Question
If the distance between two planets decreases how does the gravitational force between them change?
Answers
GPT-4o mini
The gravitational force between two objects, such as planets, is described by Newton's law of universal gravitation. According to this law, the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by the formula:
\[
F = G \frac{m_1 m_2}{r^2}
\]
where \( G \) is the gravitational constant.
From this equation, we can see that the gravitational force is inversely proportional to the square of the distance between the two objects. This means that if the distance \( r \) decreases, the gravitational force \( F \) increases.
Specifically, if the distance between the two planets decreases (i.e., \( r \) becomes smaller), the denominator \( r^2 \) also becomes smaller, leading to an increase in the value of the gravitational force. Therefore, as the distance between the two planets decreases, the gravitational force between them increases significantly due to the \( r^2 \) relationship.
\[
F = G \frac{m_1 m_2}{r^2}
\]
where \( G \) is the gravitational constant.
From this equation, we can see that the gravitational force is inversely proportional to the square of the distance between the two objects. This means that if the distance \( r \) decreases, the gravitational force \( F \) increases.
Specifically, if the distance between the two planets decreases (i.e., \( r \) becomes smaller), the denominator \( r^2 \) also becomes smaller, leading to an increase in the value of the gravitational force. Therefore, as the distance between the two planets decreases, the gravitational force between them increases significantly due to the \( r^2 \) relationship.