Determine the acceleration of the moon with respect to the earth using the following data: the distance between the earth and the moon is 3.85 10^5 km , and the time taken by the moon to complete one revolution around the earth is 27.3 days .

Step-by-step solution

The distance between the earth and the moon is r = 3.85 10^5 km = 3.85 10^8 m . The time period of revolution of the moon is T = 27.3 days = 27.3 24 60 60 s 2.36 10^6 s . The centripetal acceleration of the moon with respect to the earth is given by: a = ^2 r = ( 2 T )^2 r = 4 ^2 r T^2 Substituting the values: a = 4 ^2 3.85 10^8 (2.36 10^6)^2 a = 4 9.87 3.85 10^8 5.57 10¹² a = 152 10^8 5.57 10¹² a 27.3 10⁻⁴ m/s ^2 a = 2.73 10⁻³ m/s ^2