Question

the force of gravity between any two celestial objects can be determined using newtons 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 stars mass is shown in solar masses (m₀). the sun has a mass of 1 m₀. a star twice as massive as the sun has a mass of 2 m₀.
select the model that shows the stars with the strongest gravitational force between them.

Explanation:

According to Newton's law of universal gravitation, the 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). Given that \(m_1 = 1M_{\odot}\) and \(m_2=2M_{\odot}\) (masses are constant for the three models), the force is inversely proportional to the square of the distance \(r\). The smaller the \(r\), the larger the \(F\).

Answer:

The second model (the one with the shortest distance between the \(1M_{\odot}\) and \(2M_{\odot}\) stars) shows the stars with the strongest gravitational force between them.