* Gravity: The Sun's gravity is what keeps Earth in its orbit. Without the Sun's pull, there's nothing to keep Earth in a circular path.
* Inertia: Earth already has a lot of momentum from moving around the Sun. This inertia would keep it moving in a straight line.
What would happen:
* Initially, nothing noticeable: It takes light about 8 minutes to travel from the Sun to Earth. So, for the first 8 minutes after the Sun vanished, Earth would continue orbiting as usual. Then, the sky would go dark.
* A straight trajectory: Earth would fly off in a straight line, forever. The direction of this line would be determined by Earth's velocity at the moment the Sun disappeared.
* The future is cold and dark: Without the Sun's energy, Earth would freeze. Life as we know it would cease to exist.
Important Note: This is a theoretical scenario. It is highly unlikely that the Sun would suddenly vanish.