# Gravitational Fields Problem: Find the fraction ΔgM /g

1. Apr 15, 2012

### hardygirl989

1. The problem statement, all variables and given/known data

Let ΔgM represent the difference in the gravitational fields produced by the Moon at the points on the Earth's surface nearest to and farthest from the Moon. Find the fraction ΔgM /g, where g is the Earth's gravitational field. (This difference is responsible for the occurrence of the "lunar tides" on the Earth.)

2. Relevant equations
F=(Gm)/R^2

3. The attempt at a solution
R = Radius of Earth = 6.37*10^8 m
r,min = 378033000 m
r,max = r,min + (2*radius of the earth) = 378033000 + (2 * 6.37*10^8) = 1.65*10^9 m
G = universal gravitational constant = 6.67 * 10^-11 Nm^2/Kg^2
m = mass of moon = 7.36 * 10^22 Kg
M= Mass of the Earth = 5.98*10^24 Kg

ΔgM = -((G*m)/(r,min^2)) + ((G*m)/(r,max^2))
ΔgM = -((6.67 * 10^-11*7.36 * 10^22)/(378033000^2)) + ((6.67 * 10^-11*7.36 * 10^22)/(1.65*10^9^2))

ΔgM = -.000036 N

g = F = (6.67 * 10^-11*5.98*10^24)/6.37*10^8^2 = .000983 N

ΔgM/g = -.000036/.000983 = -.036776N

This answer does not seem to make sense...Did I do something wrong? Thanks.