# Universal Gravitation Question!

1. Jul 13, 2010

### elasticities

1. The problem statement, all variables and given/known data
At a certain point between Earth and the Moon, the net gravitational force exerted on an object by the Earth and the Moon is ZERO. The mass of the Moon is 1.2% the Mass of the Earth. The centre to centre distance between the Moon and the Earth is 3.84*10^5 km.

i) WHERE IS THIS POINT LOCATED?
ii) What is the meaning of the quadratic root whose value exceeds the Earth-Moon distance?

2. Relevant equations
Fg=Gm1m2/R^2

3. The attempt at a solution
Fnet=0
Fnet=Fmoon-Fearth
Fmoon=Fearth
Rmoon=x
Rearth=3.84*10^8m-x
Mmoon=1.2
Mearth=100

Uh....what's next? And am I right so far?

2. Jul 13, 2010

### Staff: Mentor

So far, so good. Now use the Gravity equation to get expressions for Fmoon and Fearth. Hint: Let the mass of the object be 'm'.

3. Jul 13, 2010

### elasticities

Do I need to put a value in for 'm' or can I just get rid of it since its on both sides of the equation.

4. Jul 13, 2010

### Staff: Mentor

What do you think?

5. Jul 13, 2010

### elasticities

100/(3.84*10^8m-x)^2 = 1.2/x^2

Is that right? Do I isolate for x?

6. Jul 13, 2010

### Staff: Mentor

Looks good to me. You'll have to solve for x. Rearrange terms to put the quadratic into standard form.

7. Jul 13, 2010

### elasticities

I'm not getting the right answer which is supposed to be 3.5*10^5m from Earth's centre. I will try again.

8. Jul 13, 2010

### Staff: Mentor

Realize that you've defined your variable X to be the distance from the Moon's center. Once you have X, you can then figure out the distance from the Earth's center.

9. Jul 28, 2010

### elasticities

Ok thanks, I think the textbook answer was just wrong. :)

10. Jul 28, 2010

### Staff: Mentor

I suspect that the book's answer was in km, not m.