* Light Travel Time: Light travels at an incredible speed - approximately 299,792 kilometers per second (186,282 miles per second).

* Distance from Sun to Jupiter: Jupiter orbits quite far from the Sun, at an average distance of about 778 million kilometers (483 million miles).

Calculation:

1. Time = Distance / Speed

2. Time = 778,000,000 km / 299,792 km/s

3. Time ≈ 2,595 seconds

Therefore, it would take approximately 2,595 seconds, or about 43 minutes, for Jupiter to become dark after the Sun ceased to shine.

Important Note: This calculation assumes that the Sun *completely* stops emitting light instantaneously. In reality, the process of a star ceasing to shine would likely be gradual and complex.