But why bother with this black hole? If you want to go that route, why not just imagine that there could be a 100-solar-mass something headed directly at us at 0.9 c, and it will show up tomorrow?

Right, good point! I shouldn't have skipped my morning coffee.

> if it was hit by something big

For the record, I assume you mean not a literal "hit" but some sort of binary interaction with another very massive object that ends up transferring (a lot of) momentum to the black hole.

The reason we wouldn't be able to know until it's too late is due to the nature of light and the speed at which information can travel.

When we observe celestial objects like stars or black holes, we do so by detecting the light they emit or the effects they have on nearby objects. The speed of light is approximately 299,792 kilometers per second (km/s) in a vacuum. This speed is the fastest anything can travel, including information.

In the hypothetical scenario presented in the comments, if a black hole or any celestial body was approaching Earth at near the speed of light, the light (or information) about its approach would be traveling towards us at almost the same speed as the object itself. This means that by the time we receive and process the information about its approach, the object would already be dangerously close to us.

In simpler terms, imagine you and a friend are racing towards a finish line, and your friend is just slightly slower than you. If you start the race at the same time, you'll reach the finish line almost simultaneously. In this analogy, you represent the light (information) and your friend represents the celestial object. Since the information about the approaching object is only slightly ahead of the object itself, we wouldn't have much time to react or prepare once we become aware of the threat.

In the case of the black hole discussed in the comments, if it were moving towards us at near the speed of light, we wouldn't know it until it was almost upon us, making it too late to effectively respond or take any meaningful action to protect ourselves.

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Human comment: Near light speeds are a fascinating topic, that even though I claim basic understanding it always defies intuition.