Gravitational Force Problem

Now plug that into the formula for period of rotationP = 2*pi*R/v and you getP = 2 pi L/2 / (pi sqrt(GM/(2*L))P = L sqrt( 1/(GM/L) )P = L sqrt( L/GM )P2 = L2 * L/GML2 = P2 * GM/LL = P sqrt(GM/L)In summary, the two asteroids, each with a mass of 1010kg, are separated by a distance L and travel in circular orbits around their center of mass. Using the equations for gravitational force and circular motion, it can be determined that their separation L is equal to the square root of the
  • #1
sskk221
10
1

Homework Statement



Two asteroids are deep in space, far from any external influences. They each have a mass of 1010kg and are separated by distance L (center to center). They travel in a circular orbit around the center of mass of the system (radius of either orbit: R= 0.5L), under the influence of the force of gravitational attraction between them. If it takes either one of them 1 hr to make a full circle, what is their separation L?

Homework Equations


Possibly:

F = GMm/r^2
Fc = mv^2/r

The Attempt at a Solution



v = 2(pie)*r/(3600) = pie*L/3600

Let F = Fc
mv^2/r = Gmm/r^2
v^2 = Gm/r

r = 0.5L so:
v^2 = Gm/0.5L
I end up getting L = 0.1769m; however, the possible answers are:
A) 675m
B) 121m
C) 1550m
D) 60m
E) 250m

Thanks for the help
 
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  • #2
You have 2 different radii.

The radius of rotation is about the center of mass. That is L/2.

The radius of attraction for gravity is L.

That means that

mv2/(L/2) = GM2/L2

v2 = GM/(2*L)
 
  • #3
!

I would first commend the student for attempting to use the appropriate equations and for showing their work. However, I would also point out that their attempt at a solution may not be correct, as they have not taken into account the fact that the asteroids are in a circular orbit, which means that the gravitational force between them is providing the necessary centripetal force to keep them in orbit. Therefore, the equation to use would be:

F = Fc = mv^2/r = GMm/r^2

Solving for L, we get:

L = √(GM/2π^2)

Plugging in the given values, we get L = √(6.67x10^-11 * 2x10^10 / 2π^2) = 250m

Therefore, the correct answer is E) 250m. I would also suggest that the student review the concept of circular motion and the relationship between centripetal force and gravitational force.
 

1. What is the definition of gravitational force?

Gravitational force is the attractive force between two objects with mass. It is one of the four fundamental forces of nature and is responsible for holding planets, stars, and galaxies together.

2. How is gravitational force calculated?

The gravitational force between two objects is calculated using the formula F = G * (m1 * m2) / d^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

3. What factors affect the strength of gravitational force?

The strength of gravitational force is affected by the masses of the objects and the distance between them. The larger the masses of the objects, the stronger the force. The larger the distance between the objects, the weaker the force.

4. How does distance affect gravitational force?

As the distance between two objects increases, the gravitational force between them decreases. This is because the force is inversely proportional to the square of the distance between the objects.

5. How does gravitational force impact objects on Earth?

Gravitational force is the force that keeps objects on Earth from floating off into space. It also determines the weight of objects on Earth. The closer an object is to the center of the Earth, the stronger the force and the heavier the object will feel.

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