Gravity is a fundamental force of nature that acts between two masses. According to Newton's law of universal gravitation, the force of gravity between two objects is given by the formula:
[tex]\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force between the objects,
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\(6.67430 \times 10^{-11} \, \text{m}^3 \cdot \text{kg}^{-1} \cdot \text{s}^{-2}\)[/tex]),
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two objects,
- [tex]\( r \)[/tex] is the distance between the centers of the two masses.
From this formula, you can see that the force of gravity is inversely proportional to the square of the distance between the objects. That is, as the distance [tex]\( r \)[/tex] increases, the gravitational force [tex]\( F \)[/tex] decreases.
This relationship can be described as follows:
- If the distance between two objects is doubled ([tex]\( r \)[/tex] becomes [tex]\( 2r \)[/tex]), the gravitational force becomes a quarter ([tex]\( \frac{1}{4} \)[/tex]) of what it was.
- If the distance is tripled ([tex]\( r \)[/tex] becomes [tex]\( 3r \)[/tex]), the gravitational force becomes one-ninth ([tex]\( \frac{1}{9} \)[/tex]) of what it was.
Therefore, the correct answer is:
c. It decreases with the square of the distance
