After reading the article it became clear to me that every time that something falls to the Earth, the Earth also falls up to the object. It's just that when we drop something small like a baseball, hammer, or 747's, that the Earth just doesn't move very much, hardly at all. But on a smaller object, like a 300 m asteroid, and with a ship that masses perhaps a hundred tons, then the mutual gravitational attraction can be such that the asteroid will move with a tiny bit of acceleration. In fact, it would move proportionaly to the gravitational force exerted:
F=G*m1*m2/r^2
This force acts on both m1 and m2, equally though in opposite directions. It's just that when m2 is so much larger than m1, then m2's apparent motion is very, very tiny.
Let's toss some numbers around:
Let's assume we have an asteroid that masses, oh, say 30 million metric tons. And lets say our space craft is a hefty 100,000 kg. Let's further suppose that the spacecraft maintains a steady distance from the center of gravitation of 200m. If G=Newton's gravitational constant of 6.672*10^-11 N*m^2/Kg^2, then the gravitational attraction generation will be:
F=(6.672*10^-11)*100000*(30*10^9)/200^2
F=5.0 N
A force of 5 N acting on the space craft will generate a gravitational acceleration of:
5N/100000*kg = 5.0*10^-5*m/s^2;
whereas the asteroid will accelerate toward the ship by the amount:
5N/(30*10^9*kg)=1.67*10^-10 m/s^2.
O.K., so this isn't much. But what is interesting, is that if the 100,000 kg ship could use ion engines to thrust against the gravity from the asteroid to sustain its standoff distance, then the ship could move and the asteroid would actually follow. Albeit very, very slowly, unless we use a bigger ship. A larger ship with more gravitational mass could also generate more thrust, which would be more effective at moving big rocks.
It's interesting that non contact methods could be used to jockey asteroids around, it's simply a question of applying mass and thrust (and power) in creative ways. Good article!
Gravity has in fact figured in asteroid deflection concepts in the past, albeit in a somewhat different context : If you explode a nuke bomb next to a loosely-bound asteroid and cause it to shatter, the result will NOT be, as is often claimed, that many big chunks will hit the earth instead of one big one. Rather, the asteroid re-assembles in time, due to gravitational attraction between the separate pieces, and contiue on the new deflected trajectory. This did not, incidentally, occur in the case of comet Shoemaker-Levy (when it hit Jupiter), because it was too close to the planet, whose gravitational field disrupted it in the first place.....
Yes, because the comet came within the Roche limit of Jupiter the first time around and the pieces were sufficiently perturbed to continue to spread out before the final collision.
I wonder, if you deposit enough energy within the asteroid (perhaps in the form of a nuclear detonation,) if the energy exceeds the gravitational binding energy of the body in question, then dissassembly ought to be permanent. Other pieces may gravitationally reassemble later, but the resultant body will be smaller.
Also, I suspect that there are probably several different classes of asteroids in which the mechanics of the composition range the full spectrum from low density rubble pile/loosely bound dust, to solid nickel-iron. Some asteroids could be completely disintigrated by a nuclear explosion, others would be genlty nudged by the same yield of blast. I suspect that mechanically speaking, asteroids are fairly complex objects because of the wide range of their compositions...
if the 100,000 kg ship could use ion engines to thrust against the gravity from the asteroid to sustain its standoff distance, then the ship could move and the asteroid would actually follow.
Perhaps Im missing something but...
Wouldnt the exhaust from the ion engine impact on the asteroid surface and push the asteroid away with just the same force as the attractive one provided by gravity?
This would be the case if the ion exhaust was directed directly backward. However, in the article, the engines were located at the top end of the vehicle, farthest away from the asteroid. The exhaust was then directed away at an angle (see the artist conception from the cited article, and you'll understand.) The axial thrust is proportional to the cosine of angle made between the axis of the vehicle, and the engine offset angle. Infact, it has the form:
T=Te*cos(theta) where Te=the total developed thrust of the engine, T is the total 'delivered' thrust along the axis of the vehicle, and theta is the offset angle. For small angles, 5-10 degrees, then the total thrust delivered will still be about 98+% of the total thrust; even for a severe 30 degrees (which implies a thrust spread of 60 degrees!) the axial thrust is still 86.6% of total thrust, so there is a fairly low penalty for off setting the engines.
