What Is the Net Force on the Moon During Eclipses?

[Chutzpah]

Homework Statement

mass of star = 2.53 x 1030 kilograms
mass of planet = 5.25 x 1024 kilograms
mass of moon = 8.09 x 1022 kilograms
average distance from star to planet = 1.14 x 1011 meters
average distance from planet to moon = 4.59 x 108 meters

Use the data above to determine the net force exerted on the moon by the planet and the star during:
a. a solar eclipse.
WebAssign will check your answer for the correct number of significant figures. wrong check mark N
b. a lunar eclipse.
WebAssign will check your answer for the correct number of significant figures. wrong check mark N

Homework Equations

Fg=G x M1 x M2/Dsquared
Note that the lineup for a solar eclipse is Sun-Moon-Earth
A lunar eclipse lineup is Sun-Earth-Moon
This I am sure of.

The Attempt at a Solution

My attempt was to find the netforce of gravity on the moon.
Here is my work which produced a wrong answer.
a) Fgrav,net=Gm(moon)M(sun)/Dsquared(the distance between the star and the planet- the distance between the planet and the moon) - GM(moon)M(earth)/dsquared
Perhaps I added the distances wrong- but I know when the moon is in the middle I will have opposite signs for the forces from each planet and the lunar eclipse should produce. I got 9.18E20 rounded for my answer to part a. Any ideas? Am i using the distance wrong? Any similar answers? Any other forces to be accounted for in the net sum? Thanks.

 

[berkeman]

It looks like you are using the correct approach. Can you write out your math steps to make it easier to check them?