Question

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

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force is \(F = G\frac{m_1m_2}{r^2}\), where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between them.

Step2: Analyze the first model

In the first model, \(m_1 = 1M_{\odot}\), \(m_2 = 1M_{\odot}\), assume the distance \(r_1\) (since it's a reference for comparison). The force \(F_1=G\frac{1\times1}{r_1^2}=G\frac{1}{r_1^2}\)

Step3: Analyze the second model

In the second model, \(m_1 = 1.5M_{\odot}\), \(m_2 = 1M_{\odot}\), assume the distance \(r_2=r_1\) (same as the first model's distance for fair mass - only comparison). The force \(F_2 = G\frac{1.5\times1}{r_2^2}=G\frac{1.5}{r_1^2}\) (because \(r_2 = r_1\))

Step4: Analyze the third model

In the third model, \(m_1 = 0.25M_{\odot}\), \(m_2 = 1M_{\odot}\), assume the distance \(r_3 = 2r_1\) (visually larger distance). The force \(F_3=G\frac{0.25\times1}{r_3^2}=G\frac{0.25}{(2r_1)^2}=G\frac{0.25}{4r_1^2}=G\frac{0.0625}{r_1^2}\)

Since \(F_2>F_1>F_3\)

Answer:

Second model, First model, Third model