Final answer:
The hypothetical mini-companion star to the Sun, dubbed Nemesis, would need to be at a distance where it can periodically disturb Kuiper Belt Objects and cause impacts on Earth.
The correct distance is option B. 9000 AU, which would allow such periodic disturbances matching the mass extinction patterns observed in the fossil record.
Step-by-step explanation:
The concept of a hypothetical companion to the Sun, named Nemesis, suggests that this star could periodically cause a bombardment on Earth by disturbing the orbits of objects in the Kuiper Belt. If Nemesis is responsible for mass extinctions occurring every 27 million years, it would need to be far enough to have a long orbital period while still being able to influence the Kuiper belt. Considering the options provided and the effects described, the correct option that would allow Nemesis to disrupt the orbits of Kuiper Belt Objects (KBOs) and potentially cause periodic impacts and mass extinctions on Earth is B. 9000 AU (Astronomical Units). 200 AU is too close for such a long orbital period; 25,000 AU, 90,000 AU, and options E through G are at distances that would likely cause Nemesis to not be gravitationally bound to the Sun or to have interaction periods that do not match the 27 million year extinction pattern.
The correct distance is option B. 9000 AU