Where Is the Point of Zero Net Gravitational Force Between Earth and the Moon

[elasticities]

Homework Statement

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?

Homework Equations

Fg=Gm1m2/R^2

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?

 

[Doc Al]

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'.

 

[elasticities]

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'.

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.

 

[Doc Al]

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.

What do you think?

 

[elasticities]

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

Is that right? Do I isolate for x?

 

[Doc Al]

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

Is that right? Do I isolate for x?

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

 

[elasticities]

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

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

 

[Doc Al]

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

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.

 

[elasticities]

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

 

[Doc Al]

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

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