Although the Sun’s gravity is indeed stronger than the Earth’s, the Moon revolves around the Earth due to the nature of gravitational forces and orbital mechanics. The key factors are:

1. Relative Distances and Forces: The gravitational force between two objects is influenced by both their masses and the distance between them. The Sun’s gravitational pull on the Moon is weaker compared to the Earth’s gravitational pull on the Moon because the Moon is much closer to the Earth than to the Sun. This proximity makes Earth’s gravitational influence on the Moon much stronger than the Sun’s.

2. Orbital Mechanics: The Moon orbits the Earth because the Earth’s gravity exerts a stronger force on the Moon than the Sun’s gravity at that distance. The Moon is caught in a stable orbit around the Earth due to this stronger local gravitational force.

3. Two-Body vs. Three-Body Problem: In celestial mechanics, the Moon-Earth system is a two-body problem where the Earth’s gravity dominates the Moon’s orbit. While both Earth and Moon orbit the Sun, the Moon’s orbit around the Earth is the dominant effect at that scale.

Thus, the Moon orbits the Earth due to the stronger local gravitational influence, while the Earth-Moon system orbits the Sun together.