asteroid strike 100% likely, but... (warning - physics post)

[[xeno]Julios]

Watching the arm chair physicist argue with the physics grad student is funny

i tutor high school physics as a means of income, but that's irrelevant.

and there's a difference between discussion and argument.

[Nightshade]

menkent's right. One of the problems in creating mathematical models is sacrificing accuracy for generality and vice versa. You CAN'T ignore gravitational effects in a celestial mechanics problem and have it mean anything significant.

[menkent]

let me ask you this: if we ignore earth's gravity, do you agree that the stationary asteroid example is identical in terms of figuring out how much force is required along the orthogonal axis?

absolutely not - you're changing its position instead of its vector. and ignoring the earth's gravity defeats the entire thing. you're not trying to keep a golf ball from hitting the hole but ignoring that the hole is at the bottom of a large funnel.

[tnf]

whats your vector victor?

That's all I can contribute to this science stuff.

[[xeno]Julios]

menkent's right. One of the problems in creating mathematical models is sacrificing accuracy for generality and vice versa. You CAN'T ignore gravitational effects in a celestial mechanics problem and have it mean anything significant.

If we ignore earth's gravity, then it will require less tugging. The whole purpose of my post was to assess the feasibility - if it turns out that you'll require a 30 years of tugging without earth's gravity, then we can safely say that with earth's gravity, it'll require more time.

[[xeno]Julios]

...and ignoring the earth's gravity defeats the entire thing. you're not trying to keep a golf ball from hitting the hole but ignoring that the hole is at the bottom of a large funnel.

ffs read above

[[xeno]Julios]

here, let me spell it out more explicitly:

please try to read this carefully, and if you find any genuine conceptual mistakes, address them explicitly.

the purpose of my original post was to attempt a feasibility assessment of the tugging solution.

1) If Earth's gravitational field magically disappeared, it would be easier to deflect an incoming asteroid.

2) If we calculate how much force would be required to deflect an incoming asteroid, within a timelimit, and compare that to the force that a "small apollo sized tractor ship" could exert, and we do this assuming no earth gravity, and it turns out to be not enough, then we can safely say that if there were earth gravity, then it would definitely not be enough.

stated another way: 2) if it's not feasible assuming no earth gravity, then it's certainly not feasible with earth's gravity, as earth's gravity only makes the task harder.

Do we agree up to this point?

3) If we assume no earth gravity, then I argue that you don't need polar coordinates (i'm not even sure what you'd do if you did want to incorporate earth's gravity, short of a computational simulation) - if you know how much you want to orthogonally displace the asteroid, and you know how much time you have to achieve this displacement, then you can calculate how much acceleration is required, using basic 2 dimensional kinematics. Furthermore, this is another leniency on the feasibility assessment since the calculations assume that the tugging force is being applied for the entire duration - so if it turns out not to be feasible with tugging for the whole duration, then it's certainly not feasible with tugging for only part of the duration.

I will now attempt to demonstrate 3):

In the first picture, we see the situation at time 1:



The black arrow going left indicates the movement of the asteroid - it is not accelerating forwards, and there is no force acting in this direction.

The blue arrow pointing upwards indicates the tugging force.

Notice that the direction of force is orthogonal to the direction that the asteroid is traveling.

Now this is our end goal:



The key point to note here is that the displacement D is solely due to the orthogonally applied force seen in the first image.

If we know what D is, and we know the time we have to achieve this displacement, then we can calculate the orthogonal force required.

Now let's see how we apply this:

Let's say that our current technology gives us the ability to tug for 6 months. This includes being able to predict a collision at least 6 months in advance, and securing a ship to tug 6 months away from collision.

We thus have:

displacement (radius of earth, assuming it's on a collision course with earth's centre)

time

initial velocity along direction of displacement (0 m/s)

we can thus calculate the necessary acceleration.

If we have the mass of the asteroid, we can then calculate the necessary force to be applied over time.

We can then see how much force an apollo sized tractor craft is capable of exerting, and see if it meets our bill.

If it doesn't, then we can be sure that it wouldn't meet the bill if there were earth's gravity to consider.

That is all i'm trying to say here.

[Nightshade]

The only conceptual mistake I see is the need to exert a pulling force over time. It's not necessary for a coarse approximation such as this. Just calculate the needed instantaneous force to be applied orthogonally to create the desired resultant path vector (based on the angle needed to miss the Earth).
My point was not that your concept was invalid, merely that this is in no way an accurate approximation.

[menkent]

your problem is still set up wrong to determine whether or not the deflector ship idea is feasible. you don't want the asteroid to miss earth, after all. you want it to miss the far edge of earth's gravitational well... a far smaller deflection. second, your time-table of five days is ausurdly small. the damn thing is 30 years away? 10 years R&D, 10 years to travel out to it, 10 years to deflect.

[[xeno]Julios]

The only conceptual mistake I see is the need to exert a pulling force over time. It's not necessary for a coarse approximation such as this. Just calculate the needed instantaneous force to be applied orthogonally to create the desired resultant path vector (based on the angle needed to miss the Earth).

Furthermore, this is another leniency on the feasibility assessment since the calculations assume that the tugging force is being applied for the entire duration - so if it turns out not to be feasible with tugging for the whole duration, then it's certainly not feasible with tugging for only part of the duration.

My point was not that your concept was invalid, merely that this is in no way an accurate approximation.

Right - I've never disagreed on this point - but for purposes of feasibility you see why ignoring earth's gravity is completely valid right? (i.e. if it turns out to be infeasible without earth's gravity, then this is a useful result, as it will surely be infeasible with earth's gravity. If, on the other hand, it turns out to be feasible without the earth's gravity, it doesn't really tell us much. It's more of testing a lower level of feasibility. The same logic explains why I'm assuming a long sustained force.

[[xeno]Julios]

your problem is still set up wrong to determine whether or not the deflector ship idea is feasible. you don't want the asteroid to miss earth, after all. you want it to miss the far edge of earth's gravitational well... a far smaller deflection.

Yes, if in reality, an asteroid's trajectory was only just within the boundary of the gravity well, you would only need a tiny displacement. This analysis assumes the worst case scenario - asteroid headed straight into centre of earth. (I already brought up this point before).

second, your time-table of five days is ausurdly small. the damn thing is 30 years away? 10 years R&D, 10 years to travel out to it, 10 years to deflect.

five days? you mean six months right? Either way, that's just an arbitrary figure to illustrate my approach. We can just as easily plug in 10 years.

[Nightshade]

The only conceptual mistake I see is the need to exert a pulling force over time. It's not necessary for a coarse approximation such as this. Just calculate the needed instantaneous force to be applied orthogonally to create the desired resultant path vector (based on the angle needed to miss the Earth).

Furthermore, this is another leniency on the feasibility assessment since the calculations assume that the tugging force is being applied for the entire duration - so if it turns out not to be feasible with tugging for the whole duration, then it's certainly not feasible with tugging for only part of the duration.

My point was not that your concept was invalid, merely that this is in no way an accurate approximation.

Right - I've never disagreed on this point - but for purposes of feasibility you see why ignoring earth's gravity is completely valid right? (i.e. if it turns out to be infeasible without earth's gravity, then this is a useful result, as it will surely be infeasible with earth's gravity. If, on the other hand, it turns out to be feasible without the earth's gravity, it doesn't really tell us much. It's more of testing a lower level of feasibility. The same logic explains why I'm assuming a long sustained force.

Yes, I know what you're talking about, I just don't see the need for half measures here, unless you're talking about making it a freshman-level problem.

[SIK]

http://www.sciencenews.org/articles/20051112/fob8.asp

From the article:-

"The gravitational tractor, as the researchers call their proposed craft, would require the sustained power of a nuclear-propulsion system to reach the asteroid and perform the maneuvers that would be required to deflect it. For general space exploration, NASA has already proposed a fleet of suitable vehicles, although their funding is currently uncertain.

As envisioned by Ed Lu and Stan Love of NASA's Johnson Space Center in Houston, the gravitational tractor would hover some tens of meters from a spinning asteroid. Only the force of gravity would connect the two.

Careful control of the tractor's thrusters would keep the craft close to the asteroid as it slowly pulled the rock off its collision course. Given enough lead time, it would take just a year for a 20-ton spacecraft to drag a 200-meter-wide asteroid weighing about 60 million tons away from Earth's path, Lu and Love calculate in the Nov. 10 Nature. Towing would have to begin at least 20 years before the projected collision. "

[[xeno]Julios]

Yes, I know what you're talking about, I just don't see the need for half measures here, unless you're talking about making it a freshman-level problem.

I'm using the tools I have available - I don't yet know calculus and don't have access to simulation software.

And even if I did, this would be a logical approach since if turned out to be infeasible making these assumptions, then you could stop wasting your time to check for feasibility without those simplifications.

Think of it as running a graphics test on your computer for a game that's coming out. You have access to two benchmark utilities - one of them stresses the card in 640x320 resolution, and the other at 1024x768. The game that's coming out runs at 1024x768.

What I'm doing here is running the 640x320 benchmark - if the framerate sucks, I don't have to waste time running the 1024 benchmark.

[[xeno]Julios]

http://www.sciencenews.org/articles/20051112/fob8.asp

From the article:-
it would take just a year for a 20-ton spacecraft to drag a 200-meter-wide asteroid weighing about 60 million tons away from Earth's path, Lu and Love calculate in the Nov. 10 Nature. Towing would have to begin at least 20 years before the projected collision. "

ah thanks for this!

bit confused though - is it one year, or 20 years?

edit: nm i think i get it - start 20 years before collision, but apply tugging for one year.

[[xeno]Julios]

Ok, using their figures (and ignoring earth's gravity, which may be legit given that this is 30 years away from collision)

F = GM1M2/r^2

F = G(20,000)(60,000,000,000)/10*10

= 800.4 newtons

to find the acceleration of the asteroid due to the tractor craft:

a = f/m = 800.4/60,000,000,000

= 0.00000001334m/s/s = 1.3x10^-8 m/s/s

time = 1 year
= 31.5 x10^6 seconds

d = v1*t + 0.5*a*t^2

displacement = 0.5*1.3*10^-8*(31.5*10^6)^2

= 6618 km

(pretty close to radius of earth, but that's probably a coincidence - will check out the nature paper).

I'm also assuming the craft and asteroid are spherical, which is not the case in reality.

[Turbine]

What's with the arguing, when this rock is going to miss us by a long margin?

"(99942) Apophis (previously known by its provisional designation 2004 MN4) is a near-Earth asteroid that caused a brief period of concern in December 2004 because initial observations indicated a relatively large probability that it would strike the Earth in 2029. However, additional observations provided improved predictions that eliminated the possibility of an impact on Earth or the Moon in 2029. However there remained a possibility that during the 2029 close encounter with Earth, Apophis would pass through a "gravitational keyhole", a precise region in space no more than about 400 meters across, that would set up a future impact on April 13, 2036. This possibility kept the asteroid at Level 1 on the Torino impact hazard scale until August 2006.

Additional observations of the trajectory of Apophis revealed the "keyhole" would likely be missed and on August 5, 2006, Apophis was lowered to a Level 0 Torino impact hazard scale. As of October 19, 2006 the impact probability for April 13, 2036 is estimated at 1 in 45,000. An additional impact date in 2037 has been identified, however the impact probability for that encounter is 1 in 12.3 million.

Despite the fact that there is no longer any significant probability of an Earth impact, The Planetary Society is offering a $50,000 prize for the best plan to put a tracking device on or near the asteroid."

- Wiki

[mjrpes]

julez... you unemployed right now?

[[xeno]Julios]

ok just read the paper:

The mean change in velocity required to deflect an asteroid from an Earth impact trajectory is about 3.5x10^-2/t m/s , where t is the lead time in years(4). So a 20-tonne gravitational tractor hovering for one year can deflect a typical asteroid of about 200m diameter given a lead time of roughly 20 years.

So they're using a predetermined formula to figure out the required velocity change (they use the gm/r^2 to calculate the actual velocity change).

The reference for this calculation is:

4.Chesley, S. R. & Spahr, T. B. in Mitigation of Hazardous Comets and Asteroids(eds Belton, M. J. S.et al.)22–37 (Cambridge Univ. Press, Cambridge, 2004).

They also assume spherical asteroid:

The asteroid (assumed to be spherical)...

[[xeno]Julios]

julez... you unemployed right now?

on reading week, and preparing for grad school this fall. Tutoring this semester is down to a minimum, and the one student I have right now comes over to my place.

Only got 3 courses this semester - spending most of my other time running my lab study, and meeting and corresponding with potential supervisors (and reading their research).

[[xeno]Julios]

What's with the arguing, when this rock is going to miss us by a long margin?

I love applying physics and math whenever possible. It's amazing what you can do with highschool physics and grade 9 math. It's a good intellectual exercise.

[xer0s]

Average schmucks trying to be rocket scientists.

[[xeno]Julios]

Average schmucks trying to be rocket scientists.

yea you'll go far in life with that attitude

[Turbine]

What's with the arguing, when this rock is going to miss us by a long margin?

I love applying physics and math whenever possible. It's amazing what you can do with highschool physics and grade 9 math. It's a good intellectual exercise.

Good point. :icon14:

Using the Orbiter ( http://www.orbitersim.com ) you can get a greater perspective of how things actually work in space. Including what it takes, and how to maneuver in real life space. Not sci-fi space.

[[xeno]Julios]

oh man i remember someone posting that link a while back - mighta been you - one of those simulations where you actually have to read a manual to lift off. I remember playing something like that as a kid - mighta been a flight sim, but the sense of satisfaction once you got the engines going was awesome