Question

each model below shows two stars of varying masses separated by the same distance. select the model that shows the stars with the strongest gravitational force between them.

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force \(F = G\frac{m_1m_2}{r^2}\), 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. Since \(G\) and \(r\) are the same for all models (distance \(r\) is given as same, \(G\) is a constant), we only need to compare \(m_1m_2\).

Step2: Calculate \(m_1m_2\) for each model

• First model: \(m_1 = 1M_{\odot}\), \(m_2=2M_{\odot}\), so \(m_1m_2=(1)(2)M_{\odot}^2 = 2M_{\odot}^2\).
• Second model: \(m_1 = 1M_{\odot}\), \(m_2 = 0.5M_{\odot}\), so \(m_1m_2=(1)(0.5)M_{\odot}^2=0.5M_{\odot}^2\).
• Third model: \(m_1 = 1M_{\odot}\), \(m_2 = 1M_{\odot}\), so \(m_1m_2=(1)(1)M_{\odot}^2 = 1M_{\odot}^2\).

Answer:

The first model (with masses \(1M_{\odot}\) and \(2M_{\odot}\)) shows the stars with the strongest gravitational force between them.