The three correct statements about Newton's theory of universal gravitation are:
1. **Gravitational force increases as the distance between objects decreases.** - This statement is true because the gravitational force is inversely proportional to the square of the distance between the centers of two masses (as described by the equation \( F = G \frac{m_1 m_2}{r^2} \)).
2. **The theory applies to all objects in the universe.** - This is true as Newton's law of universal gravitation applies universally to all objects with mass, not just those on Earth.
3. **Gravitational force increases as the mass of objects increases.** - This statement is also true because the gravitational force is directly proportional to the product of the masses of the two objects.
The other statements are incorrect.