Question

newtons law of universal gravitation describes how celestial objects are gravitationally attracted to each other based on their masses and distance from each other. each model below shows two stars of varying masses separated by different distances. put the models in order from strongest to weakest gravitational force. strongest image of two stars: 2m₀ and 1m₀ image of two stars: 0.5m₀ and 0.5m₀ image of two stars: 2m₀ and 2m₀ weakest submit

Explanation:

Newton's law of universal gravitation is given by \( F = G\frac{m_1m_2}{r^2} \), where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between their centers. The force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

Step 1: Analyze the third model (2\( M_⊙ \) and 2\( M_⊙ \), closest distance)

Let the distance between the stars in the third model be \( r_3 \). The product of the masses is \( (2M_⊙)(2M_⊙) = 4M_⊙^2 \).

Step 2: Analyze the first model (2\( M_⊙ \) and 1\( M_⊙ \), middle distance)

Let the distance between the stars in the first model be \( r_1 \). The product of the masses is \( (2M_⊙)(1M_⊙) = 2M_⊙^2 \).

Step 3: Analyze the second model (0.5\( M_⊙ \) and 0.5\( M_⊙ \), largest distance)

Let the distance between the stars in the second model be \( r_2 \). The product of the masses is \( (0.5M_⊙)(0.5M_⊙) = 0.25M_⊙^2 \).

Assuming the distances: From the diagram, the third model has the stars closest together (\( r_3 \) is the smallest), the first model has a middle distance (\( r_1 \) is larger than \( r_3 \) but smaller than \( r_2 \)), and the second model has the stars farthest apart (\( r_2 \) is the largest).

Now, let's consider the relative forces. Since \( F \propto \frac{m_1m_2}{r^2} \), the third model has the largest product of masses and the smallest distance, so it will have the strongest force. The first model has a product of masses of 2 (compared to 4 for the third and 0.25 for the second) and a middle distance. The second model has the smallest product of masses and the largest distance, so it will have the weakest force.

So the order from strongest to weakest is: third model (2\( M_⊙ \) and 2\( M_⊙ \)), first model (2\( M_⊙ \) and 1\( M_⊙ \)), second model (0.5\( M_⊙ \) and 0.5\( M_⊙ \)).

Answer:

From strongest to weakest:

1. The model with two stars of mass \( 2M_⊙ \) (closest together)
2. The model with stars of mass \( 2M_⊙ \) and \( 1M_⊙ \) (middle distance)
3. The model with two stars of mass \( 0.5M_⊙ \) (farthest apart)