Re: Dodging Doomsday With a Space Tug

In article <1132104393.558861.229210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Mark Martin" <qed100@xxxxxxxxxxx> writes:
>
>Boris Mohar wrote:
>
>> Has anybody proposed spinning in until it flies apart? Sure it is a
>> cockamamie idea.
>
> It's not a stupid idea, but there are reasons why it may not be
>effective. For one, just off the top of my head it'll probably take a
>lot more energy to spin an asteroid to destruction than to just impart
>enough delta-V to allow it to miss Earth.
>
> But there's an even more interesting problem. Let's start out by
>considering a satellite orbiting with Earth. For a given radius the
>satellite is subject to a certain gravitational force which accelerates
>it towards Earth. (And earth towards the satellite.) If the satellite
>is given just the right amount of horizontal speed, it'll balance the
>force of gravity and travel in a circular orbit. Now let's give it a
>boost somewhere on its orbit. If we give it enough extra velocity
>tangent to its circular orbit, it'll have escape velocity and travel
>away from Earth indefinitely. But if the increase is less than escape
>velocity, it'll just assume an eccentric elliptical orbit. The highest
>point on the new orbit will be higher than the original circular path,
>but the low point will be right back on that circular orbit.
>
> Now if we spin an asteroid, essentially all the parts are on orbital
>paths. They're held on cicular paths by central forces, including
>gravity. If we spin it fast enough, the parts could be given escape
>velocity, and they'll fly apart and never meet again, in which case
>Earth is saved. But what'll happen if we apply torque to increase the
>spin rate is that the parts out near the surface will experience
>breakaway velocity before the core does. So they'll break away, leaving
>the core to continue on its Earth crossing trajectory.
>
> To make it even worse, the outer pieces will necessarily break off
>only as they just barely aquire enough velocity to enter into an
>ellipical orbit about the whole system's mass center. (It's like being
>on a carousel that's steadily spinning faster & faster. If I'm on the
>perimeter, once my tangential speed overcomes whatever force is holding
>me to a cicular path, I fling off and am no longer subject to the
>torque. I fly off with only whatever velocity I had at the moment I
>broke free.) The pieces will then all return together and collide.
>Overall, the entire asteroid will survive on its Earth crossing path.
>
Nice thinking but no, it is not going to work like this. A small
piece of rock is held together by cohesive forces (effectively,
chemical forces), the gravitational forces are negligible. So, once
you break the cohesive forces, the pieces will just fly, the
gravitationla forces will be way to weak to pull them back. The model
you present would work for much larger bodies, ones where the
gravitational bounding energy exceeds the cohesive one. This'll be
much larger then little asteroids.

Mati Meron | "When you argue with a fool,
meron@xxxxxxxxxxxxxxxxx | chances are he is doing just the same"
.