   Psychological Experiment: Guess the answer to physical question.
  There are 2 solid copper spheres of radius 1cm, at separation 1cm, flying in space far away from stars. Spheres are initially at rest relatively to each other, and are not electrically charged.Using just your head (no paper-n-pencil, no notepad, no wikipedia, no wolfram alpha, etc), try to guess how long it takes until spheres will touch each other due to gravitational attraction. Post your guess. Note: please don't just post 42. At least give units (42 seconds or 42 thousands years, whatever). If you don't know answer, you can take a guess anyway. And don't worry, almost nobody would remember all the constants involved and really calculate it just in their head, so there should be no embarrassment from being wrong.(I know the formula but didn't calculate it yet to avoid biasing this guessing experiment)I'm just curious how far the average answer deviates from correct when big and small numbers are involved.edit: clarification for nitpickers: solid copper. Pure copper, if you wish, or any particular alloy consisting mostly of copper (e.g. "alloy used in wires").[Edited by - Dmytry on May 18, 2009 12:28:27 PM]
  Welllll... Gravity is /amazingly/ weak, unless you talk about massive objects. So, given the fact that these spheres have 0 impulse to start with, it is going to take, well... ages. :)So, without knowing any values, the equation would sort of be:How much energy is needed to move the mass of a 1cm copper sphere over 1 cm, and how much potential energy does gravity have, and what is the specific impulse?Geez, I give up.100.000 years.;  My bet: 1 billion years.   ;  Tuesday.   ;  About a week.   ;  Don't we need to know the mass for this to even be a guess?  I am not to sure if you can have more dense copper or less dense, so I guess it may not be that drastic.I say... several hundred thousand years.   ;  Without knowing the mass, this question is rather meaningless. (I actually remember the formula for acceleration due to gravity, I just don't remember the value of the gravitational constant...)   ;  I think it would be expressed in years. (Earth is 10e8 times larger than copper ball, so mass is 10e24 times larger, time is proportional to square root so 10e12 slower, which means about decade).   ;Quote:Original post by ApochPiQWithout knowing the mass, this question is rather meaningless. (I actually remember the formula for acceleration due to gravity, I just don't remember the value of the gravitational constant...)Copper has rather constant density which you as well could guess, and the radius of spheres is given. The answer actually can be guessed to correct order of magnitude without knowing gravitational constant or exact density of copper.   ;  Mmmh... I don't agree. IMHO the more factors that have to be guessed, the less likely you are to get any meaningful data on your actual question. In other words, making us guess the mass is going to introduce yet another inaccuracy in the calculation, which will skew the results towards inaccuracy (unless someone gets lucky of course). This means you introduce sampling noise into the experiment; you're no longer testing the ability of people to think in both large and small numeric terms - you're testing the random luck of people to guess an overly complex problem.   