Answer:
26days
Explanation:
Centripetal force is the force that tend to pull an object moving in a circular path towards the centre.
Mathematically;
Centripetal force Fc = mv²/r where;
m is the mass of the moon = 9.4×10^21kg
v is the velocity of the moon in a circular orbit
r is the radius of the circular orbit = 1.5×10^8m
Fc is the gravitational force experienced by the moon = 1.1×10^19N
Before we can get the period, we need to know the velocity at which the moon is moving around the circular orbit.
Substituting the given datas in the formula above we have;
1.1×10^19 = 9.4×10^21v²/1.5×10^8
Cross multiplying we will have;
1.65×10^27 = 9.4×10^21v²
v² =1.65×10^27/9.4×10^21
v² = 0.176×10^6
v= √0.176×10^6
v = 419.53m/s
To get the moon orbital period T, we will use the relationship;
T = 2πr/v where
T = 2π(1.5×10^8)/419.53
T = 9.42×10^8/419.53
T = 2,246,508.7seconds
Converting to days
If 24hours = 1day
(24×60×60)seconds = 1day
If 86400seconds = 1day
2,246,508.7seconds = x days
Cross multiplying we have
x × 86400 = 2,246,508.7
x = 2,246,508.7/86,400
x = 26days
Therefore the moon orbital period in earth days is approximately 26days.
