Question

gravity is a fundamental interaction in the universe. the gravitational force between two celestial objects can be determined using newton’s law of universal gravitation. determine whether each statement is true or false. 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 star’s gravitational pull. 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. gravity is a type of energy that can be found throughout the universe. the gravitational force between a 1 m_☉ star and a 0.5 m_☉ star separated by a distance of 100 light - years is stronger than the gravitational force between a 1 m_☉ star and a 0.5 m_☉ star separated by a distance of 10 light - years.

Explanation:

First Statement:

By Newton's third law, the gravitational force between two objects is an action - reaction pair. So the planet and the star exert equal - magnitude gravitational forces on each other, opposite in direction. According to Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration), acceleration \(a=\frac{F}{m}\). Since the planet has less mass (\(m\) is smaller) than the star, for the same force \(F\), the planet will have a larger acceleration. This means the planet is more significantly impacted by the star's gravitational pull. So this statement is true.

Newton's law of universal gravitation is given by \(F = G\frac{m_1m_2}{r^2}\), where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between their centers. In this case, the distance \(r\) between the planet and each moon is the same (300,000 kilometers). The force \(F\) is directly proportional to the product of the masses (\(m_1m_2\), where \(m_1\) is the planet's mass and \(m_2\) is the moon's mass). So, if one moon is more massive (larger \(m_2\)), the product \(m_1m_2\) will be larger, and thus the gravitational force between the planet and the more massive moon will be stronger. This statement is true.

Gravity is a fundamental force, not a type of energy. Gravitational potential energy is associated with the gravitational field, but gravity itself is a force that causes objects with mass to be attracted to each other. So the statement that "Gravity is a type of energy" is false.

Answer:

True

Second Statement: