Question

the force of gravity between any two celestial objects can be determined using newton’s law of universal gravitation, which states that all objects in the universe are gravitationally attracted to each other. the gravitational force between two celestial objects depends on two factors: distance and mass. - the greater the distance between two objects, the weaker the gravitational force between them. - the greater the masses of the two objects, the stronger the gravitational force between them. each model below shows two stars at a different distance from each other. each star’s mass is shown in solar masses ($m_odot$). the sun has a mass of $1 m_odot$. a star twice as massive as the sun has a mass of $2 m_odot$. select the model that shows the stars with the strongest gravitational force between them.

Explanation:

Step1: Recall gravity force formula

The gravitational force is given by $F = G\frac{m_1m_2}{r^2}$, where $G$ is a constant, $m_1,m_2$ are masses, $r$ is distance.

Step2: Compare mass products

All models have $m_1=1M_\odot$, $m_2=2M_\odot$, so $m_1m_2=2M_\odot^2$ for all.

Step3: Compare distances

The third model has the smallest $r$, so $\frac{1}{r^2}$ is largest here.

Step4: Determine strongest force

Largest $\frac{m_1m_2}{r^2}$ gives strongest $F$.

Answer:

The third model (stars with masses $1 M_\odot$ and $2 M_\odot$ at the shortest distance between them)