To badly misquote the delightful old song: You can use any oment of minertia you want, in Alice's Restaurant. Even including the right one. By the way, the thread starter did not specify the faze of the moon. Another deliberate and disgustingly obvious obfuscatory maneuver?
Granted - not much to look at. Please Register or Log in to view the hidden image! Do you happen to recall the line where he had been "inspected, infected, injected, rejected..." and about two or three more "-ected's" ?
As starter of the poll (if that confers any authority) until I reverse or modify my view, lets all follow Pete's suggestion, but you may use 5E37 kg.m^2, if only that smaller value gives you the personnal satisfaction of being "correct" as it may be true. I also suggest that we use the radial distance SL has found in Google, etc. if your method requires any of these more detailed values. All this is open to critical comment, and potentially changeable, if you are unhappy with these "standard numbers."
I notice the "bottomless band" has recently lost relative support. I don't expect any of the more recent voters to admit to cheating. - I still do not know what the correct answer is, so perhaps none have. I.e. the "bottomless band" may be correct answer, as the majority still thinks.(An alternative possiblity, if the bottomless band is correct, yet losing support, is that we now have a few "inept cheaters", who miss-calculated, but I doubt this.) In any case, it would be interesting to hear why most newer voters are avoiding the "bottomless band." - I gave my reasons for guessing the answer is in the 99cm of the 1M band some time back. - I am courious if any of the newer voters were infulenced by that post as well as what other thoughts had influence on them.
Yes, Pete and probably all others, are correct to assume everything except the 1000Kg of the satellite has fallen back to earth. (Any "global wind" the exhaust gases made has also disipated in friction with the ground. Likewise, the Earth's core is co-spinning with the crust. - I am confident, based on SL's comments after he found the answer, that none of this matters, but just trying to completely define the question. Interesting that no one yet likes the 900Meters target available in the 1000M band.
There is a philosophical sublety here. If I ask BillyT," What is 1 plus 1?", he may get his calculator and perform calculation(s), check, and then give his answer. If I ask Stephen Hawking the same question he might immediately mentally calculate the answer so quickly and reflexively that even if he wanted to, he could not avoid "calculating" the answer. PS Nobody has told me yet what the faze of the moon is during the science experiment.
I find this thread to be highly entertaining. It's fascinating to test your intuition against reality. Sometimes we are astounded to find that our intuition can be SO wrong. I voted after about two minutes of just visualizing the masses and distances involved. I think the faze(sic) of the moon during the experiment should be assumed to be waxing gibbous, 2 days past half moon. :m:
NO, that is too easy. I do not think, even my quick correct answer (2) is a "calculation." - That would be more "recall," but you provoke an interesting question: What is "calculation?" For example, to be thread related: I still do not know the answer, and do not think I have done any calculations, but I did go thur the thought process below, partially to just pose the question and set up some answer choices, but also to cast my vote. Tell if you think I did any “calculations” in the following 13 steps: (1) Earth spins slower because of launch of Satellite "B." - Only physics, I think, no calculation. (2) Therefore: Satellite B is higher than A, which was geostationary with the pre-B launch spin rate of Earth. (I happen to already know that a very low Earth orbit’s period is about 90 minutes and moon's is much longer, so B is in between A and the moon.) - Any calculation yet? I think not. (3) Decrease in Earth's angular momentum is exactly the angular momentum of B. - Pure physics, no calculation here, surely. (4) Angular momentum of B is mass, velocity, radius product. - more definition than calculation, I think, but does concern “product.” (5) B's radius will be bigger than A {only (2) again}. Thus it will travel farther each orbit. - Perhaps a little bit "calculation"? What do you think? (6) For B the day is longer, so it has more time to travel this greater distance. - Calculation?, I think not, just logic. (7) In view of (6), speed will not be greatly different from A's speed. At least not a linear change with radius, anyway. - How can I be thinking about "linear" etc. without at least some "calculation"? Yet nothing numeric here. - Not a calculation, I think. (8) If speed of B were same as A, then B's angular momentum is greater than A's linearly in the radius. - some "calculation."? Yet again, nothing numeric. (9) Angular momentum of Earth is HUGE, compared to B's and only changed by this tiny "B amount" - physics, general knowledge only, no calculation, I think. (10) As B is higher {5 & 2 again} and angular momentum is stronger function of radius than of speed, plus vague and uncertain recall that speed also drops with altitude as angular rate certainly does, perhaps, I may need to boost radius not only to make more angular momentum in B than in A, but also too compensate for slightly lower speed of B. (11) Despite (9), (7) with (8) tend to tell me most of the change in angular moment is going to come from increasing the radius and in view of (10), perhaps by more than my gut feeling tells me. Although my gut feeling, and fact I have never heard anyone mention that the geostationary altitude is a function of total mass already in geostationary orbit, both support the "bottomless" range choice, that may be wrong. It seems true that I must make most of B's greater angular momentum by its greater radius. Perhaps the difference in radius is not extremely small after all. Lets look at the other choices. - Mainly physics, logic and "betting strategy", I think, not calculation? (12) The 9mm wide band is a "dam small target" to hit. If I am going to let (11) over rule my gut feelings, the 99cm wide target of the 0.01 to 1 Meter band looks like a better bet. (I am usually not far off in my gut feelings, so better not ignore them entirely and select an even greater target.) (13) I'm sure many will go with the "bottomless band" and if they are correct and I choose a much greater difference, I will look silly. Ok that is it. - It is the 1M band for me, lets vote. - No calculation here, surely. If I define "calculation" as mathematical processing of numbers, but not including recall of previously calculated results, then there is no calculation in steps (1) thru (12) above, nor in 1+1 = 2 or 13 is a prime etc. For me, at least deciding if 345* is a prime, definitely is calculation, but I am sure that for some it is only "recall." Any other comments on what is "calculation" or my mental "vote selection" process? ------------------------------------------ *now changed to 567, thanks to Dale - see my later reply to him.
ouch, that truth hurt. Please Register or Log in to view the hidden image! (I had first typed 234, but noticed that it was even, so made it 345, without any more thought as that solved the "its even problem.") let me replace with 567. Ok? I don't think you "calculated" but just "already knew", that if it it ends in 2, 4, 5, 6, 8 or 0, it is not prime. PS this is a good example of how one can know something, but fail to apply it when needed.
I can't resist sorry, 567 is divisible by 3. I didn't actively think about any calculation, it just sort of happened, the divisibility by 3 test was just obvous here. Maybe something like 23415167 would be a better choice Please Register or Log in to view the hidden image!
Thanks. You are much better mathematician than me, but I was not making any claim about 567's status as a prime, only noting that for me to find out, I would require what I call a "calculation" - as experienced as you are, perhaps it does not require any calculation for your - it just "pops out at you" that it is not any prime you recognize, so probably is divisible by 3 (only other choice is 7 and if not by 3 then can't be by 9 and now list of possibilites is exhausted, at least usually I think for such small numbers, but may be something bigger, but less than square root, perhaps?) and you can not help but immediately realize that it is divisible by three, skilled mathematician that your are. In some ways, you are helping to prove my main point: Namely that what is a "calculation" is both hard to define and may be a calculation for one person and only "recall" for another. So I give you thanks again. PS - Did you vote? I am courous what a mathematician thinks about this so tell you selection, if you do not mind. The ID of the various voters and their choicers were available prior to voting. Perhaps someone who has not voted can still see who voted for what and will post that information before voting. PS2 - Perhaps someone thinks a new thread "what is calculation?" is desirable? If so, then it will be at least the "grandchild" of the thread that started this one, but I do not remember which thread would be the "grandfather," (father of this pole thread.)
If using brute force, you have to check for divisors up to the square root of a number to see if it's prime, the worst case for this kind of procedure would be the square of a prime as you won't find any divisor before that. Of course finding a divisor earlier, you'd stop and declare it composite. Absolutely. I think the spirit of your 'no calculation' rule was clear, I was just being difficult Please Register or Log in to view the hidden image!. When I first saw the poll I was going to vote for the "less than 1km" option, taken literally it looked to have no chance of being incorrect and I was going to be difficult Please Register or Log in to view the hidden image! . Then I saw the discussion with Ophiolite get a little out of hand and thought the better of it. Again, the spirit of your poll's options were clear and I am perfectly willing to forgive the form of your options given the medium as well as it being your first go at formatting a poll (lots of other things to worry about). I didn't really have any intention of voting, besides being difficult, so I haven't bothered.
Correct, it was recognition not calculation. For me also. I would have to fire up Mathematica, which undoubtedly would qualify the rest as a calculation. -Dale
I have avoided this thread because I work with spacecraft. Why isn't "less than 0" one of the answers? It should be. Suppose two objects are rigidly coupled and that the combined objects have an angular velocity of w about the combined center of mass. The velocities of the centers of mass of the individual objects in the combined center of mass frame is be w x r_i, where r_i are the coordinates of the i<sup>th</sup> object's center of mass with respect to the combined center of mass. Now suppose the objects detach from each other. At that instant, each object will still have an angular velocity of w about their individual centers of mass and will still have a velocity of w x r_i with respect to the combined center of mass. Spacecraft launch does not change the Earth's rotation rate one iota. With an eastward launch, the accelerating spacecraft also accelerates the atmosphere. The momentum added to the atmosphere will eventually be transfered to the Earth, speeding up the Earth's rotation rate by a tiny, tiny amount. Thus I vote for a tiny, tiny decrease in the geosynchronous altitude.
Conservation of angular momentum says it must. Any system with angular momentum that changes it's moment of inertia must have a resultant change in angular velocity(w) since the mass of the system is constant. By distributing a portion of the mass of the system away from the initial center of rotation, the system must, as a whole, decrease it's angular speed.
