"Let's Do the Physics Of Knocking an Asteroid Into the Sun" Topic

"I don't know how to start this analysis without a spoiler. I can try setting it up with a generic physics question, but if you are behind on the excellent SyFy program The Expanse, you may want to walk away and do something else, like read about why flying at light speed is pretty much impossible unless you're Han Solo.

Still with me? OK. Here's the problem: I've got a spaceship orbiting the sun somewhere in the asteroid belt between Mars and Jupiter, and I want to destroy some other asteroid. Maybe the best way to obliterate an asteroid is to just push it into the Sun. Could I crash this spacecraft into the asteroid to knock it into the Sun?

Yes, this is a pretty tough problem, but I can break it down into three parts: Traveling to the asteroid, colliding with the asteroid, and the resulting trajectory of the asteroid. Before getting started, though, I must make some assumptions. I'll use estimated values from The Expanse, because they've already done the work.

The asteroid is Eros. It follows a circular orbit around the sun (not technically true, but close enough), with an orbital radius of 1.5 AU (where 1 AU, or astronomical unit, is the distance from the sun to Earth). Eros has a mass of about 6.7 x 1015 kg.

The spacecraft is the Nauvoo, a large ship designed for interstellar travel. It's basically a cylinder with a radius of 0.25 km and a length of 2 km. Its starting orbital distance is 2.5 AU…"
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Amicalement
Armand

You can do the physics if you want to, but tossing it into the sun is not going to be the easiest way to destroy it. In fact, that would require so much energy as to be the show-off way to do it. Throwing it into the sun also takes longer.

The Nauvoo, according to the article, has something irrelevant x 10^10 kg. That means Eros is 10^5 or 100,000 times more massive. To have a meaningful impact on the inertia of something with 100,000 times your mass you'll need a lot of velocity. A *lot*. At those velocities things don't just smash, the atoms can't get out of each others' way fast enough. Things vaporize. So for a lot less energy you can smack into Eros with enough energy to vaporize your Nauvoo and a good chunk of Eros, with the rest of Eros accelerating outward in all directions in tiny pieces. That's *almost* as destroyed as a thing can get.

This destruction would be instantaneous.

If you removed *all* of Eros's momentum it would take months to fall into the sun. Without doing any math I'd say 4 to 12 months, based on someone else's math that it would take two months for the Earth to fall into the sun in the same situation. The distance is only 1.5 times, but Eros is far less massive than the Earth, so the acceleration is far less.

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If you took away less than all Eros's momentum it could take any length of time to get to the sun.

Tiny things orbiting planets can experience enough orbital decay that they can fall out of orbit within human life times, but really big things orbiting stars have *much* more inertia. It's very hard to knock them into the sun.

Ironically, despite the tremendous gravitational attraction of the sun it's actually pretty difficult to get there. This is why it is bone ignorant to be afraid of the black hole at the center of our galaxy – yes, it's immense, all-consuming, and pulling at us with incredible force. But it would take an incredible amount of energy to put yourself on a path to that spot, never mind that it would take many lifetimes to get there.

Thanks!

Amicalement
Armand

How are they gonna knock an asteroid into the sun when they can't even reconstruct a local road project in three years??
Grumble.