The Sun's gravitational pull is already much stronger than the Earth's. The gravitational force between two objects depends on their masses and the distance between them. The Sun has a mass of about 1.989 × 10^30 kilograms, while the Earth has a mass of about 5.972 × 10^24 kilograms. Therefore, the Sun's mass is significantly greater than the Earth's mass.
However, what keeps the Earth in orbit around the Sun is not just the Sun's gravitational pull, but the balance between the Sun's gravitational force and the Earth's orbital velocity. The Earth is moving at a speed of about 30 kilometers per second (18.5 miles per second) in its orbit around the Sun. This velocity creates a centrifugal force that counteracts the Sun's gravitational pull, keeping the Earth in a stable orbit.
If, hypothetically, the Earth were to lose its orbital velocity or slow down significantly, the Sun's gravitational pull would begin to dominate, and the Earth's orbit would start to change. Depending on the specific conditions, there are several possible outcomes:
The Earth could spiral inward toward the Sun, eventually colliding with it. This would be a catastrophic event, leading to the destruction of the Earth.
The Earth's orbit could become more elliptical, causing significant variations in temperature and climate. This would have profound effects on the Earth's ecosystems and could lead to extreme weather patterns.
In some cases, if the Earth's orbit becomes highly eccentric, it might be flung out of the solar system altogether. This would result in the Earth becoming a rogue planet, drifting through space without the Sun's gravitational influence.
It's important to note that the scenario you described, where the Sun's gravitational pull becomes stronger than the Earth's, is not a natural progression. The gravitational forces between celestial bodies are well understood, and the Earth's orbit around the Sun is stable in the current configuration. However, major disturbances or interactions with other celestial bodies could potentially disrupt this stability and lead to the outcomes mentioned above.