Physics
posted by Anna .
The Moon causes tides because the gravitational force it exerts differs between the side of the Earth nearest the Moon and that farthest from the Moon. Find the difference in the accelerations toward the Moon of objects on the nearest and farthest sides of the Earth. (The mass of the Moon is Mm = 7.36 1022 kg, the radius of the Earth is RE = 6.37 106 m and the distance between the Earth and the Moon is d = 3.82 108 m.)

Moon orbit radius r = 3.84•10^8 m
Earth radius R = 6.37•10^6 m
F1 = G •m₁•m₂/(r+R)²
m₁ = mass of the object
m₂ = moon's mass
r+R = 3.84•10^8 + (m)
far side
F2 = G• m₁•m₂/(rR)²
m₁ = mass of the oject
m₂ = moon's mass
rR = 3.84•10^8  6.37•10^6 (m)
∆F = G• m₁•m₂/(rR)² – G• m₁•m₂/(r+R)²
∆F = G• m₁•m₂[ 1/(rR)² – 1/(r+R)² ]
∆F/m₁ = ∆a = G•m₂[ 1/(rR)² – 1/(r+R)² ]