Research team casts light on asteroid deflection

In 2029 and 2036, the asteroid Apophis (named after the Egyptian god of darkness and the void), at least 1,100 feet in diameter, 90 stories tall, and weighing an estimated 25 million tons

It takes a tremendous amount of energy to move something that size by even a little bit.

You need a LOT of warning time, because you have to calculate the trajectory, and you need to calculate all possible trajectories the object will have during the acceleration phase to prevent the predicted impact.

You need preferably decades of warning: The more time you have the more you can accelerate it obviously. The earlier you apply a unit of acceleration the bigger the difference that unit of acceleration makes down through time.

Changing the velocity of a 25million tons object by 0.01m/s requires a change in kinetic energy of 1,250,000 joules.

Doesn't look like much, but most of the energy you put in via a laser or solar collector is not useful for work.

That is to say, only rock fragments that break away from the object by either vaporizing or exploding away from the object at he object's escape velocity will be acting as "propellant". Thankfully, the escape velocity of an object this size is very low.

So your "propellant" comes from the vaporized rock, water-ice, or methane-ice. And let's say these materials explode away from the asteroid at 10m/s velocity.

then for every kilogram the laser or solar collector vaporized, exploding away at 10m/s, the objects velocity would only be changed by about 4E-10m/s.

If you vaporized 1/100th of the object with matter exploding away at 10m/s, you would only affect the remaining 99% of the object by about 0.1m/s velocity. These are "round" numbers, but they approximately conserve momentum.

You will have vaporized roughly 0.6% of apophis' mass in order to accelerate the remaining 99.4% by 1m/s.

If matter escapes at just 1m/s

In my oppinion, to be effective, you need the "propellant" (vaporized material) to obtain much higher velocities than these.

If you can get the vapors, ions, or other ejecta to velocities of 100m/s or 1000m/s, then that is much, much more useful.

===

If you change the object's velocity by 0.1m/s, then here is how far the course changes at time benchmarks, with no further acceleration:

1 year: 3,153.6km*
2 year: 6,307.2km*
5 year: 15,768km
10 year: 31,536km

* Given the earth's radius, these might not be enough if the asteroid is in a head-on collision or a perfect t-bone collision with earth.

Once you've changed the object's velocity by 0.1m/s, then 5 years should cause enough change in timing to be enough to turn a worst case scenario into a near miss.

As you can see, you need several years warning for a small nudge to change the object's position through time enough to prevent any chance of a future repeat or capture...

Changing the velocity of a 25million tons object by 0.01m/s requires a change in kinetic energy of 1,250,000 joules.

That might be true, but only if you were trying to stop it. We wouldn't be trying to stop it. We'd be trying to push it to the "left or right" so to speak. That requires far less energy.

I have no idea why you said anything about escape velocity.

Changing the velocity of a 25million tons object by 0.01m/s requires a change in kinetic energy of 1,250,000 joules.

That might be true, but only if you were trying to stop it. We wouldn't be trying to stop it. We'd be trying to push it to the "left or right" so to speak. That requires far less energy.

I have no idea why you said anything about escape velocity.

Because only matter that escapes the asteroid contributes to thrust...and this is determined by the asteroid's escape velocity...

Because only matter that escapes the asteroid contributes to thrust...and this is determined by the asteroid's escape velocity...

No, that's nonsense.

The goal of the matter jet isn't to escape the asteroid. It is to produce thrust. Each molecule that breaks free from the asteroid produces a minor amount of thrust in the opposite direction. We don't evaluate rocket fuel based on whether it reaches escape velocity from the mass of the rocket, we evaluate it based on the amount of thrust it applies in a particular direction.

That might be true, but only if you were trying to stop it. We wouldn't be trying to stop it. We'd be trying to push it to the "left or right" so to speak. That requires far less energy.

SH:

I beg to differ. Even a push to the side is subject to all the laws of inertia, linear momentum, angular momentum, and conservation thereof.

Regardless of which direction you are trying to accelerate the object, the required energy and required thrust is the same for the same change in velocity.

So if the object has velocity: 11000i + 0j + 0k

It takes the same amount of change in momentum/kinetic energy to accelerate it by 0.1m/s, regardless of which direction it is accelerated.

So if you have initial object velocity as:

Vi = 11000i + 0j + 0k

And wanted to achieve any of these three scenarios

11000.1j +0k +0j
11000j +0.1k +0j
11000j +0k +0.1j

or any diagonal which has the same vector sum, all take the same exact amount of energy to achieve.

The goal of the matter jet isn't to escape the asteroid. It is to produce thrust. Each molecule that breaks free from the asteroid produces a minor amount of thrust in the opposite direction. We don't evaluate rocket fuel based on whether it reaches escape velocity from the mass of the rocket, we evaluate it based on the amount of thrust it applies in a particular direction.

Rocket's mass is so small that the propellant always escapes a rocket.

If the vaporized matter does not exceed escape velocity, it will be trapped by the asteroids gravity and will fall back to the surface. Conservation of momentum would mean that the main body would experiece zero net thrust.

Thrust is only achieved when the propellant totally escapes the body in question.
==

If you throw a pebble up on earth, the reason the earth eperience no net change in momentum is because gravity traps the pebble and it falls back to the surface, leaving the system unchanged.

If the vaporized matter does not exceed escape velocity, it will be trapped by the asteroids gravity and will fall back to the surface. Conservation of momentum would mean that the main body would experiece zero net thrust.

This is false because you have a vector-based energetic input.

Thrust is only achieved when the propellant totally escapes the body in question.

Also false.

If you throw a pebble up on earth, the reason the earth eperience no net change in momentum is because gravity traps the pebble and it falls back to the surface, leaving the system unchanged.

No, this is completely false. The reason why there is no net change in momentum is because there has been no net change in energetic input.

Regardless of which direction you are trying to accelerate the object, the required energy and required thrust is the same for the same change in velocity.

So if the object has velocity: 11000i + 0j + 0k

It takes the same amount of change in momentum/kinetic energy to accelerate it by 0.1m/s, regardless of which direction it is accelerated.

Correct

So if the object has velocity: 11000i + 0j + 0k

It takes the same amount of change in momentum/kinetic energy to accelerate it by 0.1m/s, regardless of which direction it is accelerated.

Incorrect.

If you're running at me it will take an equal and opposite amount of force for me to stop you in your tracks. If you're running past me it will take far less energy for me to change your direction.

You are completely ignoring force vectoring. That's amateur.

Th is is why you cannot use a chemical rocket engine to move a large moon or planet.

The nozzle velocity of the propellant would be less than the escape velocity of the planet/moon.

So the gases would fly up like a fountain or geyser and then fall back to the surface, apply no net thrust.

An asteroid is not as large as a planet or moon, but it is large enough that this becomes an issued.

===

When you are launching a rocket from earth, the rocket's mass is small enough that it's Ve is negligible, so the propellant escapes. This provides a net thrust on the rocket, which over time overcomes Earth's gravity.

The business of launching a rocket from the surface of a planet, moon, or asteroid is much easier than moving an entire asteriod.

Apophis is 12315.27 times as massive as the entire Space Shuttle...

You will never be able to change it's velocity by more than a few m/s even through entire human life times.

Your still ignoring force vectoring.

Basic physics dictates that when you push on something, it pushes on you as well. If I built a chemical rocket on apophis with the thrust occuring at a right angle to the present velocity vector it would never produce a non-zero thrust, regardless of the escape velocity.

If you're running at me it will take an equal and opposite amount of force for me to stop you in your tracks. If you're running past me it will take far less energy for me to change your direction.

You are completely ignoring force vectoring. That's amateur.

You're a moron.

Nobody is trying to stop an asteroid in it's tracks you idiot.

Inertia is the EXACT SAME regardless of which direction you are trying to accelerate something.

Go back to 9th grade you loser.

You're entire sequence of posts on this thread betrays complete ignorance of even high school level math and physics....

QC:
Thrust is only achieved when the propellant totally escapes the body in question.

SH:
Also false.

You rally are ignorant, SH.

The thing that propels a rocket is the fact that momentum must be conserved, and the fact that for every force there is an equal and opposite force.

If propellant doesn't escape there is no net force...

Your still ignoring force vectoring.

Basic physics dictates that when you push on something, it pushes on you as well. If I built a chemical rocket on apophis with the thrust occuring at a right angle to the present velocity vector it would never produce a non-zero thrust, regardless of the escape velocity.

Chemical rockets have nozzle velocities exceeding escape velocity of apophis, but your statement "regardless..." is wrong dude.

If you had an inefficient rocket, such as shining a laser or light to vaporize the surface...

For apophis, because it's very dense, the escape velocity on it's surface is:

0.1479m/s.

Now try to picture if you had a weak thrust that did not achieve this.

The gases would go "up" and then fall right back to the surface.

The "force" that pushed such gases "up" would be canceled by the opposite force, gravity, when it pulls it back down.

You're a moron.

Nobody is trying to stop an asteroid in it's tracks you idiot.

Then why are you ignoring force vectoring?

Inertia is the EXACT SAME regardless of which direction you are trying to accelerate something.

Do you know what inertia is?

Go back to 9th grade you loser.

You're entire sequence of posts on this thread betrays complete ignorance of even high school level math and physics....

Ha!

You rally are ignorant, SH.

Oh "rally"?

If you put the Space Shuttle's engines on the surface of Apophis and burned them completion, you would only change it's velocity by 0.63m/s.

I swear, you have the audacity to be that fricken stupid that you think Inertia somehow has less effect in one dimension than in another, and then you have the audacity to give ME negative feedback and argue with me...

you're a joke...

If you put the Space Shuttle's engines on the surface of Apophis and burned them completion, you would only change it's velocity by 0.63m/s.

I swear, you have the audacity to be that fricken stupid that you think Inertia somehow has less effect in one dimension than in another, and then you have the audacity to give ME negative feedback and argue with me...

Hey swifty, you have an asteroid hurtling towards Earth at 10,000 m/s with a mass of 5000kg at a distance of 500,000km.

How much constant force must you apply at a right angle to divert the asteroid by 6,000km prior to impact?

Show us you're not an idiot.

explain why the damming of water in the Northern hemisphere affects the rotational velocity of the planet.

*sigh*

That has nothing to do with linear momentum or thrust in a rocket.

That is caused by conservation of ANGULAR MOMENTUM, because ANGULAR MOMENTUM is conserved as the water is farther away from the CoG of the earth. This causes the length of the day to increase by a very tiny amount.

If the water is let out, which will eventualy happen when the dam breaks some time in the future, then conservation of angular momentum will cause the rotational velocity to eventually return to what it was before, as the water re-enters the natural hydrology cycle.

*sigh*

That has nothing to do with linear momentum or thrust in a rocket.

The principles are exactly the same. Force vectoring is essential to understand these things and you're completely ignoring it because you seem to have confused inertia with friction.

That is caused by conservation of ANGULAR MOMENTUM, because ANGULAR MOMENTUM is conserved as the water is farther away from the CoG of the earth. This causes the length of the day to increase by a very tiny amount.

Shorten, smart guy.

Angular momentum is an expression of force vectoring, which, once again, YOU ARE COMPLETELY IGNORING.

Hey swifty, you have an asteroid hurtling towards Earth at 10,000 m/s with a mass of 5000kg at a distance of 500,000km.

How much constant force must you apply at a right angle to divert the asteroid by 6,000km prior to impact?

Show us you're not an idiot.

At that initial velocity you'd only have 50,000 seconds of acceleration time.

Vi = 10000i + 0k = 10000m/s

Vf = 10000i + 120k

Vf = sqrt (10000^2 + 120^2) = 10000.7199741m/s

You are confused because you are applying the force vector equations in reverse. The hypoteneuse is the combination of the component orthogonal vectors, whether we're talking about force, velocity, mementum, etc.

Orthogonal vector sums are found by pythagorean theorem.

the acceleration needed is:

Aj = 0.0048m/s^2 j

Fj = MA = 24N j

We need no force applied along the i portion of the vector.

The object was accelerated by 240m/s, having an average velocity of 120m/s in direction j, throughout the 50,000 seconds.

In short, accelerating an object in any one direction is unaffected by whatever velocity it already has, excluding relativistic effects.

Of course, vector sums for orthogonal vectors uses pythagorean theorem, as I showed above, which I think a 9th grader can do...maybe.

Although I should point out, what I did above was the AVERAGE velocity, because that's what matters most.

Vf = 10000i + 240j = sqrt(10000^2 + 240^2)

Vf = 10002.8795854m/s.

The above post shows what the AVERAGE was during the "burn"...

Because in 50,000s, the object averaged 120m/s to move by 6000km (6000000m), but the Vf in j was actually 240m/s, which I labelled wrong above.

Hope you see what I'm saying here.

Average total velocity of object was:

V = sqrt(10000^2 + 120^2)

Final total velocity was:

V = sqrt(10000^2 + 240^2)

So it takes 24Newtons constant in j for 50,000 seconds to move the object by 6,000,000m in the same direction as j.

Well, SH, get a life then.

The total velocity of an object is the vector sum of it's component velocities.

The initial velocity in i is irrelevant to the force required to accelerate an object in j.

In fact, once you have the time required for the object to hit earth if you did nothing at all, which was distance divided by velocity, which was 50,000 seconds, then this problem actually becomes a 9th grade position problem in j...

delta p = 6000000m = (0*t + (1/2)at^2) j

12000000m = at^2 = a*(50,000^2)j

aj = 12000000/(50,000^2)

a = (0i + 0.0048j)m/s^2

F = MA

F = 5000kg *(0i + 0.0048j)m/s^2

F = (0i + 24j) kg*m/s^2

Since no acceleration is neeed in i, the force vector is in an identical direction as the needed motion.

Total final Velocity is the sum of component velocities:

V = = sqrt(10000^2 + 240^2)

total average velocity is the sum of component average velocities.

V = = sqrt(10000^2 + 120^2)

At that initial velocity you'd only have 50,000 seconds of acceleration time.

Correct as given by dividing the distance by the velocity. 50,000 seconds.

0.0048m/s^2 j

What?

So it takes 24Newtons constant in j for 50,000 seconds to move the object by 6,000,000m in the same direction as j.

No.
Divide the distance by the amount of time. 6,000,000m/50,000 seconds=120 m/s
This is the average acceleration you need to produce over 50,000 seconds to move the object to the required distance.

Force is given by the simplistic F=ma.

5,000kg * 120m/s = 600,000 kg*m/s or 600,000 Newtons in total for an instant acceleration to that speed.

The answer is not 24 N per second it is 600,000 N/ 50,000 s. or 12

Forward velocity is irrelevant outside of determining the amount of time you have to apply the force.

excuse me, above should read 5,000kg* 120 m/s^2.

The final result unit should be 12 kg*m/s

Divide the distance by the amount of time. 6,000,000m/50,000 seconds=120 m/s
This is the average acceleration you need to produce over 50,000 seconds to move the object to the required distance.

No it's not. You're ridiculous.

Distance divided by Time is average velocity.

m/s = average velocity

v = distance/time

6000000/50000 = 120m/s = average velocity...

Average velocity is NOT acceleration.

Change in Velocity divided by time is acceleration.

Delta V = at

Since we need to average 120m/s, we need delta v to be 240 m/s.

240 = at

a = 240m/s / 50,000s = 0.0048 m/s^2

F = MA

F = 5000kg * 0.0048m/s = 24kg*m/s^2 = 24 Newtons

Crap, edit function is busted.

Last line should be:

F = 5000kg * 0.0048m/s^2 = 24kg*m/s^2 = 24 Newtons

Previous version forgot the "^2" in the middle segment.

Average velocity is NOT acceleration.

Correct, you are attempting to accelerate an object from zero to an unknown velocity to reach a distance of 6,000,000m.

So you were correct to involve delta where I did not. 24N is correct.

Now apply that to Apophis and determine why your joule statement is incorrect.

Run an experiment that decelerates it and steers it into a stable orbit suitable for asteroid mining.

If something goes wrong it could always be dropped on Mecca since its been slowed down somewhat.. :)

It's a sign from God!

I'd vote for dropping it on the Vatican instead. Once we have the proof of concept, THEN we drop one on Mecca. Mecca, or the Shriners HQ.

To accelerate apophis by the same amount as the example object takes either 5000000 times the force, or 5000000 times the duration.

apophis mass 25,000,000,000kg...

to Accelerate apophis by:

Delta V = 240m/s

It would take 120Mega-Newtons for 50,000 seconds...

Which is to say 6E12 Newton*seconds.

===
In that post I used a target Delta v of 0.01m/s for apophis as an example.

This would mean you'd need 250,000,000 Newton*seconds.

If you applied ths accross 50,000 seconds then you'd need

5000 Newtons constant for 50,000 seconds to accelerate apophis by Delta v = 0.01m/s.

If we define a reference frame such that apophis' current instantaneous velocity is in i, then the change in kinetic energy in j is still equal to as if i never existed.

Ek = 0.5*m*v^2.

Delta Ek j = 0.5* 25,000,000,000kg *(0.01m/s)^2 j

Delta Ek j = 125,000,000 joules.

At the top, I incorrectly wrote "1,250,000 joules".

I accidentally cubed the Delta v, I'm sure...

At the top, I incorrectly wrote "1,250,000 joules".

I accidentally cubed the Delta v, I'm sure...

There you go.

If you see where I screwed up, you called me on it, I looked over my figures again and saw my error, stating you're correct.

When I called you on it, you just stuck your fingers in your ears and started shouting.

"If you throw a pebble up on earth, the reason the earth eperience no net change in momentum is because gravity traps the pebble and it falls back to the surface, leaving the system unchanged."

That is not correct. Conservation of energy rules. What is missing from your pebble analogy is the energy released when the the ejected material falls back and collides with the asteroid applying a force in the accelerating it. For there to be no net acceleration, all the energy from the reflector would need to be converted in the asteroid as heat.
Also if you remember the equation "a=acceleration (ms^-2)", it's not linear. Try thinking through this again.

I must say, my space shuttle analogy was wrong. It's even worse than that.

If you totalled all the thrust of the space shuttle, if you coudl get the whole thing in space with that much fuel...

12.5MN * 124s = 1.55 billion Newton*seconds
+
5.45MN * 480s = 2.616 billion Newton*seconds
+
53.4KN * 1250s = 66.75 million Newton*seconds

Total: 4,232,750,000 Newton*seconds

That would get apophis up to:

Delta V j = 0.16931m/s j

Of course, the launch vehicle you'd need to escape earth and put the entire existing space shuttle launch vehicle into space and match course with apophis would be unimaginably large....

That is not correct. Conservation of energy rules. What is missing from your pebble analogy is the energy released when the the ejected material falls back and collides with the asteroid applying a force in the accelerating it. For there to be no net acceleration, all the energy from the reflector would need to be converted in the asteroid as heat.
Also if you remember the equation "a=acceleration (ms^-2)", it's not linear. Try thinking through this again.

For the 'not escape velocity" scenario...

You can't neglect the fact that the equal and opposite force applied to apophis by the ejecta is also canceled by the gravity of the ejecta during this time.

The masses are small enough that we can't neglect this.

Assuming no escape velocity, then.

When the ejecta moves away and equal and opposite force acts on apophis.

When the ejecta moves back towards apophis over some time, t, an equal and opposite force pulls apophis back by the time the ejecta lands.

For gravity:

F = G*Mm/r^2

Apophis pulls on a pebble by exactly the same FORCE that the pebble pulls on apophis.

The pebble's mass is smaller, so it accelerates more and has larger change in velocity, but the objects affect one another by the same Force.

If the pebble does not achieve escape velocity, then it pulls on apophis by exactly the same force that pushed it away at first. This produces no net thrust if the pebble falls back to the surface.

In order to conserve momentum, the forces must be equal and opposite.

Conserve momentum:

Delta p1 + Delta p2 = 0

Always, whether or not the ejecta escapes, momentum is conserved.

If the ejecta is back on the surface, then final velocity mustn't have changed.

Always wondered, what about changing the albedo of one side of the asteroid, or selective parts of it. Paint one side of it black (or white). Over enough time would not that have an effect.

The pebbles momentum hasn't changed but the asteroid's has twice. First the pebble exerts a force on the asteroid = to the kinetic energy of the pebble leaving the surface (the force, added to the system, by the reflector. The same way a gun kicks when fired). Then, the same amount of energy is returned on impact. You are correct about the force of gravity being negated but you're not including the transfer of energy from the reflector.
Delta p1 + Delta p2 does = 0 looking at only gravity, but when you include the energy to accelerate and decelerate the pebble there is a net force in the opposite direction on the asteroid = to the energy needed to move the pebble (minus the energy loss from the inelastic collision transfered as heat).

If you are going to try to deflect Apophis then why not deflect its orbit so that it crashes into the sun?
This would eliminate the risk of it entering "one of two keyholes" and thus eliminate the risk of an impact on its return journey.

Your still ignoring force vectoring.

Basic physics dictates that when you push on something, it pushes on you as well. If I built a chemical rocket on apophis with the thrust occuring at a right angle to the present velocity vector it would never produce a non-zero thrust, regardless of the escape velocity.

This is too funny! SH is proposing nothing less than a propellantless propulsion scheme! I love it!

It's like saying; If I push down real hard on the earth, I can change its momentum!

I don't think he understands that gravity acts like a rubberband, which pulls the propellant and asteroid back together. That is, if your propellant doesn't escape the system, the system's momentum must be conserved in its entirety (which includes the exhaust/propellant).

The escape velocity for a perfect object (sphere and uniform density and a universal gravity constant) of this volume and mass has an escape velocity of 0.13m/s. For comparison this is .3 miles per hour, or about 10 times the speed of a snail. You could escape the gravity field of this rock by jumping.

Anything being launched or ejected from the asteroid able to produce a relative force against it should be able to meet this escape velocity. Those who published this report know about this, they've done the simulations and know if a method will clear this hurdle, then look at feasibility and the practicality of the they're proposing.

Remember that while these asteroids have a lot of force behind then, they aren't planets or moons and they don't have a large gravity well.

Quantum Conundrum, what power output of a laser would you need to deflect Apophis by about 6000km over a 5 year period. I took into consideration the energy needed to produce a jet stream by raising the temperature of a specific mass of Apophis, And for this total jet stream to produce a force to move Apophis at a given speed over 5 years to a distance of 6000km. The result was not what I expected. The laser power output was very high.

Thank you.

Some of you guys seem to be ignoring some facts. Almost any force on it will alter its course, there's no huge minimum like QC said. QC, are you saying that a force applied that is less than that figure you quoted will do nothing?

QC is partially right about escape velocity but gases that are formed like a rocket exhaust on the surface will apply almost all of their force at a vector as SH says and if it does not reach escape velocity (which it probably will since gravity is extremely weak on an asteroid) it will indeed return that energy but it will be dispersed all around the asteroid and not return it at a vector thus not negating the initial force vector.

...What could happen if a 25-million-ton chunk of rock slammed into Earth?...

This is a common way to describe this and it's WRONG. Public opinion on this needs to be swayed and describing these things in terms of 'if' or 'could' is wrong, it should be WHEN. It IS going to happen again, the only question is when.

This is too funny! SH is proposing nothing less than a propellantless propulsion scheme! I love it!

Care to tell me where I said that?

It's like saying; If I push down real hard on the earth, I can change its momentum!

Well technically, you very well could if you could push down hard enough. One would question where you're getting the energy from.

I don't think he understands that gravity acts like a rubberband, which pulls the propellant and asteroid back together.

I don't think you understand energetic input

That is, if your propellant doesn't escape the system, the system's momentum must be conserved in its entirety (which includes the exhaust/propellant).

And then let's discuss heat, and potential vs kinetic energy. Go ahead and support your stance.

I love this argument! Too bad you turned it into a catfight, ladies please, there enough math for everybody to share. The good news is, we get it. Hit it hard, hit it early, hit it often.

it will indeed return that energy but it will be dispersed all around the asteroid and not return it at a vector thus not negating the initial force vector.

Dispersed by pressure and gravity. The exhaust will be pulled back to the asteroid by GRAVITY which works both ways. The asteroid must also move towards the exhaust it deflects. Thus the exhaust pushes the asteroid on its way UP the gravity well and is slowed by the gravity of the asteroid which accelerates toward the exhaust by gravity.

The momentum of a closed system must remain unchanged by anything going on within the system.

The only way I can see gravitationally bound exhaust changing the orbit of the asteroid is if it being deflected by a much larger gravity field, thus not having a closed system. In that case the time it takes for the exhaust to return to the asteroid's surface might result in deflection.

Have to be pretty damn slow exhaust for this to have any meaning.

Ethelred

Gravitationally bound exhaust could deflect an asteroid
if it was not uniformly distributed around the asteroid.

By having a region of higher pressure on one side of
asteroid (thanks to brownian motion and gas laws),
there would be a net force applied to the rock.

It's entirely possible that solar wind would scour
gravitationally bound exhaust from the asteroid
before the feeble gravity could distribute it evenly
around the asteroid.

You're a moron.... you idiot. Go back to 9th grade you loser.

You're entire sequence of posts on this thread betrays complete ignorance of even high school level math and physics....

You rally are ignorant, SH.

This from the guy that posts miles and miles of garbled nonsense while confusing radius and diameter (you can ask GSwift about that one, he got the same treatment. LOL). Not much of a conundrum here.

Hmmm, I actually worked out that it requires more energy to produce the vapour for the jet stream, than that needed by it, to impart a force on the asteroid over a time period. Much more in fact. Not sure if this is true but I wanted to see what other people think.

Care to tell me where I said that?

For one, in the post I was replying to. You stated the escape velocity is irrelevant.

Well technically, you very well could if you could push down hard enough. One would question where you're getting the energy from.

Unless I push hard enough to obtain escape velocity in the reaction, we'll just fall right back together again with no net momentum change.

I don't think you understand energetic input

I don't think you understand the difference between kinetic energy and momentum.

And then let's discuss heat, and potential vs kinetic energy. Go ahead and support your stance.

Kinetic energy and momentum aren't the same thing. Kinetic energy is scalar, momentum is a vector quantity.

http:/www.euclideanspace.com/physics/dynamics/energy/index.htm

Also:

http:/en.wikipedia.org/wiki/Momentum#Conservation_of_linear_momentum

Gravitationally bound exhaust could deflect an asteroid
if it was not uniformly distributed around the asteroid.

Nope. This could only change it's orientation. It'd be like picking up a rock and moving it somewhere else. As you move the rock, the asteroid moves in an equal and opposite reaction beneath you. When you stop, so does the asteroid. Spaceships use this principle to orient themselves, using internal gyros.

Gravitationally bound exhaust could deflect an asteroid
if it was not uniformly distributed around the asteroid.

Nope.

Yep.

Even releasing a gas on one side of an asteroid, at low speed and without a nozzle, will cause an asteroid to translate. Diatomic hydrogen at 300 Kelvin has an average molecular velocity of around 1500 meters per second. As the gas expands, it will push on the asteroid as if it were a piston, and the asteroid will translate. It's calculus, but it will continue to do work until it has been scrubbed away by solar wind or expanded to unmeasurable thinness.

Rocket exhaust or "steerable jets" would have to be very, very cold before their average molecular speed falls below the escape velocity of this little rock.

...Spaceships use this principle to orient themselves, using internal gyros.

Nope.

Satellites orient themselves with reaction wheels, not gyroscopes. Gyroscopes are gimballed, and impart no torque on their satellite.

Diatomic hydrogen at 300 Kelvin has an average molecular velocity of around 1500 meters per second.

Which only serves to prove my point, as this would be well above the escape velocity for this asteroid, now wouldn't it?

If the exhaust gasses do not fall to back to the asteroid and do not escape, you've only expanded the system and (slightly) moved it's center of mass, but you've not changed the system's net momentum.

If the gas is scrubbed away before it falls, that would be another example of escape, again serving only to prove my point.

Satellites orient themselves with reaction wheels, not gyroscopes. Gyroscopes are gimballed, and impart no torque on their satellite.

You're right, of course, but I was trying to avoid technical jargon. I could have used "flywheel," I suppose.

I felt "reaction wheel" might be easily confused with "steering wheel" (like on a car).

The point remains valid though.

Consider the simplest possible instance of this scenario: two objects are held together by solely by gravity and are initially at rest at the origin in the (inertial) coordinate system chosen. If one of these objects is then hit by a laser beam (nothing is detached), the beam is absorbed, and that object starts moving. If the imparted momentum is within the appropriate range, the two objects now orbit one another, coming arbitrarily close at one point in the orbit. However, consider that the two bodies are now in motion relative to the origin, since the coordinate system was not the center of momentum coordinate system (due to the momentum of the laser beam). It is clear that neither object reached escape velocity, but conservation of momentum dictates that the 2-object system's center of mass is set into motion. So, it is not required that the ejected material reach escape velocity, only that momentum is introduced to the asteroid from elsewhere.

...two objects are held together by solely by gravity and are initially at rest at the origin in the (inertial) coordinate system...

For this to be true, they'd essentially have to be touching each other.

...coming arbitrarily close at one point in the orbit

They'd already be touching.

...it is not required that the ejected material reach escape velocity, only that momentum is introduced to the asteroid from elsewhere.

Right. In this case, it's acted upon by the laser (an outside force). That's a fundamental law of motion.

Technically, rockets don't change the momentum of the entire system, except that we ignore the exhaust which has escaped (as a matter of practicality). So it's imperative for the exhaust to escape, for us to consider a net momentum change to the part of the system in question.

So it's imperative for the exhaust to escape, for us to consider a net momentum change to the part of the system in question.

Good point. I agree that as long as the dust and rocks propelled by the vaporization of the ice are moving faster than escape velocity they (or rather, the expanding vapor) will have produced a net force on (what remains of) the asteroid. Indeed the article implies (and it is not hard to believe) that the ice vaporization produces much more thrust than the laser alone.

In regards to non-escape velocity fuel particles, the following commenters are wrong:
Skeptic_Heretic
Moebius
retrosurf
S_Bilderback

The following commenters are right:
Quantum_Conondrum
ubavontuba
Ethelred
Iomed

In the case of QC and uba, many of you owe them an apology and some 5 ratings from your vast army of sockpuppets. I know that they are usually wrong and have earned thousands of 1 ratings from me over the years, but give credit where credit is due (carefully - some of QC's many posts in this thread are laughably wrong).

So it's going to be close to the earth, what about our moon? It could deflect or take a hit as well.

Or, like Steven Chu wants to do to earth roofs, paint it white, or at least change its albedo and that should slow it down or speed it up a touch.