We will calculate the synodic period, as it is the time it takes for the object to reappear at the same point in the sky with respect to the sun, when viewed from Earth. For this problem we will apply the concepts related to the orbital period ( Kepler's Third Law ) which is determined as
[tex]T = 2\pi \sqrt{\frac{r^3}{G\cdot m}}[/tex]
Where,
r = Radius/Distance
G = Gravitational Universal Constant
m = Mass of the object
Replacing,
[tex]T = 2\pi \sqrt{\frac{(3.8*10^8)^3}{(6.67*10^{-11})(5.97*10^{24})}}[/tex]
[tex]T = 2332411.53s[/tex]
[tex]T = 26.99days[/tex]
