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 weakest

Explanation:

Step1: Recall Newton's law of universal gravitation

The formula 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. Assume \(G\) is a constant. For simplicity, we can compare the products \(m_1m_2\) (since if we assume \(r\) is the same for the first - two models and larger for the third model, and we just focus on the mass - product effect for relative comparison).
For the first model: \(m_1m_2=(1M_{\odot})\times(1M_{\odot}) = 1M_{\odot}^2\).
For the second model: \(m_1m_2=(1.5M_{\odot})\times(1M_{\odot})=1.5M_{\odot}^2\).
For the third model: \(m_1m_2=(0.25M_{\odot})\times(1M_{\odot}) = 0.25M_{\odot}^2\). Also, the third model has a larger distance. The gravitational force is directly proportional to the product of masses and inversely proportional to the square of the distance.

Answer:

Second model (strongest), first model, third model (weakest)