You are describing the fundamental principles of Newton's Law of Universal Gravitation. This law states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula for this gravitational force (\(F\)) can be expressed as:
\[ F = G \frac{m_1 m_2}{r^2} \]
Where:
- \(F\) is the gravitational force between the two objects,
- \(G\) is the gravitational constant (approximately \(6.674 \times 10^{-11} , \text{N(m/kg)}^2\)),
- \(m_1\) and \(m_2\) are the masses of the two objects,
- \(r\) is the distance between the centers of the two objects.
From this formula, you can see:
-
Mass and Gravity: As the masses (\(m_1\) and \(m_2\)) decrease, the product \(m_1 m_2\) becomes smaller, leading to a decrease in the gravitational force \(F\).
-
Distance and Gravity: As the distance (\(r\)) between the objects decreases, the value of \(r^2\) becomes smaller, which increases the gravitational force \(F\). Specifically, since the force is inversely proportional to the square of the distance, halving the distance results in a fourfold increase in gravitational force.
Therefore, to summarize:
- Decreasing the masses results in a decrease in gravitational force.
- Decreasing the distance results in an increase in gravitational force.