Newton's universal theory of gravitation states that every mass attracts every other mass in the universe 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. This can be mathematically expressed with the formula:
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force between two objects,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects, and
- \( r \) is the distance between the centers of the two masses.
This theory provided a comprehensive explanation for various phenomena, such as the motion of planets, the behavior of tides, and the fall of objects toward the Earth, and laid the groundwork for classical mechanics and our understanding of gravitational interactions.