Can Eight Retrograde (seen from Earth) planets occur? First of all, for the purposes of this question Pluto is a planet. So the eight planets being considered are Mercury, Venus, Mars, Jupter, Saturn, Uranus, Neptune and Pluto. 

My question is: can all eight of these planets go retrograde† at the same time? I know that seven can do so on rare instances; there were 12 days of that in the 20th century all in the 1940's and the 1980's. But to show how rare that is there was a block of 400 years in the middle ages with no days of seven retrogrades. Has eight ever happened? Or is it impossible? 

†Retrograde motion as seen from Earth, not retrograde orbits around the Sun.
EDIT: I used the DE431 ephemeris to get the results below. However, if you visit HORIZONS (https://ssd.jpl.nasa.gov/horizons.cgi) and create an ephemeris for Pluto (actually Pluto's barycenter, object 999), the results include this warning:


  The Horizons output log may report using DE431 as the source of target
  or center data, but it is nevertheless using DE433 as an override if
  Pluto is involved. This is to maintain ephemeris consistency for the
  New Horizons  spacecraft encounter at Pluto.


Therefore, my calculations may be inaccurate, above and beyond the normal inaccuracy of predicting planetary data in the past and future.

There are 2 times in the past 15,000 years and 5 times in the next 15,000 years where all 8 planets are in retrograde as observed from Earth.

The table below lists the times when this happens:


The last column is the ephemeris time, the number of seconds since '2000-JAN-01 12:00:00 UTC', which NASA refers to as "the epoch".
The first line in each pair shows the start time of when all 8 planets are in retrograde, and the final planet to enter retrograde to make this true.
The second line in each pair shows the end time when at least one planet is no longer in retrograde, and the planet whose retrograde period has ended.



B.C. 12435-AUG-10 07:52 JUPITER STARTS RETROGRADE -455482152466.038696
B.C. 12435-AUG-24 17:12 MERCURY ENDS RETROGRADE -455480909251.797852

B.C.  4139-MAR-23 15:02 MARS STARTS RETROGRADE -193692373029.630005
B.C.  4139-MAR-28 21:57 MERCURY ENDS RETROGRADE -193691916114.978455

A.D.  7662-APR-27 19:33 MARS STARTS RETROGRADE 178685595220.195740
A.D.  7662-MAY-12 05:19 NEPTUNE ENDS RETROGRADE 178686840014.478882

A.D.  8807-JAN-07 02:02 MERCURY STARTS RETROGRADE 214808680981.726929
A.D.  8807-JAN-20 01:05 JUPITER ENDS RETROGRADE 214809800771.851685

A.D. 10575-FEB-14 21:34 VENUS STARTS RETROGRADE 270604748086.593933
A.D. 10575-FEB-24 18:53 NEPTUNE ENDS RETROGRADE 270605602468.037781

A.D. 13679-NOV-06 16:03 VENUS STARTS RETROGRADE 368580427477.379639
A.D. 13679-NOV-19 01:05 MERCURY ENDS RETROGRADE 368581496795.683594

A.D. 16364-MAR-11 19:25 MERCURY STARTS RETROGRADE 453290109945.561157
A.D. 16364-MAR-13 08:53 MARS ENDS RETROGRADE 453290244824.895996


Notes and caveats:


I wrote https://github.com/barrycarter/bcapps/tree/master/ASTRO/bc-retrograde.c to print out retrograde times for all planets.
The file https://github.com/barrycarter/bcapps/tree/master/ASTRO/all-retrogrades.txt.bz2 shows start and end retrograde times for all 8 planets. NOTE: the lines indicating that planets leave retrograde at "17191-MAR-01 00:00" is incorrect-- that's simply the maximum time for which I could make calculations.
I wrote https://github.com/barrycarter/bcapps/tree/master/ASTRO/bc-moving-backwards.pl to determine which planets were in retrograde at any given time, and used the results to find the times above where all 8 planets were in retrograde.
I spot checked my results against https://www.calsky.com/ -- note that I am computing "ecliptic retrograde", when a planet's ecliptic longitude is decreasing, not "equatorial retrograde", when a planet's right ascension is decreasing.
As always, I invite people to double check my results, and remind everyone not to use my results for anything critical.