Jupiter and Saturn: will "opposites attract"??

Event Date: March 6th

Time: 11:36(.05)PM

Brief

   Alright, so you may be thinking that subject header for this entry--which I came up with on the fly in about 15 seconds--is awkward and perhaps wondering what it has to do with astronomy.  There is a connection however--albeit an abstract one--with what I will talk about here!

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Almost 12 years ago, May 28th 2000, Jupiter and Saturn had a separation of 1.1º.   A little over 10 years later on August 13th of 2010, they were at their furthest separation possible, at opposite sides of the celestial dome.  Since then, faster Jupiter has closed the gap and has started to catch up with Saturn in orbit.  

In regards to my header, are you catching on yet?? Let's examine further.

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   The image below shows 180º of celestial dome, while Jupiter sets and Saturn rises.  Each day as it catches up with Saturn, this month specifically, the gaps between Jupiter's [prograde] setting times are larger than Saturn's [retrograde] rising.

click on images to enlarge: courtesy of Starry Night Pro Plus, version 6.4.3, by Simulation Curriculum Corp.

Detailed

At 152.8º separated and shrinking, both planets are 12º 37.4' in altitude at the time above.  If you have an alt/az telescope centered on Jupiter about a minute earlier, slew it in azimuth only to Saturn over the course of a minute or less, and Saturn would appear in the field at about the same centered spot as Jupiter.  This is a fun thing to try because each evening, the precise-same altitude for both will be slightly higher.  The opposite would hold true if Jupiter was currently in retrograde and slower Saturn in prograde, although such would mean that we would see them "flipped" in the sky at this time of night; Jupiter rising and Saturn setting, that is.  Jupiter's retrograde at peak is not much slower than its prograde.

   The rate of catchup each year until their next encounter depends on which planet is in prograde or retrograde motion.  In some cases, one may be moving one way to another while the other is stationary.  Jupiter has started to pick up speed in prograde as mentioned in recent entries, while Saturn is starting to increase in retrograde.  As a result, Jupiter is starting to catch up a little more quickly than it was even a week ago.  Can you predict when Jupiter catches up with Saturn?  The separation at closest encounter will even differ from the Y2K aforementioned, since it will happen in a part of the sky where the orbits for the two will be closer or further from each other.  Can you figure that part out too?  I already looked up the answer, which I will obviously not reveal here.

 If watching Jupiter close in on Saturn annually, give it a try, and see how close you come in predicting correctly!