Final answer:
The orbit of Earth would not change if the Sun turned into a black hole because the orbital period is determined by the mass of the Sun, which would stay the same. Only if Earth came very close to the black hole's event horizon would the strong gravitational forces affect its orbit significantly.
Step-by-step explanation:
If the Sun were to suddenly become a black hole, Earth's orbit around it would remain largely unaffected. The key reason is that the mass of the Sun would remain the same even if it collapsed into a black hole, which means Earth's gravitational interaction with the Sun would not change. The orbit of Earth is determined by the mass of the Sun, and as long as that mass remains consistent, the orbital period would also remain unchanged. It's important to note that only very near the event horizon of a black hole does gravitation become strong enough that Newton's laws of motion break down. For objects like Earth orbiting at a safe distance, these laws would adequately describe the motion of the planet, ensuring that Earth's orbital period around a black hole of the same mass as the Sun would be the same as it is now. However, if the Sun were to lose mass before collapsing into a black hole, or if Earth ventured too close to the event horizon, only then would significant gravitational effects occur. Earth's orbit could then potentially be affected. Fortunately, such catastrophic scenarios are highly unlikely and not related to simply the transformation of the Sun into a black hole.