# Do all dangerous asteroids first pass through keyholes?

Now MIT researchers have devised a framework for deciding which type of mission would be most successful in deflecting an incoming asteroid. Their decision method takes into account an asteroid’s mass and momentum, its proximity to a gravitational keyhole, and the amount of warning time that scientists have of an impending collision — all of which have degrees of uncertainty, which the researchers also factor in to identify the most successful mission for a given asteroid.

“People have mostly considered strategies of last-minute deflection, when the asteroid has already passed through a keyhole and is heading toward a collision with Earth,” says Sung Wook Paek, lead author of the study and a former graduate student in MIT’s Department of Aeronautics and Astronautics. “I’m interested in preventing keyhole passage well before Earth impact. It’s like a preemptive strike, with less mess.”

Questions:

1. Do all or at least most astroids that will pose a danger to Earth pass through a keyhole first?
2. If so, why? Why would previous but fairly recent close passes to some gravitational body be important for making an asteroid pose a danger to Earth?

For more on gravitational keyholes see answers to the following (and links therein)

as well as Wikipedia's Gravitational keyhole.

• I love a question that teaches me something before there are even any answers. Nice! Commented Feb 20, 2020 at 14:28
• @WayneConrad perhaps this question can be a "keyhole" to the world of orbital mechanics
– uhoh
Commented Feb 20, 2020 at 15:01
• A definition of gravitational keyhole in the question would be helpful, I think ) Also an interesting question, but maybe beyond of the scope - what percent of close asteroid flybys yields to a gravitational keyhole catch and later impact event? Commented Feb 21, 2020 at 8:19
– uhoh
Commented Feb 21, 2020 at 9:22

Dangerous asteroids are those that can hit the Earth, and are large enough to cause substantial damage. There are currently no such known asteroids. (2020-02-21)

There are two ways an asteroid could end up as considered dangerous:

1. We discover it. There may be an asteroid bound for Earth at this moment, we just haven't seen it yet. This is fairly straight forward.
2. An asteroid passes through a gravitational keyhole.

This implies that every known asteroid would have to pass through a gravitational keyhole to become dangerous.

How does 2) turn asteroids dangerous?

Asteroid orbits are only known to some limited precision. Even when the uncertainties are small enough that we can rule out a collision when it approaches Earth, even small uncertainties will cause large differences in how close it is going to get.

That is, exactly how the asteroid is going to fly by us is "blurry", we don't really know exactly how it's going to look.

That's where the butterfly effect sets in. Even tiny differences in how close the asteroid passes by is going to have a huge effect on its future orbit.

Those future orbits may be dangerous. What if, for instance, the new orbit of the asteroid is exactly 1 year? Then the Earth and the asteroid will meet again in the same spot. And we don't want to "meet" asteroids. Same goes for 2 years, 3/2 years, etc., every simple fraction is a potential future disaster.

A gravitational keyhole is essentially that "if the first encounter turns out this way, which we don't know for certain, the future orbit will make the asteroid hit the Earth."

What those scientists are suggesting is that we can knock asteroids slightly of course, so the future fly-by is certain to not happen in a way that leads to a dangerous orbit in the future

• Could I interpret your answer to "Do all dangerous asteroids first pass through keyholes?" as a qualified "more or less yes"?
– uhoh
Commented Mar 8, 2020 at 10:52
• I can't really accept an answer until it either takes a clear position on the question or explains why that's not possible.
– uhoh
Commented Apr 11, 2020 at 3:59

### Novel keyhole-less asteroids could exist

An extrasolar asteroid such as ʻOumuamua would not need to pass through a gravitational keyhole within our solar system, but the odds of a such a collision are incredibly low.

One could hypothesise a contemporary catastrophic event within the solar system involving a bigger-than-dangerous-asteroid body which happens to catapult a dangerous asteroid in precisely our direction, without any fly-bys, but this seems unrealistic.

### But they can't have been created a long time ago

Let us assume a dangerous asteroid in an earth-crossing orbit in the relatively recent solar system, a billion years ago, which will hit Earth tomorrow, without ever passing through a keyhole. It must cross the orbit of the Earth tens of millions of times (assuming a <100 year orbit), but remain outside of 20,000 km (the 2029 approach of Apophis, a sample keyhole event). Since the Earth could be anywhere on its 9.4e8 km orbital path, then the closest historical approach would be 200km from the centre of the earth; not only within the 20,000 km for a keyhole event (2029 Apophis approach) but within the earth's radius -- i.e. a direct strike.

Therefore there are no current earth-crossing asteroids that have not passed through a keyhole -- they've all hit us.

(There's a small gap in this logic for asteroids which are synchronised to the Earth's orbital time, but either long term resonance effects will build up to distort that, or we retain the synchronisation and the asteroid can never hit as it must remain in sync.)

(Keyhole events arguably occur at any distance, the 20,000 km is mostly an illustrative example)

## The question is a little backwards.

When we talk about a "gravitational keyhole", what we mean is we have an object that has a known orbit with some degree of uncertainty, which is going to interact with another body, and there is some range of positions within that uncertainty where the interaction will put it on a collision course with Earth.

Keep in mind that there aren't predefined areas of space that act as keyholes; "keyhole" is just a term we use for the specific range of values in a given interaction that would result in a dangerous course. So in a sense, this is a little like asking "Do people always die from a fatal shooting?" It's fatal because somebody died from it. It's a keyhole because it sets up a future collision.

We don't really talk about keyhole interactions in the past. A keyhole is defined by our uncertainty, it's a conceptual space between what we know and what we don't know. Once the interaction has happened, there isn't a keyhole, just an interaction that has occurred and the object's current course.

Sure, we can identify threats that we never saw during a keyhole interaction. We could discover a new body tomorrow that's already on a collision course with Earth. There might have been a keyhole before, if we had seen it and had some uncertainty about how Jupiter was going to change its orbit, but we didn't, so there was never a keyhole to talk about.

I know what Paek getting at, and it's true: We want to deflect dangerous or potentially dangerous objects many orbits in advance of a collision, when a tiny nudge would fix it, rather than wait for an imminent threat and blow it to rubble like some Hollywood film. And a keyhole interaction is a good time to make such an adjustment, because it's happening close to another body -- a good place to station some kind of device, and where the smallest change in orbit can have the largest effect.

But if a keyhole interaction happens, it doesn't mean the object is now an imminent impact. Most keyhole interactions we talk about are like "If its orbit changes by this exact amount, then three orbits later it will inevitably hit Earth" which might mean an impact three, ten, even fifteen years in the future, and that's plenty of time to give it a little nudge out of our path even after observing the keyhole interaction. That far in advance, even a minuscule orbital change will fix the problem. It's just that after the keyhole passes, you'd have to catch it in solar orbit with a gravity tractor or laser or whatever device you come up with, rather than being on-station around Jupiter where you're relatively close to the target already.