To solve this problem it is necessary to apply the kinematic equations of movement description, where the speed of a body is defined as the distance traveled in a given time, that is to say
[tex]v = \frac{x}{t}[/tex]
where,
x = Displacement
t = time
Since the moon is making a path equal to that of a circle, we know by geometry that the perimeter of a circle is given by
[tex]x = 2\pi r[/tex]
[tex]x = 2\pi (3.8*10^8)[/tex]
[tex]x=2.39*10^9m[/tex]
At the same time we have that time is equal to
[tex]t = 28days(\frac{86400s}{1day})[/tex]
[tex]t = 2419200s[/tex]
Using the equation for velocity we have finally that
[tex]v= \frac{x}{t}[/tex]
[tex]v = \frac{2.39*10^9}{2419200}[/tex]
[tex]v = 987.92 m/s[/tex]
Therefore the speed of the Moon in its orbit is 987.92m/s
