This post is the second in a series by B612 Chair Emeritus and former NASA astronaut Rusty Schweickart. You can read his previous post here.

Part 1: Essential Orbital Mechanics

The next couple of entries here will be a run through of the basics of how to cause an asteroid, on a predicted collision course with the Earth, to miss that rendezvous with destiny. This entry will deal with the nature of the environment we’re working in; i.e. the motions of bodies orbiting around the Sun. We’re not going to get into equations <whew!> but we do have to deal with the fact that orbital motion is very different from motion in “flat space,” which is what your intuition is based on. Unless, that is, you are a space geek.

Now just as a reminder, recall that we’re talking about being able to predict these collisions decades in the advance, so wrap your mind around both the Earth and the asteroid at issue making several trips around the Sun before ending up in the intersection of their two orbits at the same time. Think of the actual deflection occurring a decade or so prior to that predicted event.

If you think about it, there are essentially three things you can do to any object in orbit, whether around the Earth (as in my personal case) or around the Sun (as in our collective case) to modify its orbit. By pushing on it you can slightly change its velocity which then slightly modifies its orbit. The issue is what happens when you push on it in each of the three basic directions.

The three basic directions (any other direction is simply a combination of these three) are; 1) parallel to the direction it is currently going, 2) perpendicular to the asteroid’s orbit plane, let’s say up or down, and 3) perpendicular to those two directions, i.e. essentially toward or away from the sun, let’s say in or out. And the question we need to answer is what happens in each of these cases, and which is most effective in making the asteroid miss the Earth in 10 years?

In this simple diagram we’re looking at the asteroid from slightly inside its orbital path and just above its orbital plane. The asteroid is moving from right to left along its orbital path and its speed is represented by the length of the arrow. The three directions we can push it (six if you count + and -) are illustrated by the double headed arrows. We can therefore, 1) add (or subtract) a small amount of velocity by pushing (+v) in the same (or opposite, -v) direction it is currently moving, 2) push it up or down giving it a slight velocity in those directions, or 3) push it in toward the Sun or outward away from the Sun.

The result of each of these (I’ll use the + sense only to make this point, you can figure the – sense out) is what counts. Adding the +v to the length of the asteroid’s velocity puts in into a very slightly larger orbit. Adding a little up velocity will very slightly tilt the asteroid’s orbit upward beginning at this point. Adding a little velocity inward will cause the asteroid to fly slightly sunward from its former orbit for 180 degrees, then slightly outside its former orbit until returning to the point of application one full orbit later.

The importance of these effects is that changing the direction of the velocity (the second & third options) has no cumulative effect on the asteroid’s position, whereas changing the magnitude of the velocity does. In all three cases the asteroid will come back through the identical same spot in space after one full period (i.e. asteroid “year”). However that period (i.e. the asteroid year) is slightly lengthened by the application of a +v, whereas for any rotation of the asteroid’s velocity (technically its velocity vector), the period is unchanged.

We’ve got to use just a few numbers now to get the sense of how wimpy our deflection capability, and its effect, actually is. So let’s take an example of an asteroid 90 meters in diameter that we deflect by running into it with a 1,000 kg (i.e. 1metric ton (MT)) spacecraft at an impact velocity of 10,000 meters/sec. The change in velocity we give the asteroid by “rear-ending” it is all of 1 cm/sec! Since the asteroid was initially traveling at about 30 km/sec, we’ve now increased its velocity by 1 cm/sec or 1 part in 3 million!

(For the non-metric out there, this is respectively, in English units, a 295 ft diameter asteroid that we hit with a 2200 lb mass traveling (with respect to the asteroid) at 22,400 mph. The resultant change in the asteroid’s initial velocity of 67,100 mph is 0.022 mph, i.e. 1 part in 3 million!)

The important result here is that even though we’ve changed the velocity of the asteroid by only 1 cm/sec, it now takes it about 20-25 seconds longer to complete one orbit around the Sun. Therefore, if after 10 trips around the Sun, our asteroid was going to hit right in the middle of the Earth, it will now arrive ~225 seconds late which means that the Earth will just squeak through the intersection before the asteroid gets there! In other words… a successful deflection (albeit, in this case, a very close call!)

Bottom line; by ramming an asteroid at an achievable closing velocity with a modest sized spacecraft we can slightly enlarge (or shrink) its orbit just enough so that 10 orbits later it misses the Earth vs. hitting it. The only productive component of such a maneuver is the part that either adds to or subtracts from the velocity of the asteroid. The up/dn and in/out components are of essentially no real value. Since there is no cumulative effect on the asteroid’s orbit they will shift the impact point on the Earth’s surface by only a few miles.

A note from Rusty: I tried to write this blog entry with as little techno-babble as I could.  I tried not to use the word vector, but it really is futile since the concept of a vector quantity is so linked to reality!  So a little primer (or reminder!) on vectors.

The definition is simple; a quantity with both magnitude and direction.  The alternative, BTW, is a scalar quantity, which has only magnitude.  Scalars are plentiful; weight, length, cost, etc.  Perhaps one of the most common uses of a vector would be a question like, “where is New Town from here?”  Your friend is helpful if she says, “about 12 miles northeast of here.”  If he were to simply say 12 miles from here, that might be somewhat helpful, but it could be in any direction.  Similarly saying northeast of here might be helpful but it could be 500 miles away and you really want to know that.

On the earth velocity is often understood simply as speed.  This is because most familiar things like cars, airplanes, boats, bicycles, etc can only move in the direction dictated by their wheels or long axis.  But in space an object, regardless of its shape or size can be moving in any direction, so giving not only its speed, but also the direction it is moving in is critical.  And it turns out that any space object will have a trajectory (or orbit) that is parallel to its velocity vector.  (The pointy end of the spacecraft, however, can be pointed in any direction.  You don’t necessary go in the direction you are pointed in a spacecraft!)

Now it’s a bit more clear that we can change a velocity vector in two fundamental ways; by changing its length (or magnitude) or its direction.  If you physically picture the velocity vector of an asteroid as 60,000 miles/hour long and pointed parallel to its orbit in the direction it is moving, then you can change that velocity vector by “adding” small vectors to the arrowhead at the far end of the velocity vector, as per the diagram in the blog.  The “new” velocity vector will then end up in the same direction, but very slightly longer or shorter, or it will end up the same length, but be pointed in a very slightly different direction.  Again, for deflection purposes, only the changing of its length makes a real difference.

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Russell Schweickart, Chair Emeritus

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.