[AZ-Observing] Re: Mars and the Moon

To quote Mythbusters: Warning! Science Content

   I posted a link yesterday to this plot of the separation between Mars 
and the Moon over the span of a few hours Sunday:

<http://members.cox.net/f7j9jwirjsljejic/separation.jpg>

   At the time, I mentioned that I was intrigued by but didn't know the 
reason for the difference in slope before and after minimum separation. 
  Giving the question further consideration, I decided that it was most 
likely the result of the changing point of observation over the time 
period plotted, due to rotation of the Earth.  To investigate further, I 
expanded the range of the plot to cover a 48-hour period.

<http://members.cox.net/f7j9jwirjsljejic/separation_48t.jpg>

   In this plot, the X-axis shows Julian date - 2454450.0.  A bit more 
interesting, and if you look carefully, you can see that there is some 
sign of a one-day component in the shape of the curve (note the bend at 
about 8.0 and again at about 9.0 on the X axis).  To further test my 
speculation, I plotted the same data in the geocentric rather than 
topocentric reference frame.

<http://members.cox.net/f7j9jwirjsljejic/separation_48g.jpg>

   Now the plot appears highly symmetrical, and I'm satisfied that I've 
answered my question.

   Now for anyone who hasn't moved on to other messages or gone to watch 
a rerun of The Apprentice, you may be thinking, "Right, but what the 
heck do geocentric and topocentric mean?"  It's fairly simple, and 
except in special cases, the difference is usually negligible.  The 
geocentric reference frame is that of a hypothetical observer located at 
the Earth's center, whereas the topocentric frame relates to us ordinary 
mortals at some particular point on the surface of the planet.  Going 
back to my first plot, it showed the separation between the Moon and 
Mars as seen from my observatory a few kilometers southwest of Maricopa. 
  As I mentioned in the initial posting, there was an occultation of 
Mars by the Moon for observers in the far north.  The difference is 
that, as seen from the Moon, the Earth subtends an angle of about two 
degrees.  Those two degrees are significant in the case of close 
apparitions involving the Moon, as well as the occasional Earth-crossing 
asteroid, spacecraft, etc.

   As for the difference in slope in the original plot, as the Earth 
rotates our vantage point changes by almost two degrees.  This caused 
the apparent separation to decrees faster than it increased following 
closest approach Sunday evening.

                                -- Mike --
-- 
cal_donley@xxxxxxx
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