Breaking out of Earth's orbit around the Sun would require a significant increase in the planet's orbital velocity. The orbital velocity of Earth is approximately 29.8 kilometers per second (18.5 miles per second). To calculate the increased velocity needed to escape Earth's orbit, we can use the concept of escape velocity.
Escape velocity is the minimum velocity required for an object to overcome the gravitational pull of another object and escape its gravitational field. For Earth, the escape velocity is about 11.2 kilometers per second (6.95 miles per second) at the surface.
To break out of Earth's orbit, the planet would need to reach a velocity greater than the escape velocity. However, simply increasing the Earth's spin wouldn't be sufficient, as spin refers to the rotation around its axis, not its orbital velocity.
The actual velocity required to escape Earth's orbit would depend on the specific trajectory and the gravitational influence of other celestial bodies. Nevertheless, to provide a rough estimate, if we assume that the Earth's spin could somehow contribute to its orbital velocity, it would need to be significantly increased.
In reality, it is not feasible for Earth's spin to achieve the necessary velocity to break free from the Sun's gravitational pull. The forces involved and the conservation of angular momentum make it impossible for Earth's spin alone to overcome the gravitational binding energy of its orbit around the Sun.