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 gravitation formula

Newton's law: $F=G\frac{m_1m_2}{r^2}$, where $G$ is constant.

Step2: Assign variables to each model

Let the shortest distance = $r$, longest = $2r$.
Model 1: $m_1=1M_\odot, m_2=1M_\odot, r_1=r$
Model 2: $m_1=0.25M_\odot, m_2=1M_\odot, r_2=2r$
Model 3: $m_1=1.5M_\odot, m_2=1M_\odot, r_3=r$

Step3: Calculate relative force for each

Model1: $F_1=G\frac{1 \cdot 1}{r^2}=\frac{G}{r^2}$
Model2: $F_2=G\frac{0.25 \cdot 1}{(2r)^2}=G\frac{0.25}{4r^2}=\frac{0.0625G}{r^2}$
Model3: $F_3=G\frac{1.5 \cdot 1}{r^2}=\frac{1.5G}{r^2}$

Step4: Compare force magnitudes

$F_3 > F_1 > F_2$

Answer:

1. Strongest: Model with $1.5M_\odot$ and $1M_\odot$ (short distance)
2. Middle: Model with $1M_\odot$ and $1M_\odot$ (short distance)
3. Weakest: Model with $0.25M_\odot$ and $1M_\odot$ (long distance)