Gravitational Fields Problem: Find the fraction ΔgM /g

[hardygirl989]

Homework Statement

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.)

Homework Equations

F=(Gm)/R^2

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.

 

[anathema]

Thank you for your post. Your attempt at a solution looks correct, but there is one small mistake in your calculation. When calculating the fraction ΔgM/g, you should not use the negative sign in front of ΔgM. This is because the negative sign indicates the direction of the force, not the magnitude. So the correct answer should be 0.036776, not -0.036776.

I hope this helps. Keep up the good work in your studies!