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

In summary: I will have to recalculate.I suspect that the book's answer was in km, not m. I will have to recalculate.
  • #1
elasticities
25
0

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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  • #2
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
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.
 
  • #4
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:
 
  • #5
100/(3.84*10^8m-x)^2 = 1.2/x^2

Is that right? Do I isolate for x?
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
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.
 

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

What is universal gravitation?

Universal gravitation is a physical law that describes the attraction between all objects in the universe. It states that every object with mass attracts every other object with mass, and the force of attraction is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

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Sir Isaac Newton is credited with discovering universal gravitation in 1687. He developed the theory of gravity and published it in his book "Philosophiæ Naturalis Principia Mathematica".

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Universal gravitation is responsible for keeping us grounded on the Earth and allowing objects to fall towards its surface. It also governs the movements of planets, stars, and galaxies, and plays a significant role in the formation and evolution of the universe.

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Universal gravitation is a fundamental law of physics that applies to all objects in the universe, regardless of their size or composition. However, at the quantum level, scientists are still exploring the role of gravity, and it may behave differently than predicted by the theory of universal gravitation.

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