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ronnywhite
SFN Regular
501 Posts |
 Posted - 12/27/2005 : 06:20:48 [Permalink]
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I hope ya'all had a good Christmas!
Since I've already covered most of my quick-takes on the asteroid stuff regarding questions raised to this point in the thread, I'll add my final nickel's worth and finish it off.
Considering the smaller travel distances required (or commensurately smaller deflection angles- take your pick) consistent with the lower kinetic energies calculated when I guesstimated the radial movement of Apophis towards Earth during the trip after deflection with more precise estimation (integrating the equations of motion and such) the other day... after previously taking the "skeptical quick guesstimation" approach (using maximums and minimums and sticking to arithmetic as demonstrated, which can be a really useful technique to quickly "get a feel" for many problems, in my own experience/opinion- in fact, that's the impetus of these posts) I think the deflection issue might be very manageable because additionally... relativistic issues wouldn't present a problem, and a moving versus a stationary intercept should be easily doable because positioning and timing can be made easier with lasers, and all things considered, using a nuclear device might be the best option as opposed to other strategies.
Disclaimer-
A thread I've read lately on SFN seemingly suggests that there really are no satellites with rather their alleged existence being a propaganda ploy as part of some kind of grand conspiracy to deceive the public for reasons unbeknownst (although doubtlessly evil- maybe Newton and Kepler were wrong- or for that matter, maybe they were in on it... "it," of course, meaning ongoing plans for establishment of the New World Order, probably including using the Apophis impact as an excuse to assemble UN troops who will enforce injection of mind-controlling nanodevices into everyone's bloodstreams. Yes, that's right... I mean the same nanodevices the Katrina debacle was construed to distract the public from noticing, as final nano-firmware updates were being finished, while ongoing beta tests proceeded on troops sent to Iraq (how could anyone think those are really vaccines they're given? I mean, obviously the Avian Flu scare is just a ploy to prepare us for voluntary "vaccination" to pacify most of the public, so the UN troops will thereafter encounter minimal resistance as they similarly turn the rest of us into automated zombies controlled by the New World Order's supercomputer, right??? Anyway, just Newton and Kepler being wrong would really throw a monkey wrench into my Apophis guesstimates... nonetheless I'll briefly elaborate on each of these final thoughts, and "tie a string around all of this" to conclude my Apophis opinions...
...relativistic issues...
Suppose Apophis were deflected at a distance when it's within 10 years of reaching Earth (a likelihood, should an attempt be necessary)... the distance is great, and the delivery vehicle and Apophis travel at high relative velocities to Earth, and to each other. Telemetry/tracking signals to/from Earth, and both light and radar between the vehicles and Apophis would be relativistically effected... but how much? At 10 km/sec 10 years of travel distance would be 10 * 10 * 365 * 24 * 60 * 60 = 3.15e9 km. Time = distance / velocity = 3.15e9 / 3e5 = (about) 1e4... 10,000 seconds or a little under 3 hours, since c (the speed of light) = 3e5 km/sec. Estimating how much the movement towards or away from Earth will effect our time perception... if T is relative time, and T0 is perceived time from our reference frame, then T = T0 / sqrt ( 1 – ( v / c )^2 ) = 10000 / sqrt (1 – ( 10 / 3e5 )^2 ) = 10000.0000056 seconds, including 5.6e-6 seconds temporal adjustment due to the time dilation effect. In 5.6e-6 seconds Apophis would travel ( 10e3 km / sec * 5.6e-6 sec ) = 5.6e-2 km = 56 meters (for data and control signal transmissions)... and doubling that for radar tracking for 112 meters... at over 100 meters of tracking error due to relativistic effects when Apophis is 10 years away, and still a significant amount when it's closer, that's far too much variance to allow accurate enough positioning unless this is compensated for. That's not a big problem, and if onboard radar and lasers assist in the tracking as the asteroid approaches the vehicles, it seems to me that the non-mechanical aspects of positioning and timing would be a cinch, as I'll describe.
...a moving versus a stationary intercept...
I assumed the stationary placement of a device for detonation in the prior post, as both Apophis and a delivery vehicle both approaching each other at high speed would make the placement (timing) difficulties harder (i.e. if both converged at 10km/sec the elbow-room for timing error would half... to under 1 millisecond.) But the positioning and timing problems might actually not be as troublesome as I implied, for reasons I'll explain shortly... so perhaps it's just a matter of designing, testing, and building the system, and getting it out there where it can do us some good in a timely enough fashion. We could intercept the asteroid faster by increasing our rocket velocity, the tradeoff being a method to de-accelerate the device ("put on the brakes") prior to positioning and intercept time might need to be included- which would require tremendous chemical energy, greatly increasing the rocket's initial mass and complexity necessary to really "push the pedal to the floor" and deflect Apophis at a greater distance from Earth. This might possibly include some kind of scheme to exploit gravity from a nearby massive body to absorb some of its kinetic energy (e.g. reducing momentum using gravity from a large celestial mass, like a planet.)
Along those lines, I laughed when I saw the Star Trek episode where Captain Picard used a "joystick" to "manually control the Enterprise," taking advantage of gravity from a large nearby asteroid to "slingshot" his spaceship out of a problematic asteroid belt... considering the masses, distances, and timeframe involved- assuming it were possible, he'd still have to be nuts to try it without computers, and incredibly lucky to succeed but I don't think "putting on the brakes" would be necessary to deflect Apophis, because...
...positioning and timing can be made easier with lasers...
The reason I suspect the technical obstacles aren't at all insurmountable is that in conjunction with Earth tracking/telemetry data and control... onboard Doppler and conventional radar equipment, working with lasers/optical sensors and computers in the vehicle... could automate the positioning/timing process with great accuracy. For example, suppose when nearing the target area, 3 separate units were jettisoned for positioning, possibly with small independent rocket burns, or gaseous discharges (which would also be used for the small-incremental positioning as the near-approaching asteroid were tracked.) The 3 laser/sensor units, if properly positioned, could triangulate from the laser tracking, along with radar data, when Apophis was in optical tracking range, which would simplify the positioning and timing problems dramatically... and with microprocessors operating on the order of billions of instructions per second, the computational side of that would be a cakewalk with current technologies.
...using a nuclear device might be the best option...
Having perhaps 3 or 5 independent devices so properly placed, similarly automated, and possibly using multiple detonation-sequenced smaller explosives instead of one large explosive could have an advantage of improving deflection control, and reducing the proba |
Ron White |
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Dave W.
Info Junkie
USA
26020 Posts |
Posted - 12/27/2005 : 10:56:21 [Permalink]
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quote:
Originally posted by ronnywhite
...relativistic issues...
Suppose Apophis were deflected at a distance when it's within 10 years of reaching Earth (a likelihood, should an attempt be necessary)... the distance is great, and the delivery vehicle and Apophis travel at high relative velocities to Earth, and to each other. Telemetry/tracking signals to/from Earth, and both light and radar between the vehicles and Apophis would be relativistically effected... but how much? At 10 km/sec 10 years of travel distance would be 10 * 10 * 365 * 24 * 60 * 60 = 3.15e9 km. Time = distance / velocity = 3.15e9 / 3e5 = (about) 1e4... 10,000 seconds or a little under 3 hours, since c (the speed of light) = 3e5 km/sec. Estimating how much the movement towards or away from Earth will effect our time perception... if T is relative time, and T0 is perceived time from our reference frame, then T = T0 / sqrt ( 1 – ( v / c )^2 ) = 10000 / sqrt (1 – ( 10 / 3e5 )^2 ) = 10000.0000056 seconds, including 5.6e-6 seconds temporal adjustment due to the time dilation effect. In 5.6e-6 seconds Apophis would travel ( 10e3 km / sec * 5.6e-6 sec ) = 5.6e-2 km = 56 meters (for data and control signal transmissions)... and doubling that for radar tracking for 112 meters... at over 100 meters of tracking error due to relativistic effects when Apophis is 10 years away, and still a significant amount when it's closer, that's far too much variance to allow accurate enough positioning unless this is compensated for. That's not a big problem, and if onboard radar and lasers assist in the tracking as the asteroid approaches the vehicles, it seems to me that the non-mechanical aspects of positioning and timing would be a cinch, as I'll describe.
Actually, given that Apophis' aphelion is a little less than 1.1 AU, then we know that the light time from it to Earth will never be more than 17.01 minutes. Plus, gamma is 1/sqrt(1-(v2/c2)), not 1/sqrt(1-(v/c)2).
Now, Apophis will be going fastest when closest to the Sun, and slowest when furthest away. We know it's mean orbital velocity to be 30,370 m/s, but it's got a far more eccentric orbit than Earth's nearly circular path. Now, I've been trying to figure out its specific orbital velocity at perihelion, but my math skills aren't up to snuff right now. We can guesstimate that it won't be more than 125% of its mean velocity, though (a fairly insane 38,000 m/s, just to round up).
Now, the largest difference in velocities will occur when Apophis' perihelion coincidentally occurs on the opposite side of the Sun from Earth's perihelion, giving a delta-V of about 68,300 m/s across 258,731,074 km of space (863.034 light-seconds, or 00:14:23.034).
Plugging those numbers into the time-dilation (gamma) equation, we find gamma to be 1.0000000260, the time difference itself to be 22.4 microseconds, and thus the relativistic effects across that distance could induce a 1.53-meter navigation error if uncorrected (3.06 m for round-trip errors).
Again, this only when delta-V is largest, when the Earth's perihelion coincides with Apophis' perihelion, and they're 180° apart, Sun-wise (if this ever happens, it can repeat about every eight years, or nine orbits of Apophis). At any other time, the delta-V will necessarily be smaller, and thus relativistic effects on navigation will be smaller.
[Edited to switch from Earth's aphelion to its perihelion, adding 4 centimeters to the possible error.] |
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too. |
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ronnywhite
SFN Regular
501 Posts |
Posted - 12/27/2005 : 21:25:26 [Permalink]
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Good call... thanks Dave, I should have considered the contingency of a highly eccentric orbit with a short period to begin with (just went mostly from the numbers in the original link.) And now that you mention it, I really should have integrated acceleration due to Sun's gravity into my more-rigorous estimation attempt and consequent max/min-type guesses (when I started them I just arrived at Starbucks and probably wasn't sufficiently caffeinated) because assuming a 10m/sec impact approach terminal velocity towards Earth from the opposite side of the Sun, that would have meant a longer trip and more radial deviation towards Earth, less from the opposite direction etc.) But no matter, just ballpark stuff anyway.
Without prolonging the diatribe, I'd speculate this actually might make the overall deflection problem less-demanding as far as blast energy and payload launch requirements, but possibly trickier in terms of the necessity for precise calculations and room for error in device placement/timing (i.e. given the short period, nudging it a little the wrong way might make things even worse, but making that kind of call right's why I imagine NASA, JPL and the like pay astrophysicists enough to drive Rolls Royce, have houses on Venice Beach, and all that.) I should have Googled some info as to the nature of the Apophis ephemeris... apologies as astronomy's just not high on my list of interests (maybe in my next reincarnation, assuming I don't return as a cow.)
Anyway, this Wikipedia is really good- I'm glad SFN brought this site to my attention... I could have got all the vitals from one webpage. I'll try that next time around.
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Ron White |
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Dave W.
Info Junkie
USA
26020 Posts |
Posted - 12/27/2005 : 21:39:19 [Permalink]
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Well, the most-important point I was trying to get across was that in your analysis, it seemed that you were assuming a more-or-less straight-line path of the asteroid over the next 30-odd years (more like a comet), when in reality, it's spinning around the Sun just like we are. The calculations you did are mostly fine (save for the gamma problem), for something that's coming at us from the depths of space.
And yes, nudging this thing the wrong way (or at the wrong time) could spell disaster for us faster than if we leave it alone. |
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too. |
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ronnywhite
SFN Regular
501 Posts |
Posted - 12/27/2005 : 22:00:50 [Permalink]
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| You're exactly correct about my erroneous assumption of the path shape... I should have looked into the specifics of Apophis just a little more, because it could have made a big difference depending on the nature of the questions... glad you brought it to my attention (live n' learn.) As soon as I started reading your link, it occurred to me what they had really meant by those times they threw out in the original link, and I immediately thought "oh, crap!" A lesson learned- I gotta' think-through the contingencies of these matters unfamiliar to me in the future, and again, this Wikipedia rocks. |
Ron White |
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