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Hypothetical question about objects in the asteroid belt
"Arie Kazachin" om wrote in message ... Suppose that all (most) of the objects in the asteroid belt had been brought together till they're touching one another and then left alone. Will their combined gravity hold them together or the Jupiter's tidal forces will spread them again to form a belt? Is there a "critical mass" above which they'll remain together and below which they'll not? I'd expect they'd stay stuck together. Jupiter's influence kept tiny fragments from combining into a planet, rather than disrupting an existing planet, which is what you'd practically have by that point. Still, it'd be a pretty dinky planet; smaller than our moon. There are much better uses for the belt than making another worthless planet... -- Regards, Mike Combs ---------------------------------------------------------------------- We should ask, critically and with appeal to the numbers, whether the best site for a growing advancing industrial society is Earth, the Moon, Mars, some other planet, or somewhere else entirely. Surprisingly, the answer will be inescapable - the best site is "somewhere else entirely." Gerard O'Neill - "The High Frontier" |
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Hypothetical question about objects in the asteroid belt
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Hypothetical question about objects in the asteroid belt
In message - "Mike Combs"
Tu e, 23 Mar 2004 12:58:20 -0600 writes: Still, it'd be a pretty dinky planet; smaller than our moon. There are much better uses for the belt than making another worthless planet... Except maybe making somewhat more predictable the trajectories of NEOs over LONG periods of time... ************************************************** **************************** * Arie Kazachin, Israel, e-mail: * ************************************************** **************************** NOTE: before replying, leave only letters in my domain-name. Sorry, SPAM trap. |
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Hypothetical question about objects in the asteroid belt
Arie Kazachin wrote:
In message - (Gordon D. Pusch)23 Mar 2004 13:02:59 -0600 writes: For a layperson's summary of Roche's limit, see: http://www.world-builders.org/lessons/less/les1/moons/roche.html For a simple heuristic derivation of Roche's limit, see: http://www.merlyn.demon.co.uk/gravity3.htm#Roche. -- Gordon D. Pusch Thanks! ************************************************** **************************** * Arie Kazachin, Israel, e-mail: * ************************************************** **************************** NOTE: before replying, leave only letters in my domain-name. Sorry, SPAM trap. Ok, 550 thousand CD's in a slightly tilted, very circular Lunar orbit? 2.423 * Radius of Luna * density of Luna all divided by density of a CD So... 2.423 * 1 (Radius of Luna) * 3.34 (density of Luna) all divided by the density of a CD disk (greater than 1, cuz they sink in water) (anybody???) |
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Hypothetical question about objects in the asteroid belt
(Arie Kazachin) wrote in message ...
In message - "Mike Combs" Tu e, 23 Mar 2004 12:58:20 -0600 writes: Still, it'd be a pretty dinky planet; smaller than our moon. There are much better uses for the belt than making another worthless planet... Except maybe making somewhat more predictable the trajectories of NEOs over LONG periods of time... ************************************************** **************************** * Arie Kazachin, Israel, e-mail: * ************************************************** **************************** NOTE: before replying, leave only letters in my domain-name. Sorry, SPAM trap. The best way to predict something is to control it certainly. We do have the capacity to find and change orbits of objects in space. Defense against an errant asteroid is an interesting benefit. But, more profitable is the ability to find and capture very rich asteroids and bring them into useful orbits around Earth. Once in Earth orbit, we can then place remotely controlled factories that use solar power to process the asteroid into useful products. These products may be used in space, to expand our capacity there, or sent back to Earth, to pay the bills. Ultimately, we'd be able to transfer all our productive capacity, including farms and forests, to space. This would leave the Earth as a vast natural preserve, in which humans lived. People would report to work via remote control through a wireless broadband connection supported from space. Products would descend like JDAMs, and come to a soft landing near each customer. Delivery would occur in minutes. Costs would be very low. How much energy would it take to move an asteroid into Earth orbit? http://nssdc.gsfc.nasa.gov/planetary...eroidfact.html Well, let's look at Ida; NAME SIZE MASS ROTATION PERIOD TYPE AXIS ECCENT. INCL. 243 Ida 58 x 23 100 4.633 hrs 4.84 yrs S 2.861 AU 0.0451 1.14 deg So Ida is in a nearly circular orbit 2.861 times the distance from the Sun Earth is. Its 58x23 km and masses 100x10^15 kg. Its an 'S' type asteroid, so likely not of much interest to humanity for that reason. But, Ida is typical of the orbit and mass of the asteroids any company that made money moving industrial asteroids would be asked to tackle. Those responsible for nudging dangerous asteroids into less dangerous orbits have a far easier task. Since the masses are so large, minimum energy is an interesting approach. This calls for Hohmann transfer orbits. http://liftoff.msfc.nasa.gov/academy...s/hohmann.html http://scienceworld.wolfram.com/phys...sferOrbit.html To simplify things, we'll assume no plane change, this gets us a rough estimate of the total energy needed with Ida since it has a low inclination. ANd lets us use simpler math since we don't have to include 3D vector analysis which plane changes require. So, the circular orbit Ida is now in is 2.861 AU When Ida is captured in Earth orbit, it willbe in an orbit with 1.000 AU The minimum energy transfer orbit will have 1.931 AU semimajor axis, with an apoapsis of 2.861 and periapsis of 1.000 The velocity of Ida now is 17.635 km/sec taking the circumference of the orbit and dividing it by the period. The velocity of Earth now is 29.865 km/sec by the same procedure. This implies a constant [mu] of 890 given the units and so forth - so for our transfer orbit we have; at apoapsis v = SQRT(890*(2/r - 2/(r1+r2))) = SQRT(890*(2/2.861 - 2/3.861)) = SQRT(890*(0.6991 - 0.5180)) = 12.694 km/sec and at periapsis v = SQRT(890*(2/r - 2/(r1+r2))) = SQRT(890*(2/1 - 2/3.861)) = SQRT(890*(2 - 0.5180)) = 36.317 km/sec Now, a circular orbit at the apoapsis as we've already seen is 17.635 km/sec so the difference in speeds are; 17.635 - 12.694 = 4.941 km/sec which is the requirement of the first impulse And, a circular orbit at the periapsis as we've already computed is 29.865 km/sec so the difference in speeds are; 36.317 - 29.865 = 6.452 km/sec And we're slowing down both times, which is consistent with lowering our altitude from 2.861 AU to 1.000 AU We need a total delta vee of 4.941 + 6.452 = 11.393 km/sec To minimize energy usage in our rocket, its best to make the exhaust speed equal to the delta vee requirement. This implies an exhaust speed of 11.393 km/sec. This is easily achieved by nuclear pulse rocket technology. We'll vaporize part of the asteroid itself to produce exhaust - so the asteroid itself becomes the propellant. This is achieved by building small atom bombs that direct their energy toward the asteroid and vaporize a small controlled portion of it. In any case, we can figure the amount of the asteroid we've got to throw away - this is given by; u =1- 1/exp(1) = 0.6321 which is a lot, but if we want to minimize energy usage, that's what's called for. Of course, we could increase exhaust speeds to limit wastage, but this wastes energy. For example, if we have twice the exhaust speed as delta vee required, then we throw away; u = 1 - 1/exp(1/2) = 0.3935 Then, we could go to 3x required speeds in our exhast velocity to obtain the following propellant fraction; u = 1 - 1/exp(1/3) = 0.2835 Clearly the relative costs of energy versus the material you're moving will determine what exhaust speed a company that makes money moving material will choose. Knowing the starting mass, exhaust speed, and propellant fraction we can now compute the total energy required in the exhaust jet; E = 1/2 * m * V^2 = 0.5 * 100e15 kg * 0.3935 * (2*11,393 m/s)^2 = 10.215e24 joules That's 48.6 million times a 50 megaton blast - the largest explosion ever achieved by humanity. Now, no rocket system is perfectly efficient. There are always losses. But, most systems, even nuclear pulse systems, especially when moving large masses, are better than 0.5 - so, we would likely need 20e24 joules of energy applied as indicated in two pulses, to move this asteroid. This is about 100 million times a 50 megaton blast. http://nuclearweaponarchive.org/Library/Teller.html Now, something 10,000x as explosive can be built by adding two stages to a teller ulam bomb - which reduces the number of bombs to only a 10,000 blasts 500 Gigatons each. 10,000 is a nice round number. It gives you a lot of control, imparting only 1 meter per second per blast, and its a reasonable number to work with, How big would each bomb be physically before detonation? http://nuclearweaponarchive.org/Nwfaq/Nfaq12.html Well, if we used Li6/D - we'd get 64.0 kilotons yeild per kg mass. So, a 500 gigaton bomb would mass around 8,000 tons. Ten thousand of these puppies would mass 80 million tons. The size of the largest tanker ever built is around 500,000 tons. So, we're talking massive spacecraft here. But, the largest spacecraft ever conceived is in this size range. A nuclear pulse spaceship designed for interstellar travel was worked on briefly during project Orion that at their largest would mass nearly 80 million tons. It really takes very little fissile material to set off massive quantities of fusion meterials. We can use the same technique developed for inertial confinement fusion to compress tiny amounts of fissile materials - to use as a spark plug. As little as a few grams of plutonium perhaps per 8,000 ton bomb. We can imagine then a fleet of 300 or so massive ships with thousands of astronauts aboard each. These ships would carry tens of thousands of massive bombs, and hundreds of thousands of smaller bombs. These smaller bombs would move the spaceship itself. The larger ones would move asteroids. They would fly out into the solar system, surveying all the small bodies throughout. They would then choose the richest of these bodies to return to Earth orbit. Once there, they would enter a stable orbit along with all the other returning bodies, and they would form a vast industrial feedstock for the next step in human industrial development. Remotely controlled factories, manned by remotely controlled robots, would be orbited - http://world.honda.com/ASIMO/ and people anywhere on Earth could link in and find work via a wireless broadband internet available from space http://www.teledesic.com/default.htm Things would be manufactured and delivered ballistically from orbit anywhere they're desired on Earth. Things would also be manufactured for use on orbit - to expand the industrial capacity of orbiting industries. Power satellites could be cheaply built on orbit this way - and energy beamed to Earth. In addition to solar pumped masers we could build solar pumped lasers to support wide scale use of laser propulsion http://www-phys.llnl.gov/clementine/ATP/Lsrprp1s.gif http://science.howstuffworks.com/light-propulsion.htm This would allow people to travel ballistically throughout the world in personal rapid transit vehicles. People could travel anywhere in minutes without any roads, fuel, or pollution. Large pressure vessels could be constructed in space to grow food and forests - delivering food and fiber to people in unprecedented quantities. All industries on Earth could transfer their operations to space since this would give them access to the largest markets possible at the lowest possible price. Ultimately, personal spaceships would make it possible for people to visit orbit - and take up residences in their own personal space homes http://www.permanent.com/s-index.htm But in this visionary view of things, they wouldn't be packed in like sardines with 100,000 others, here, they'd own stations individually - with billions of stations on orbit simultaneously. http://members.aol.com/oscarcombs/settle.htm They would be organized the same way the particles of Saturn's rings would be organized - using gravitational interaction to maintain a safe and permanent separation among billions of interacting worlds http://ringmaster.arc.nasa.gov/satur...r/plate_05.gif The stable existence of Saturn's rings - consisting of trillions of individual moonlets - is an existence proof that billions of individual space stations each the size of a city - could all share the same skies above Earth. Improvements in laser propulsion - and expansion of the infrastructure that delivers laser energy to include solar orbiting stations - will give wing to the orbiting stations - making of them moveable homes that can roam the solar system, and even to other solar systems, using laser light sails. http://library.thinkquest.org/C00376...dlife/sail.jpg http://www.angelfire.com/space/cruis...Light_Sail.jpg At this point humanity will begin its history as a space faring species. William Mook |
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