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

AI Thread Summary
The discussion revolves around finding the point of zero net gravitational force between the Earth and the Moon, given their masses and the distance between them. Participants clarify that the gravitational forces from both celestial bodies must be equal for this point to exist. The correct approach involves using the gravitational force equation and rearranging terms to find the distance from the Earth's center. There is confusion regarding the expected answer, with one participant suspecting a discrepancy in units between the textbook answer and their calculations. Ultimately, the conversation emphasizes the importance of correctly defining variables and units in gravitational calculations.
elasticities
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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?
 
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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'.
 
Doc Al said:
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.
 
elasticities said:
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? :wink:
 
100/(3.84*10^8m-x)^2 = 1.2/x^2

Is that right? Do I isolate for x?
 
elasticities said:
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.
 
Doc Al said:
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.
 
elasticities said:
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.
 
Ok thanks, I think the textbook answer was just wrong. :)
 
  • #10
elasticities said:
Ok thanks, I think the textbook answer was just wrong. :)
I suspect that the book's answer was in km, not m.
 

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