Gravitational force = 0 between two planets?

In summary, a planet of mass M has a moon of mass m in a circular orbit of radius R. An object is placed between the planet and the moon on the line joining the center of the planet to the center of the moon. By setting the net gravitational force on the object to zero, we can solve for the distance, d, from the center of the planet to the object. This can be done by using the equation M/d^2 = m/(R-d)^2 and solving for d.

Which is the answer?

  • ((M-m)/(M+m))R

    Votes: 0 0.0%
  • (M+m)/(M-m)

    Votes: 0 0.0%
  • (((M^.5)+(m^.5))/(M-m)) * (M^.5) R

    Votes: 0 0.0%
  • (((M-m)/(M+m))^.5) * R

    Votes: 0 0.0%
  • (((M^.5)-(m^.5))/(M-m)) * (M^.5) R

    Votes: 0 0.0%

  • Total voters
    0
  • Poll closed .
  • #1
Hayden_
1
0

Homework Statement



A planet of mass M has a moon of mass m in a circular orbit of radius R. An object is placed between the planet and the moon on the line joining the center of the planet to the center of the moon so that the net gravitational force on the object is zero. How far is the object placed from the center of the planet?

Homework Equations



Fg=G(Mm/R^2)

I used the variable d to describe how far the object is placed from the center of the planet

The Attempt at a Solution



G(M(mass of object))/d^2 = G(m(mass of object))/(R-d)^2

G and mass of object cancel out

M/d^2 = m/(R-d)^2
 
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  • #2
find d.?
 
  • #3
Looks good to me!

Hi Hayden! Welcome to PF :smile:

Hayden_ said:
M/d^2 = m/(R-d)^2

Looks good to me!

Now all you have to do is to solve the quadratic equation … :smile:
 

1. How is it possible for the gravitational force to be zero between two planets?

The gravitational force between two objects is determined by their masses and the distance between them. If the masses of the two planets are significantly different, or if they are very far apart, the force of gravity between them can approach zero.

2. If the gravitational force is zero, does that mean the planets are not affected by each other at all?

No, the gravitational force may be zero, but the planets can still influence each other's orbits and movements through other forces, such as electromagnetic forces.

3. Can the gravitational force between two planets ever be exactly zero?

In theory, yes, if the masses of the two planets are equal and they are infinitely far apart, the gravitational force between them would be exactly zero. However, in reality, there will always be some level of gravitational force between any two objects with mass.

4. Is there any significance to the gravitational force being zero between two planets?

Yes, it can indicate that the two planets are not interacting with each other in a significant way, which may be due to their distance or mass differences. This can also affect the stability and dynamics of their orbits.

5. Can the gravitational force between two planets ever change from zero?

Yes, if the distance between the two planets changes, the gravitational force between them will also change. Additionally, changes in the masses of the planets can also affect the force of gravity between them.

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