

Star party on 10/03/03:         (61.3%)  303.127 sq.arc-secs

Star party on 10/10/03:         (52.4%)  258.985 sq.arc-secs

Middle of Oct. 10/15/03:                (46.7%)  230.743 sq.arc-secs


This total size measurement should be important both for astro-imaging 
and for the overall impressiveness of Mars in the eyepiece. Somewhat 
surprisingly, by the end of September, Mars will be at less than 2/3rds 
of it's maximum size tonight -- and before the middle of October will 
be at less than 50% of maximum.

Morale of the story:  pray for some clear skies the next two weeks!

Greg Askins
Chandler, AZ

P.S. If there are mistakes in my math, I apologize -- it's been a while!

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