Question

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.
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.
gravity is a type of energy that can be found

Explanation:

First Statement

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So, the gravitational force that a planet exerts on a star is equal in magnitude to the gravitational force that the star exerts on the planet. However, according to Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass and \(a\) is acceleration), for the same force \(F\), if the mass \(m\) of the planet is less than the mass of the star, the acceleration \(a=\frac{F}{m}\) of the planet will be greater than the acceleration of the star. So the first statement is True.

Second Statement

The formula for gravitational force is \(F=\frac{GMm}{r^{2}}\), where \(G\) is the gravitational constant, \(M\) is the mass of one object (planet in this case), \(m\) is the mass of the other object (moon), and \(r\) is the distance between them. Given that \(r\) (distance from the planet to each moon) and \(M\) (mass of the planet) are the same for both moons, if \(m_1>m_2\) (where \(m_1\) is the mass of the more massive moon and \(m_2\) is the mass of the less - massive moon), then \(F_1=\frac{GMm_1}{r^{2}}>\frac{GMm_2}{r^{2}} = F_2\). So the second statement is True.

Third Statement

The formula for gravitational force \(F=\frac{GMm}{r^{2}}\). Let \(M = 1M_{\odot}\), \(m=0.5M_{\odot}\). For the first case \(r_1 = 100\) light - years and for the second case \(r_2=10\) light - years. Then \(F_1=\frac{G\times(1M_{\odot})\times(0.5M_{\odot})}{(100)^{2}}\) and \(F_2=\frac{G\times(1M_{\odot})\times(0.5M_{\odot})}{(10)^{2}}\). Since \(\frac{1}{100^{2}}<\frac{1}{10^{2}}\), \(F_1

Answer:

1. True
2. True
3. False