The property of the Sun that most affects the strength of the gravitational attraction between it and the Earth is its mass.

Here's why:

* Newton's Law of Universal Gravitation: This law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

* The Sun's Massive Size: The Sun is incredibly massive, containing over 99% of the mass in our entire solar system. This enormous mass is the primary reason for the strong gravitational pull it exerts on Earth.

While the Sun's distance from Earth also influences gravitational attraction, the effect of its mass is far more significant. Even a slight change in the Sun's mass would have a dramatic impact on the Earth's orbit and our entire solar system.