And climate change is going to take a massive hit out of ecological productivity for a few centuries, as weather systems become increasingly unpredictable (a warm planet may have improved potential, a rapidly *warming* planet is in a state of chaotic flux). We'll need pretty major (and incredibly cheap) agricultural improvements to do anything to help most of the world's population.
>There is not a shred of evidence for "runaway processes".
You're either lying, or not paying any attention to the widespread thawing of permafrost, to name just one of the most obvious processes already begun. As permafrost thaws and decays is releases massive amounts of methane into the atmosphere, a far more potent greenhouse gas than CO2, which eventually breaks down into more CO2.
There's also massive quantities of methane hydrates in the oceans, some of which are already beginning to thaw, and much more of which will thaw if there's a warming of a degree or two.
Canada has already stopped claiming carbon credits for their huge forests, which have already warmed enough that the trees are beginning to release more CO2 rather than they sequester.
I could go on, but I imagine you're just going to come up with reasons to deny the reality right in front of your face, so why bother?
Yep. Sounds like a wonderful way to couple the sale of hundreds of dollars in expensive display technology that's inherently useless to the blind user to the usage of the head-mounted camera that's the only part actually being used.
Haven't seen you around in a while, welcome back! I'm afraid you'll be disappointed though - the trolling has degenerated tho the point that your brand of cheerful irrelevance now barely even qualifies. Thanks for brightening up the place though!
That's my point: If you want that nice optimal parabolic slingshot, then the asteroid's maximum acceleration by the planet is incredibly important - the faster the asteroid, the more acceleration is required to whip it into a parabolic trajectory. And since the acceleration is strictly limited, so is the amount of speed you can bring to the party and get anything remotely resembling a parabolic slingshot maneuver.
Basically, lets say you've lined up an asteroid for that perfect tangential-to-the-sun planet-accelerating parabolic slingshot. It zooms in, loops tight around the Earth to impart twice its own momentum and (at infinity) is going back at exactly 180 degrees from it's approach direction. Now what happens if you juice it up so it's going a little faster? You no longer get a parabolic slingshot - it's not physically possible. Instead it loops part way around the Earth on a hyperbolic trajectory, and heads back at maybe 160*. Go faster, and the loop opens wider, until you reach the point that you zoom right past the Earth with barely a nudge to your trajectory, and barely a nudge to the Earth's momentum as a result. (obviously, as the curve widens you also have to change your starting point for optimal acceleration of the Earth, but that's secondary)
Obviously as you increase speed you're still imparting some momentum, maybe even more total than you did with a perfect parabolic slingshot - but the point is you're transferring a smaller percentage of the asteroid's momentum, and that's the momentum you have to pay for: as you increase the asteroid's speed, you get diminishing returns on investment.
No, the fact that it's one of the largest extinction events in the geologic record make it one of the largest.
And such extinction events are generally pretty bad for everyone involved, even if they do open the field for interesting new evolutionary branches after several thousand years of ecosystem recovery.
Europe maybe, they're pretty far north and have a lot of large water bodies in a fairly dense area. The US is much less certain - the "Breadbasket" of inner America may very well suffer severe droughts - continent spanning global deserts were not exactly unusual during Hothouse phases.
And lets be completely clear - nothing we're seeing now is a real problem by climate change standards - we're only seeing minor fluctuations as the system begins to shift out of it's Icehouse phase - the REAL problems are still a few hundred years away once the runaway process we're setting in motion completely dwarfs our own contributions.
As for problems and responsibilities: the problem was pretty much caused by the US and Europe, though China is finally becoming a major contributor as well - I'd say that makes it our responsibility. Or is the car I pushed down the hill into your living room not my responsibility? Certainly the car itself is far more immediately your *problem*, but it's likely to become my problem as well if you ever identify me. Similarly, having the vast majority of the world's population suffering from climate-driven famine is going to become our problem, even if we're lucky enough to be doing okay for ourselves - because those people have weapons and ingenuity, and it's unlikely that they'll all choose to lie down and die quietly rather than some of them trying to take our food, or at least take well-justified revenge.
Sure, Russia and Canada look to see some serious long-term improvements in real estate values. Most of the rest of the world though will be losers. And *everyone* is liable to be short-term losers during the transition as weather becomes more unpredictable and climate lines shift faster than ecosystems and the farming industry can adapt.
We're already in the middle of one of the largest mass-extinctions the planet has ever seen (directly human driven, via hunting and habitat destruction), do you really want to add climate-driven mass extinction on top of that? Because the transition to a Hothouse Earth has historically been very traumatic, and we're promising to drive the change faster than ever before. Are you so sure that civilization we can survive a high-90% extinction event ? Because I'm not so sure much more fragile than cockroaches will be doing well. I'm sure we'll have greenhouses, etc. keeping us alive as a species, but there's a very real chance we'll see high 90s death rates as well. And maybe that'd really be for the best, but let's be clear that you're advocating genocide.
I'd be strongly in favor of banning all gene patents: lets get the direct profit motive out of developing GMOs, so that the ones we do get are at least mostly driven by less thoroughly corrupting impulses. Lots of good work has been done in academia - sometimes misguided, but at least they're generally aiming to improve the human condition.
The stuff coming out of corporations on the other hand tends to be entirely focused on improving their own profit margins, with no regard for the consequences.
The explosively hard maximum is otherwise known as impact. Acceleration increases rapidly with proximity to the center of mass - the closer an asteroid gets to the center of the earth, the greater the acceleration (of both). But acceleration is only 1g at the surface, so the asteroid is limited to less than 1g maximum acceleration without hitting the surface. Earth's gravity alone is physically incapable of accelerating it any harder than that. Even skimming the outer atmosphere a paltry 200km above the surface it'll only experience 0.894g
Meanwhile the curvature of the path is relevant. Admittedly it would be more relevant to determine the percentage of momentum transfer directly, as there are numerous non-linearities involved, but I'm not willing to sit down and do the math for speed versus momentum transfer at a given closest approach. The more curvature though, the greater the percentage of momentum is being transferred - anywhere from 200% for 180* curve, to 0% for a 0* curve.
And that's relevant because you have to pay for that asteroid's momentum up front by pushing it out of its stable orbit beyond Neptune onto a deep dive into the inner solar system to fly by Earth. It'll gain a lot of momentum falling inwards, but you're still talking 5+km/s you have to slow it down by. Unless the flyby transfers more momentum than you had to put in up front, you'd be better off imparting that momentum directly via moon-rockets.
The aid could generally be much better spent buying local food - as it is, long-term aid destroys the local market for food, causing local farmers to turn to exportable cash crops to make a living.
Basically, long-term food aid is an excellent strategic decision for turning at temporary crisis into long-term dependency, with all the political leverage that entails.
You misunderstand - They *do* take privacy very seriously: it interferes with their profit margins and they're doing their best to eliminate it without triggering excessive consumer backlash.
As yourself this: Does this incident make you substantially less likely to buy or use one of their home surveillance devices, or were you already committed to one camp or the other? If there's no substantial change, then they're doing an effective job of limiting backlash.
See? Clearly there is no bending problem - they're bending just fine and generating additional revenue in the process!
If the problem is actually just losing the connection between touch screen and logic board, rather than damaging one of them internally, you'd have to wonder why they didn't just use a more flexible connector. 1/4" of ribbon cable would easily handle any bends that didn't damage the rest of the phone, while adding minimal cost. It's enough to make a cynic suspect nefarious intent.
What does that matter? The subject under discussion is accelerating the Earth via asteroid flybys (the asteroids are losing energy as they give it to the Earth, not the other way around) - that the mutual acceleration is uniform is irrelevant to that conversation. All that matters is how much the impulse changes the momentum. If you could somehow non-destructively bounce an asteroid off the Earth the resulting momentum change to both would be the same as a gravitational slingshot that altered it's flight direction by the same amount - you'd deliver the same impulse, just over a much shorter period.
With one important difference: bouncing off the Earth wouldn't have a speed limit - you'll transfer the same percentage of momentum regardless of impact speed. Whereas a slingshot maneuver becomes less proportionally effective at high speed. And since you have to deliver substantial orbital energy to the asteroid to get it to fall far inwards toward the sun on a slingshot path past Earth, you really want to make sure you're getting the most bang for your buck. Especially since most of those asteroids will have to be trans-Neptunian objects that require massive changes in orbital energy to reach the inner system: the entire asteroid belt is estimated to mass only 4% as much as the Moon, so we could transfer 100% of its orbital energy to Earth and barely expand its orbit.
And obviously collisions aren't the most effective solution - slingshots can deliver up to twice the momentum at the same speed, I was just pointing out that there's much more restrictive limits to that approach.
I still think rockets on the moon would be the best solution - you get that nice, fairly uniform gravitational acceleration transmitting the acceleration to the Earth, and efficient usage of your rocket momentum, even if you don't get the benefit of harvesting pre-existing asteroid momentum. Put rockets on the leading and trailing sides of the moon, and fire them alternately when they're facing "behind" the Earth's path. That way you can avoid changing it's orbital speed around the Earth, while still accelerating the Earth-Moon system.
I believe that generally speaking launch costs are constant for any particular rocket, regardless of target orbit. Basically you have the cost of the rocket, the cost of ground support and other logistics, and way down at the bottom at somewhere around 5% you have the cost of the fuel - the only the only part that changes significantly based on target orbit.
Once there's competition in the heavily reusable rocket market, so that the rocket is no longer the overwhelming fraction of the cost, and those savings are passed on to customers, then eventually, maybe, fuel will become a sizable fraction of the launch cost, so that the target orbit matters to the cost.
The tightness of the turn is *extremely* relevant: In terms of changing the orbital momentum of the Earth the only thing that's relevant is the total change of momentum of the asteroid by the Earth - the two will be exactly equal by the Law of Conservation of Momentum. And the tighter the turn, the greater the percentage of momentum transferred.
A direct impact transfers 100% of relative momentum from the asteroid to the Earth. A perfect parabolic "U turn" is basically the same as if it impacted directly and bounced off in exactly the opposite direction, and transfers 200%. A less-perfect hyperbolic slingshot is basically the same as as if it bounced off at an angle, and delivers 200% times the cosine of the impact angle - at 90 degrees ("skimming the wall", or no deflection) there's no momentum transfer.
So, the formula is momentum transfer = total asteroid momentum * 2 * cos( 0.5 * angle between incoming and outgoing paths at infinity)
Where it gets complicated is that, assuming you hold the point of closest approach constant, the slowest approach possible by a non-orbiting asteroid delivers a parabolic, 200% transfer. Any faster, and you get a hyperbolic path instead, and less than 200% transfer. Your momentum increases linearly with relative speed, but the faster you approach the less you get deflected, and thus the smaller the percentage of that momentum transferred to the Earth.
My orbital mechanics is too rusty to work out the formula for angle-versus speed, perhaps someone else can locate/calculate it? But considering the non-linearity of the cosine function I feel fairly confident in saying there is an optimal relative speed at which the momentum transfer peaks, so that going any faster actually reduces the total amount of momentum transferred to the Earth.
That could work, but there's a pretty hard limit to how fast you could slingshot around the Earth: an explosively hard maximum of less than 1g acceleration at the tightest point of its turn. The faster you sling an asteroid past, the less time it spends under the Earth's influence, and the straighter its hyperbolic path will become - meaning less momentum transfer to Earth. And to actually get close to 1g you'll have to practically graze the planet. At even 1 earth-radius (6,300 km) above the surface you're down to only 1/4 g, and considerably less potential momentum transfer. Don't miss.
And of course, if you're speeding up the Earth, to draw it further from the sun, then that means you're necessarily slowing down the asteroid - no ejections there, though you could . Unless of course you use only asteroids with counter-rotating orbits - but last I checked those are *really* rare. But hey, plan it right and you could be populating the inner system with lots of more easily mined asteroids. Even counter-rotating. Or take less momentum transfer and drop them into the sun.
Meanwhile, you've got to impart considerable momentum to an asteroid to get it from the asteroid belt all the way in to the Earth's orbit - you'd need to run the numbers to see it it's actually more efficient to do it that way than just imparting it directly using the moon (or comically giant thrusters extending beyond the Earth's atmosphere). Besides, you're going to have to power the moon anyway so that you can re-stabilize its orbit after each of these flybys.
Okay, that could work. Slow though, and probably not very efficient - you'd probably be doing good to get as much momentum from the interaction as you had to put in to get the asteroid on a flyby course. If you're not getting substantially greater than unity momentum gain you may as well just put the asteroid into orbit and keep nudging it in the direction you want to go. Or just use the moon.
If you're moving asteroids, you still need a source of momentum (rockets) for that as well, though you'll be able to get a momentum-amplification effect with regards to accelerating the Earth, provided you're not using near-Earth asteroids, which already have roughly the same orbital momentum.
Of course that means bring in things from the asteroid belt or further, which are then going to be moving FAST, and do a LOT of damage when they hit (though perhaps they could be vaporized just before impact - momentum transfer would be the same, but the energy would mostly be dissipated as atmospheric heating... which might be okay.
The moon meanwhile is in a convenient vacuum - we could mount low-thrust/high efficiency ion drive rockets on the surface and just keep them going for the next several thousands or millions of years - it's not like moving a planet is likely to be a fast process. If we wanted to get really crazy we could harness matter-energy conversion, perhaps feeding mass into a small black hole, we could power such a system from the Moon's own mass almost forever. Could even put a bunch of natural spectrum lights on the near side for "sunlight" and tow the Earth across interstellar space.
Not in deep space - but low orbit is only a few hundred to a few thousand kilometers up, only a 1%-30% greater distance from the center of the earth than on the surface - which with a cubic falloff still means 97% - 45% the strength, or less depending on just how deep the fields are actually generated. More than enough for a magnetic drive to be useful given the negligible opposing forces in free fall. Many different conceptual designs of "orbital electromotor" propulsion systems have been proposed over the years, and a think a few proof of concept experiments successfully run.
Or you could mount rockets on the moon and use it as a gravitational tugboat - no messy impacts threatening to wipe out most life on the planet that way, much finer control, and assuming you're planning on taking the moon with anyway, there's no difference in impulse needed to modify the Earth's orbit.
Neither is particularly feasible with today's technology though - unless you simply mean "no fundamentally new technology would have to be discovered"
Certainly "big" and "small" are useful terms - they're just *qualitative* rather than *quantitative* - they perform much the same role as a negative sign for addition - indicating the (one dimensional) vector direction in which quantities are interpreted.
The caveat of course being that we're talking proportion(multiplication) here rather than addition, so the inverse is division rather than subtraction. And likewise, the degenerate(identity) value is 1 rather than 0.
When you say "as big as" or "as small as" you're in the degenerate case, and obviously it makes no difference which direction you don't make a change in. As big as = 1x as big as = positive change = multiply by 1 = 1 As small as = 1x as small as = negative change = divide by 1 = 1
As soon as you use a non-degenerate scale factor, everything falls into place 3x as big as = positive change = multiply by 3 3x as small as = negative change = divide by 3
The only point of ambiguity is the use of "bigger" and "smaller" rather than "as big/small as", but people are lazy, so there's no surprise that such linguistic shortcuts get used, even when they compromise clarity (heck, sometimes I think *especially* when they compromise clarity)
Yep, it might confuse engineers and pedants, though everyone else would understand it perfectly. The exact opposite of what good technical writing is supposed to accomplish, right?
I don't know - cryogenics is in large the art of cooling things off fast enough that ice crystals don't form and expand (as that ruptures cell walls). And this thing is so cold it makes typical cryogenic temperatures look positively balmy in comparison.
Slashdot Mirror
And climate change is going to take a massive hit out of ecological productivity for a few centuries, as weather systems become increasingly unpredictable (a warm planet may have improved potential, a rapidly *warming* planet is in a state of chaotic flux). We'll need pretty major (and incredibly cheap) agricultural improvements to do anything to help most of the world's population.
>There is not a shred of evidence for "runaway processes".
You're either lying, or not paying any attention to the widespread thawing of permafrost, to name just one of the most obvious processes already begun. As permafrost thaws and decays is releases massive amounts of methane into the atmosphere, a far more potent greenhouse gas than CO2, which eventually breaks down into more CO2.
There's also massive quantities of methane hydrates in the oceans, some of which are already beginning to thaw, and much more of which will thaw if there's a warming of a degree or two.
Canada has already stopped claiming carbon credits for their huge forests, which have already warmed enough that the trees are beginning to release more CO2 rather than they sequester.
I could go on, but I imagine you're just going to come up with reasons to deny the reality right in front of your face, so why bother?
Yep. Sounds like a wonderful way to couple the sale of hundreds of dollars in expensive display technology that's inherently useless to the blind user to the usage of the head-mounted camera that's the only part actually being used.
Haven't seen you around in a while, welcome back! I'm afraid you'll be disappointed though - the trolling has degenerated tho the point that your brand of cheerful irrelevance now barely even qualifies. Thanks for brightening up the place though!
Oh, there's certainly a lot of that, but it doesn't completely dominate the field, especially as you venture further outside the U.S.
That's my point: If you want that nice optimal parabolic slingshot, then the asteroid's maximum acceleration by the planet is incredibly important - the faster the asteroid, the more acceleration is required to whip it into a parabolic trajectory. And since the acceleration is strictly limited, so is the amount of speed you can bring to the party and get anything remotely resembling a parabolic slingshot maneuver.
Basically, lets say you've lined up an asteroid for that perfect tangential-to-the-sun planet-accelerating parabolic slingshot. It zooms in, loops tight around the Earth to impart twice its own momentum and (at infinity) is going back at exactly 180 degrees from it's approach direction. Now what happens if you juice it up so it's going a little faster? You no longer get a parabolic slingshot - it's not physically possible. Instead it loops part way around the Earth on a hyperbolic trajectory, and heads back at maybe 160*. Go faster, and the loop opens wider, until you reach the point that you zoom right past the Earth with barely a nudge to your trajectory, and barely a nudge to the Earth's momentum as a result. (obviously, as the curve widens you also have to change your starting point for optimal acceleration of the Earth, but that's secondary)
Obviously as you increase speed you're still imparting some momentum, maybe even more total than you did with a perfect parabolic slingshot - but the point is you're transferring a smaller percentage of the asteroid's momentum, and that's the momentum you have to pay for: as you increase the asteroid's speed, you get diminishing returns on investment.
No, the fact that it's one of the largest extinction events in the geologic record make it one of the largest.
And such extinction events are generally pretty bad for everyone involved, even if they do open the field for interesting new evolutionary branches after several thousand years of ecosystem recovery.
Europe maybe, they're pretty far north and have a lot of large water bodies in a fairly dense area. The US is much less certain - the "Breadbasket" of inner America may very well suffer severe droughts - continent spanning global deserts were not exactly unusual during Hothouse phases.
And lets be completely clear - nothing we're seeing now is a real problem by climate change standards - we're only seeing minor fluctuations as the system begins to shift out of it's Icehouse phase - the REAL problems are still a few hundred years away once the runaway process we're setting in motion completely dwarfs our own contributions.
As for problems and responsibilities: the problem was pretty much caused by the US and Europe, though China is finally becoming a major contributor as well - I'd say that makes it our responsibility. Or is the car I pushed down the hill into your living room not my responsibility? Certainly the car itself is far more immediately your *problem*, but it's likely to become my problem as well if you ever identify me. Similarly, having the vast majority of the world's population suffering from climate-driven famine is going to become our problem, even if we're lucky enough to be doing okay for ourselves - because those people have weapons and ingenuity, and it's unlikely that they'll all choose to lie down and die quietly rather than some of them trying to take our food, or at least take well-justified revenge.
Yep, it's the self-correcting part that's going to be a bitch. Especially when you throw a lot of nukes and well-armed hungry armies into the mix.
And thus those who say "hey, let the problem fix itself" are basically advocating for genocide.
Sure, Russia and Canada look to see some serious long-term improvements in real estate values. Most of the rest of the world though will be losers. And *everyone* is liable to be short-term losers during the transition as weather becomes more unpredictable and climate lines shift faster than ecosystems and the farming industry can adapt.
We're already in the middle of one of the largest mass-extinctions the planet has ever seen (directly human driven, via hunting and habitat destruction), do you really want to add climate-driven mass extinction on top of that? Because the transition to a Hothouse Earth has historically been very traumatic, and we're promising to drive the change faster than ever before. Are you so sure that civilization we can survive a high-90% extinction event ? Because I'm not so sure much more fragile than cockroaches will be doing well. I'm sure we'll have greenhouses, etc. keeping us alive as a species, but there's a very real chance we'll see high 90s death rates as well. And maybe that'd really be for the best, but let's be clear that you're advocating genocide.
I'd be strongly in favor of banning all gene patents: lets get the direct profit motive out of developing GMOs, so that the ones we do get are at least mostly driven by less thoroughly corrupting impulses. Lots of good work has been done in academia - sometimes misguided, but at least they're generally aiming to improve the human condition.
The stuff coming out of corporations on the other hand tends to be entirely focused on improving their own profit margins, with no regard for the consequences.
The explosively hard maximum is otherwise known as impact. Acceleration increases rapidly with proximity to the center of mass - the closer an asteroid gets to the center of the earth, the greater the acceleration (of both). But acceleration is only 1g at the surface, so the asteroid is limited to less than 1g maximum acceleration without hitting the surface. Earth's gravity alone is physically incapable of accelerating it any harder than that. Even skimming the outer atmosphere a paltry 200km above the surface it'll only experience 0.894g
Meanwhile the curvature of the path is relevant. Admittedly it would be more relevant to determine the percentage of momentum transfer directly, as there are numerous non-linearities involved, but I'm not willing to sit down and do the math for speed versus momentum transfer at a given closest approach. The more curvature though, the greater the percentage of momentum is being transferred - anywhere from 200% for 180* curve, to 0% for a 0* curve.
And that's relevant because you have to pay for that asteroid's momentum up front by pushing it out of its stable orbit beyond Neptune onto a deep dive into the inner solar system to fly by Earth. It'll gain a lot of momentum falling inwards, but you're still talking 5+km/s you have to slow it down by. Unless the flyby transfers more momentum than you had to put in up front, you'd be better off imparting that momentum directly via moon-rockets.
The aid could generally be much better spent buying local food - as it is, long-term aid destroys the local market for food, causing local farmers to turn to exportable cash crops to make a living.
Basically, long-term food aid is an excellent strategic decision for turning at temporary crisis into long-term dependency, with all the political leverage that entails.
You misunderstand - They *do* take privacy very seriously: it interferes with their profit margins and they're doing their best to eliminate it without triggering excessive consumer backlash.
As yourself this: Does this incident make you substantially less likely to buy or use one of their home surveillance devices, or were you already committed to one camp or the other? If there's no substantial change, then they're doing an effective job of limiting backlash.
See? Clearly there is no bending problem - they're bending just fine and generating additional revenue in the process!
If the problem is actually just losing the connection between touch screen and logic board, rather than damaging one of them internally, you'd have to wonder why they didn't just use a more flexible connector. 1/4" of ribbon cable would easily handle any bends that didn't damage the rest of the phone, while adding minimal cost. It's enough to make a cynic suspect nefarious intent.
What does that matter? The subject under discussion is accelerating the Earth via asteroid flybys (the asteroids are losing energy as they give it to the Earth, not the other way around) - that the mutual acceleration is uniform is irrelevant to that conversation. All that matters is how much the impulse changes the momentum. If you could somehow non-destructively bounce an asteroid off the Earth the resulting momentum change to both would be the same as a gravitational slingshot that altered it's flight direction by the same amount - you'd deliver the same impulse, just over a much shorter period.
With one important difference: bouncing off the Earth wouldn't have a speed limit - you'll transfer the same percentage of momentum regardless of impact speed. Whereas a slingshot maneuver becomes less proportionally effective at high speed. And since you have to deliver substantial orbital energy to the asteroid to get it to fall far inwards toward the sun on a slingshot path past Earth, you really want to make sure you're getting the most bang for your buck. Especially since most of those asteroids will have to be trans-Neptunian objects that require massive changes in orbital energy to reach the inner system: the entire asteroid belt is estimated to mass only 4% as much as the Moon, so we could transfer 100% of its orbital energy to Earth and barely expand its orbit.
And obviously collisions aren't the most effective solution - slingshots can deliver up to twice the momentum at the same speed, I was just pointing out that there's much more restrictive limits to that approach.
I still think rockets on the moon would be the best solution - you get that nice, fairly uniform gravitational acceleration transmitting the acceleration to the Earth, and efficient usage of your rocket momentum, even if you don't get the benefit of harvesting pre-existing asteroid momentum. Put rockets on the leading and trailing sides of the moon, and fire them alternately when they're facing "behind" the Earth's path. That way you can avoid changing it's orbital speed around the Earth, while still accelerating the Earth-Moon system.
I believe that generally speaking launch costs are constant for any particular rocket, regardless of target orbit. Basically you have the cost of the rocket, the cost of ground support and other logistics, and way down at the bottom at somewhere around 5% you have the cost of the fuel - the only the only part that changes significantly based on target orbit.
Once there's competition in the heavily reusable rocket market, so that the rocket is no longer the overwhelming fraction of the cost, and those savings are passed on to customers, then eventually, maybe, fuel will become a sizable fraction of the launch cost, so that the target orbit matters to the cost.
The tightness of the turn is *extremely* relevant: In terms of changing the orbital momentum of the Earth the only thing that's relevant is the total change of momentum of the asteroid by the Earth - the two will be exactly equal by the Law of Conservation of Momentum. And the tighter the turn, the greater the percentage of momentum transferred.
A direct impact transfers 100% of relative momentum from the asteroid to the Earth.
A perfect parabolic "U turn" is basically the same as if it impacted directly and bounced off in exactly the opposite direction, and transfers 200%.
A less-perfect hyperbolic slingshot is basically the same as as if it bounced off at an angle, and delivers 200% times the cosine of the impact angle - at 90 degrees ("skimming the wall", or no deflection) there's no momentum transfer.
So, the formula is
momentum transfer = total asteroid momentum * 2 * cos( 0.5 * angle between incoming and outgoing paths at infinity)
Where it gets complicated is that, assuming you hold the point of closest approach constant, the slowest approach possible by a non-orbiting asteroid delivers a parabolic, 200% transfer. Any faster, and you get a hyperbolic path instead, and less than 200% transfer. Your momentum increases linearly with relative speed, but the faster you approach the less you get deflected, and thus the smaller the percentage of that momentum transferred to the Earth.
My orbital mechanics is too rusty to work out the formula for angle-versus speed, perhaps someone else can locate/calculate it? But considering the non-linearity of the cosine function I feel fairly confident in saying there is an optimal relative speed at which the momentum transfer peaks, so that going any faster actually reduces the total amount of momentum transferred to the Earth.
That could work, but there's a pretty hard limit to how fast you could slingshot around the Earth: an explosively hard maximum of less than 1g acceleration at the tightest point of its turn. The faster you sling an asteroid past, the less time it spends under the Earth's influence, and the straighter its hyperbolic path will become - meaning less momentum transfer to Earth. And to actually get close to 1g you'll have to practically graze the planet. At even 1 earth-radius (6,300 km) above the surface you're down to only 1/4 g, and considerably less potential momentum transfer. Don't miss.
And of course, if you're speeding up the Earth, to draw it further from the sun, then that means you're necessarily slowing down the asteroid - no ejections there, though you could . Unless of course you use only asteroids with counter-rotating orbits - but last I checked those are *really* rare. But hey, plan it right and you could be populating the inner system with lots of more easily mined asteroids. Even counter-rotating. Or take less momentum transfer and drop them into the sun.
Meanwhile, you've got to impart considerable momentum to an asteroid to get it from the asteroid belt all the way in to the Earth's orbit - you'd need to run the numbers to see it it's actually more efficient to do it that way than just imparting it directly using the moon (or comically giant thrusters extending beyond the Earth's atmosphere). Besides, you're going to have to power the moon anyway so that you can re-stabilize its orbit after each of these flybys.
Okay, that could work. Slow though, and probably not very efficient - you'd probably be doing good to get as much momentum from the interaction as you had to put in to get the asteroid on a flyby course. If you're not getting substantially greater than unity momentum gain you may as well just put the asteroid into orbit and keep nudging it in the direction you want to go. Or just use the moon.
If you're moving asteroids, you still need a source of momentum (rockets) for that as well, though you'll be able to get a momentum-amplification effect with regards to accelerating the Earth, provided you're not using near-Earth asteroids, which already have roughly the same orbital momentum.
Of course that means bring in things from the asteroid belt or further, which are then going to be moving FAST, and do a LOT of damage when they hit (though perhaps they could be vaporized just before impact - momentum transfer would be the same, but the energy would mostly be dissipated as atmospheric heating... which might be okay.
The moon meanwhile is in a convenient vacuum - we could mount low-thrust/high efficiency ion drive rockets on the surface and just keep them going for the next several thousands or millions of years - it's not like moving a planet is likely to be a fast process. If we wanted to get really crazy we could harness matter-energy conversion, perhaps feeding mass into a small black hole, we could power such a system from the Moon's own mass almost forever. Could even put a bunch of natural spectrum lights on the near side for "sunlight" and tow the Earth across interstellar space.
Not in deep space - but low orbit is only a few hundred to a few thousand kilometers up, only a 1%-30% greater distance from the center of the earth than on the surface - which with a cubic falloff still means 97% - 45% the strength, or less depending on just how deep the fields are actually generated. More than enough for a magnetic drive to be useful given the negligible opposing forces in free fall. Many different conceptual designs of "orbital electromotor" propulsion systems have been proposed over the years, and a think a few proof of concept experiments successfully run.
Or you could mount rockets on the moon and use it as a gravitational tugboat - no messy impacts threatening to wipe out most life on the planet that way, much finer control, and assuming you're planning on taking the moon with anyway, there's no difference in impulse needed to modify the Earth's orbit.
Neither is particularly feasible with today's technology though - unless you simply mean "no fundamentally new technology would have to be discovered"
Certainly "big" and "small" are useful terms - they're just *qualitative* rather than *quantitative* - they perform much the same role as a negative sign for addition - indicating the (one dimensional) vector direction in which quantities are interpreted.
The caveat of course being that we're talking proportion(multiplication) here rather than addition, so the inverse is division rather than subtraction. And likewise, the degenerate(identity) value is 1 rather than 0.
When you say "as big as" or "as small as" you're in the degenerate case, and obviously it makes no difference which direction you don't make a change in.
As big as = 1x as big as = positive change = multiply by 1 = 1
As small as = 1x as small as = negative change = divide by 1 = 1
As soon as you use a non-degenerate scale factor, everything falls into place
3x as big as = positive change = multiply by 3
3x as small as = negative change = divide by 3
The only point of ambiguity is the use of "bigger" and "smaller" rather than "as big/small as", but people are lazy, so there's no surprise that such linguistic shortcuts get used, even when they compromise clarity (heck, sometimes I think *especially* when they compromise clarity)
Yep, it might confuse engineers and pedants, though everyone else would understand it perfectly. The exact opposite of what good technical writing is supposed to accomplish, right?
I don't know - cryogenics is in large the art of cooling things off fast enough that ice crystals don't form and expand (as that ruptures cell walls). And this thing is so cold it makes typical cryogenic temperatures look positively balmy in comparison.