On this web page, you can see the calculation of the synodic rotation periods of The Eight Inner Solar System bodies (ie:- The Sun, Mercury, Venus, Earth, Mars, The Moon, and Mars satellites - Phobos and Deimos).
The Sun's synodic rotation period = 26.44803 Earth days. To verify this, click on this link:-
The Moon's synodic revolution period (which is the same as its synodic rotation period, due to "tidal locking") = 29.5305882 Earth days. To verify this, click on this link:-
Earth's synodic rotation period = 1 Earth (solar) day.
The synodic rotation periods of Mercury, Venus, and Mars are calculated in the following manner:-
The (sidereal) rotation period of Mercury = 58.6462 Earth days, and The (sidereal) rotation period of Venus = 243.0187 Earth days. To verify this, click on this link:-
The (sidereal) rotation period of Mars = 1.025957 Earth days. To verify this, click on this link:-
The Earth's orbital period (The Earth Sidereal Year) = 365.25636 Earth days. To verify this, click on this link:-
Mars' orbital period = 686.9782 Earth days. To verify this, click on this link:-
With all the above information, we are now ready to calculate the synodic rotation periods of Mercury, Venus, and Mars:-
Mercury’s synodic rotation period =
1 ÷ [(1 ÷ 58.6462) MINUS (1 ÷ 365.25636)] = 69.8636 Earth days.
Venus’ synodic rotation period =
1 ÷ [(1 ÷ 243.0187) + (1 ÷ 365.25636)] = 145.9276 Earth days. (The + sign because Venus has retrograde rotation!)
Mars’ synodic rotation period =
1 ÷ [(1 ÷ 1.025957) MINUS (1 ÷ 686.9782)] = 1.02749 Earth days. (Different format because Mars is a superior planet!)
Now we will calculate the synodic rotation periods for Phobos and Deimos.
Phobos' orbital period = 0.31891023 Earth days, and Deimos' orbital period = 1.2624407 Earth days. (Their rotation periods are the same as their orbital periods, due to "tidal locking"). To verify this, click on this link:-
We have already seen (above) that Mars' orbital period = 686.9782 Earth days.
Phobos’ synodic rotation period =
1 ÷ [(1 ÷ 0.31891023) MINUS (1 ÷ 686.9782)] = 0.319058343 Earth days.
Deimos’ synodic rotation period =
1 ÷ [(1 ÷ 1.2624407) MINUS (1 ÷ 686.9782)] = 1.264764923 Earth days.