So you think global warming is a big problem? What could happen if a 25-million-ton chunk of rock slammed into Earth? When something similar happened 65 million years ago, the dinosaurs and other forms of life were wiped out.

"A collision with an object of this size traveling at an estimated 30,000 to 40,000 mile per hour would be catastrophic," according to NASA researcher and New York City College of Technology (City Tech) Associate Professor of Physics Gregory L. Matloff. What does he recommend? "Either destroy the object or alter its trajectory." Dr. Matloff, whose research includes the best means to avert such a disaster, believes that diverting such objects is the wisest course of action.

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, will make two close passes by Earth at a distance of about 22,600 miles. "We don't always know this far ahead of time that they're coming," Dr. Matloff says, "but an Apophis impact is very unlikely."

If the asteroid did hit Earth, NASA estimates, it would strike with 68,000 times the force of the atom bomb that leveled Hiroshima. A possibility also exists that when Apophis passes in 2029, heating as it approaches the sun, it could fragment or emit a tail, which would act like a rocket, unpredictably changing its course. If Apophis or its remnants enter one of two "keyholes" in space, impact might happen when it returns in 2036.

Large chunks of space debris whizzing by the planet, called Near-Earth Objects (NEOs), are of real concern. NASA defines NEOs as comets and asteroids that enter Earth's neighborhood because the gravitational attraction of nearby planets affects their orbits. Dr. Matloff favors diverting rather than exploding them because the latter could create another problem -- debris might bathe Earth in a radioactive shower.

Dr. Matloff's research indicates that an asteroid could be diverted by heating its surface to create a jet stream, which would alter its trajectory, causing it to veer off course. In 2007, with a team at the NASA Marshall Space Flight Center in Huntsville, Alabama, he investigated methods of deflecting NEOs. The team theorized that a solar collector (SC), which is a two-sail solar sail configured to perform as a concentrator of sunlight, could do the trick. Constructed of sheets of reflective metal less than one-tenth the thickness of a human hair, an SC traveling alongside an NEO for a year would concentrate the sun's rays on the asteroid, burn off part of the surface, and create the jet stream.

To do that, it is necessary to know how deeply the light would need to penetrate the NEO's surface. "A beam that penetrates too deeply would simply heat an asteroid," explains Dr. Matloff, "but a beam that penetrates just the right amount -- perhaps about a tenth of a millimeter -- would create a steerable jet and achieve the purpose of deflecting the asteroid."

For the past year, Dr. Matloff and a team of City Tech scientists have been experimenting with red and green lasers to see how deeply they penetrate asteroidal rock, using solid and powdered (regolith) samples from the Allende meteorite that fell in Chihuahua, Mexico in 1969. Dr. Denton Ebel, meteorite curator at the American Museum of Natural History in New York City, provided the samples.

Assistant Professor of Physics Lufeng Leng, a photonics and fiber optics researcher, along with student Thinh Lê, an applied mathematics senior, used lasers to obtain optical transmission measurements (the fraction of light passing through the asteroidal material). Their research was supported by a Professional Staff Congress-City University of New York research grant.

"To my knowledge," says Dr. Matloff, "this is the first experimental measurement of the optical transmission of asteroid samples. Dr. Ebel is encouraging other researchers to repeat and expand on this work."

In a related study, Dr. Leng and her student (whose research was partially supported by City Tech's Emerging Scholars Program) narrowed the red laser beam and scanned the surface of a thin-section Allende sample, discovering that differences in the depth of transmitted light exist, depending on the composition of the material through which the beam passes. From their results, they concluded that lasers aimed from a space probe positioned near an NEO could help determine its surface composition.

Using that information, solar sail technology could more accurately focus the sun's rays to penetrate the asteroid's surface to the proper depth, heating it to the correct degree for generating a jet stream that would re-direct the asteroid.

"For certain types of NEOs, by Newton's Third Law, the jet stream created would alter the object's solar orbit, hopefully converting an Earth impact to a near miss," Dr. Matloff states. However, he cautions, "Before concluding that the SC will work as predicted on an actual NEO, samples from other extraterrestrial sources must be analyzed."

Dr. Matloff presented a paper on the results of the City Tech team's optical transmission experiments, "Optical Transmission of an Allende Meteorite Thin Section and Simulated Regolith," at the 73rd Annual Meeting of the international Meteoritical Society, held at the American Museum of Natural History and the Park Central Hotel in New York City.

"At present," he adds, "a debate is underway between American and Russian space agencies regarding Apophis. The Russians believe that we should schedule a mission to this object probably before the first bypass because Earth-produced gravitational effects during that initial pass could conceivably alter the trajectory and properties of the object. On the other hand, Americans generally believe that while an Apophis impact is very unlikely on either pass, we should conduct experiments on an asteroid that runs no risk of ever threatening our home planet."

**Explore further:**
NASA Statement on Student Asteroid Calculations

## blazingspark

Jan 28, 2011## Quantum_Conundrum

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.

## Quantum_Conundrum

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

## Quantum_Conundrum

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...

## Skeptic_Heretic

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

## Quantum_Conundrum

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

## Skeptic_Heretic

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.

## Quantum_Conundrum

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.

## Quantum_Conundrum

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.

## Skeptic_Heretic

## Skeptic_Heretic

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.

## Quantum_Conundrum

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.

## Skeptic_Heretic

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.

## Quantum_Conundrum

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....

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...

## Quantum_Conundrum

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.

## Skeptic_Heretic

## Quantum_Conundrum

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...

## Skeptic_Heretic

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.

## Quantum_Conundrum

*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.

## Skeptic_Heretic

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

## Quantum_Conundrum

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.

## Quantum_Conundrum

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"...

## Quantum_Conundrum

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)

## Quantum_Conundrum

## Quantum_Conundrum

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)

## Skeptic_Heretic

What?

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.

## Skeptic_Heretic

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

## Quantum_Conundrum

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

## Quantum_Conundrum

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.

## Skeptic_Heretic

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.

## MorituriMax

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.

## Quantum_Conundrum

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...

## Skeptic_Heretic

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.

## S_Bilderback

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.

## Quantum_Conundrum

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....

## Quantum_Conundrum

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.

## Quantum_Conundrum

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.

## _ichard_raser

## S_Bilderback

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).

## Au-Pu

This would eliminate the risk of it entering "one of two keyholes" and thus eliminate the risk of an impact on its return journey.

## ubavontuba

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).

## stemfish

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.

## linearmot

Thank you.

## Moebius

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.

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.

## Skeptic_Heretic

## rproulx45

## Ethelred

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

## retrosurf

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.

## Gawad

## linearmot

## ubavontuba

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

Also:

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

## ubavontuba

## retrosurf

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.

Nope.

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

## ubavontuba

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. 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.

## lomed

## ubavontuba

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.

## lomed

## barakn

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).

## Nartoon

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.