Question

gravity is a fundamental interaction in the universe. the gravitational force between two celestial objects can be determined using newtons law of universal gravitation.
determine whether each statement is true or false.
if a planet has two moons that are each 300,000 kilometers away, the gravitational force will be stronger between the planet and the more massive moon than between the planet and the less massive moon.
the gravitational force between a 1 ( m_{odot} ) star and a 0.5 ( m_{odot} ) star separated by a distance of 100 light - years is stronger than the gravitational force between a 1 ( m_{odot} ) star and a 0.5 ( m_{odot} ) star separated by a distance of 10 light - years.
a planet exerts the same gravitational force on a star as the star exerts on the planet, just in the opposite direction. but since the planet is less massive than the star, it will be more significantly impacted by the stars gravitational pull.
gravity is a type of energy that can be found throughout the universe.

Explanation:

Step1: Analyze the first statement

According to Newton's law of universal gravitation \(F = G\frac{m_1m_2}{r^2}\). When \(r\) (distance) and \(m_1\) (planet's mass) are constant, \(F\) is directly proportional to \(m_2\) (moon's mass). So, if \(m_{2,\text{more}}>m_{2,\text{less}}\), \(F_{\text{more}}>F_{\text{less}}\).

Step2: Analyze the second statement

Using \(F = G\frac{m_1m_2}{r^2}\), when \(m_1 = 1M_{\odot}\), \(m_2=0.5M_{\odot}\), \(F_1 = G\frac{1\times0.5}{100^2}\) and \(F_2=G\frac{1\times0.5}{10^2}\). Since \(F_2>F_1\) (because \(r_2 < r_1\) and \(F\propto\frac{1}{r^2}\)).

Step3: Analyze the third statement

By Newton's third law, the gravitational force between two objects is an action - reaction pair (\(F_{planet - star}=F_{star - planet}\)). But acceleration \(a=\frac{F}{m}\), and since \(m_{planet}a_{star}\) (more impact on the planet).

Step4: Analyze the fourth statement

Gravity is a fundamental force, not a type of energy.

Answer:

1. True
2. False
3. True
4. False