Saturnday, Sunday, Moonday

The ancient Greeks inherited the practice of astrology from the
Babylonians, but introduced many new features.  For example,
where the Babylonians tended not to place the major planets in
any physically significant order, the Greeks ordinarily listed
them on horoscopes like this

     Sun  Moon  Saturn  Jupiter  Mars  Venus  Mercury

Even though they didn't have a heliocentric model of the solar
system, they were still able to deduce the order of the planets,
beginning from Saturn as the furthest out and descending to Mercury
as the closest in, based on the their periods of their "wanderings"
across the night sky.

On this list the Sun and Moon are placed somewhat arbitrarily at
the beginning, since their apparent motions obviously aren't of the 
same nature as those of the planets.  It was also common for the
Greeks to place the Moon last, so that it was considered to be 
even "lower" than Mercury.  In addition, the Greeks could distinguish
between the "interior" planets (Venus, Mercury) and the "exterior
planets (Saturn, Jupiter, Mars) based on their apparent motions,
and they sometimes placed the Sun in the "center" between these
groups.  This led to the arrangement

     Saturn  Jupiter  Mars  Sun  Venus  Mercury  Moon

Now, each of the 24 hours (an Egyptian invention) of the day was 
though to be "ruled" by one of these 7 planets, and the rulers would 
cycle around in the arrangement shown above.  Thus, if we denote 
the planets by the symbols T,J,R,S,V,Y,M respectively, and begin 
the first day with the Sun, we have

                            Hour
 Day    1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4

  1     S V Y M T J R S V Y M T J R S V Y M T J R S V Y
  2     M T J R S V Y M T J R S V Y M T J R S V Y M T J
  3     R S V Y M T J R S V Y M T J R S V Y M T J R S V
  4     Y M T J R S V Y M T J R S V Y M T J R S V Y M T
  5     J R S V Y M T J R S V Y M T J R S V Y M T J R S
  6     V Y M T J R S V Y M T J R S V Y M T J R S V Y M
  7     T J R S V Y M T J R S V Y M T J R S V Y M T J R
    
After the 7th day the cycle repeats, so the 8th day is the same as
the 1st, and so on.  (Fortunately, 7 if coprime to 24.)  Each day 
in the cycled was said to be "ruled" overall by the planet that 
rules the first hour of that day, so the rulers of the seven days 
were S,M,R,Y,J,V,T, which is to say

      Sun  Moon  Mars   Mercury  Jupiter  Venus  Saturn

According to Neugebauer, this is also the arrangement of the planets 
that was used most often in Hindu astronomy.  From this we get the 
names of the days in the week

              Latin         French      Saxon        English

  Sun       Dies Solis     Dimanche    Sun's day      Sunday
  Moon      Dies Lunae     Lundi       Moon's day     Monday
  Mars      Dies Martis    Mardi       Tiw's day      Tuesday
  Mercury   Dies Mercurri  Mercredi    Woden's day    Wednesday
  Jupiter   Dies Jovis     Jeudi       Thor's day     Thursday
  Venus     Dies Veneris   Vendredi    Frigg's day    Friday
  Saturn    Dies Saturni   Samedi      Seterne's day  Saturday

Wodin (or Odin) was one of the principal gods in Scandinavian and 
Teutonic mythology, and he seems to have somehow become identified 
with the Roman Mercurius.  Likewise Tiw was identified with Mars.  
Frigg was the wife of Odin, and likened to Venus.  The Germanic god 
Thor is similar to Jupiter, in the sense of being regarded as the 
"main" god in most northern European countries.  This shows how 
the common names for our days of the week have been influenced by 
a wide range of peoples and traditions, including the Babylonians 
(astrology), Egyptians (24 hour division of the day), Greeks 
(arrangement of the planets), Romans (Latin names of the gods), 
and Scandinavian mythology (for the Germanic names).