A synodic day is the period of time it takes for a planet to rotate once in releation to the body it is orbiting (as opposed to a sidereal day which is one complete rotation in relation to the stars).
For Earth, this is known as a Solar Day, and is 24hrs long.
As shown in the table, the rotation period and day length are nearly identical for all of the outer planets.
To explain why the day length, or synodic period of rotation, is different from the sidereal period of rotation, we consider how a given place moves around a planet, and the way in which this changes its view of the sky, during one rotation period.
For the second method, we divide the rotation period by the number of days in a year, and obtain 2 minutes 12.58 seconds as the difference between the rotation period and the length of the day, so that the day length would be 24 hours 39 minutes 35.24 seconds.
The mean length of a lunar synodic month is 29.53059 civil solar days (of 24 hours exactly) and divided by 30 this gives the lunar synodicday a mean length of 0.984353 civil solar days.
I note that the choice of 30 synodicdays and 27 sidereal days (and before that, of 27 asterism segments) in the respective months was made so that the length of each day would be closest to the length of the solar day.
Apart from that, it is obvious to the observer that a lunar synodicday can be entirely contained within a solar day so that at the start of today the synodicday number, called tithi can be 10 and at the start of tomorrow 12, day 11 being entirely contained within today.
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