This post is the third in a series by B612 Chair Emeritus and former NASA astronaut Rusty Schweickart. You can read his previous post here.
[Warning!! While I’ve done my best to simplify this subject it is inherently tricky to describe, and graphics don’t really help much. So unless you are a fairly technical person you might just want to pass on this blog!]
What are these keyholes that always seem to be mentioned when asteroid deflection is talked about? Why are they important, and what are the implications of having to deal with them?
The key to understanding keyholes (or gravitational keyholes) lies in realizing that whenever an asteroid passes close by the Earth, the Earth’s gravity modifies the asteroid’s orbit. The closer to the Earth the asteroid passes, the more its orbit is changed.
Remember that in general the asteroid and the Earth are going around the Sun in the same direction and again, in general, their paths cross at a relatively small angle. Think about two freeways crossing each other at a very small angle. If the asteroid passes through the intersection before the Earth gets there, the asteroid passes “in front of” the Earth (think looking down on them from above). Similarly, if the asteroid gets to the intersection only after the Earth has already passed through it, then that asteroid will pass behind the Earth.
For the short time that the asteroid and the Earth are in close proximity, the Earth will pull backward on an asteroid that passes in front of it (i.e. slowing it down slightly) or pull forward on an asteroid that passes behind it (i.e. speeding it up slightly). An asteroid that passes just behind the Earth will therefore end up with a slightly higher orbital velocity after it leaves the Earth’s vicinity and therefore end up in a slightly larger orbit with a longer period (the asteroid’s “year”) than it had before the encounter.
For this discussion I’ll just deal with one example; an asteroid passing close behind the Earth in a close encounter. I’m sure you can apply the mirror image for one that passes close in front of the Earth. Similarly I’ll use simple numerical examples so that they are easy to follow, however reality, while similar in principle deals with finer numbers and fractions less easy to immediately grasp.
Let’s imagine, to keep it simple, that the Earth’s year is 400 days and that prior to the encounter the asteroid’s period is 600 days. Now it is fairly easy to see that if our asteroid passes closely behind the Earth it will end up in a new orbit where its year has been increased to greater than 600 days. The closer to the Earth that it comes, the larger is the change in its period. Clearly there is then a point where its new orbit ends up being 800 days long.
Another important characteristic of orbital motion is that any change made instantaneously to an object’s velocity will modify its orbit, BUT it will, one period later, come right back through that same point. In other words the new orbit may look quite different but it will still come back through the point where the change was made. If we think of an asteroid passing close by the Earth it is close enough for the Earth’s gravity to effect it only for a few hours. Since the asteroid’s period is several hundred days the change in the asteroid’s orbit is effectively instantaneous.
Going back to our example then, every 400 days after this near miss the Earth will be right back in the same spot. However the asteroid takes 800 days to return to the same spot. That’s OK for the first year after the encounter, but the second time the Earth returns (i.e. 2 years later) the asteroid has just completed its first full orbit around the Sun, and there they both are, right back together! In other words, they are in a 2:1 resonance. Every two Earth years the Earth and the asteroid come back together.
Since they missed each other the first time, an exact resonance (exactly 2.0000:1.0000) would bring them literally back to an identical near miss. However it is easy to see that if the asteroid’s orbital period were not exactly 800 days, but 799.96 days (or some such number) instead of passing behind the Earth this time it would arrive in the intersection at the same time and there would be a collision. Since it takes the Earth about 4 minutes to get through the intersection you can see that there is a small region around the original near miss distance where the asteroid would still hit the Earth. This small region is called a keyhole. If the asteroid passed at the edge of the keyhole closest to the Earth the first time, it would end up hitting the trailing edge of the Earth 800 days later. Conversely if it missed the Earth at the farthest boundary of the keyhole, it would then impact at the leading edge of the Earth 800 days later.
However, this is not the only keyhole for our asteroid. If you imagine the first encounter being even closer to the Earth, there’s clearly a point where its new period would be not 800 days, but 1200 days. Now the Earth will go around the sun 3 times (3 years later) before the asteroid is back there. We have now a 3:1 resonance. Again, this keyhole is closer to the Earth and there is lots of space between our 2:1 keyhole and this 3:1 keyhole. However, while we won’t go into it in detail, you can work out that any fraction (non reducible fraction) can be a keyhole. E.g. 3:2, 5:3, 4:1, 11:13, etc.
So the picture to have in mind is that any time an asteroid comes close by Earth (or any other planet, for that matter) there is a field of keyholes, both behind and in front of the Earth which, if the asteroid passes through them it will come back some integral number of years later and impact the planet. Happily these keyholes are very small compared with the space between them. Nevertheless they are there and many asteroid impacts (some would argue most) are preceded by a keyhole passage several years earlier.
Just a word now to emphasize why these keyholes are important to us in thinking about deflection.
If we think about using a kinetic impact (i.e. running a mass into an asteroid to make it arrive too early or too late to impact the Earth) it is pretty clear that the primary deflection may well be successful, but the asteroid will nevertheless make a pretty close pass by the Earth. In fact it will pass, depending on our primary deflection, essentially immediately in front of or immediately behind the Earth. And guess what? That’s where there is a field of keyholes lurking!
Therefore to have a really successful deflection, we not only have to make sure that we’ve caused our asteroid to miss the Earth, but in missing it we’ve also got to insure that it also passes between any keyholes and not through one. If we were to execute a primary deflection only to have the asteroid, in missing the Earth, pass through a keyhole we would end up simply having postponed the impact for a few years.
It is for this reason that we prefer to talk about a deflection campaign, and not simply a deflection mission. A deflection campaign would not only consist of a mission to make the asteroid miss the Earth, but also include another spacecraft (e.g. a gravity tractor) capable of making a small but precise adjustment in the asteroid’s new orbit to insure that it also passes between keyholes. But this is the subject of another blog entry!
Rusty Schweickart was the Lunar Module Pilot on the Apollo 9 mission, March 3-13, 1969. From 1977-1979 Schweickart was Governor Jerry Brown’s Assistant for Science and Technology. From 1979-1983 he was Chairman of the California Energy Commission.
In 1985 he founded the Association of Space Explorers and served as President of ASE-USA until 1989.
Subsequently, Schweickart was founder and CEO of several space and Internet startups. He co-founded and served as Chairman of B612 Foundation from 2001-2011.
In 2005 Schweickart founded and chaired the ASE-NEO Committee which, with its international Panel on Asteroid Threat Mitigation produced and submitted to the United Nations Committee on the Peaceful Uses of Outer Space (COPUOS) the seminal report Asteroid Threats: A Call for Global Response (www.space-explorers.org/ATACGR.pdf). Schweickart also co-chaired, along with astronaut Tom Jones, the NASA Advisory Council’s Task Force on Planetary Defense.