3 ms·

> How much does a mile weigh? A mile of diameter weights 7 * 10^8 * density_of_the_asteroid kilograms. (mass equals volume of the body * density. Volume of th

by rimliu 9y ago

> How much does a mile weigh? A mile of diameter weights 7 * 10^8 * density_of_the_asteroid kilograms. (mass equals volume of the body * density. Volume of the sphere is 4/3radius^3. Hence 4/3(1/2mile)^3 = 4/3*(1609.344/2)^3 = about 694696971 cubic meters. 694696970,906763

barrkel 9y ago
Every mile extra adds more mass than the previous mile, in a squaring proportion, because it wraps around a larger volume and thus has a larger area.
- Retric 9y ago
  The ^3 takes care of that. His answer is for 1 mile, but you can easily substitute 37.23 or whatever miles in the formula. 4/3(x 1609.344/2)^3 = cubic meters.
  - barrkel 9y ago
    The formula he gave for a mile doesn't include a cubic term: > A mile of diameter weights 7 * 10^8 * density_of_the_asteroid kilograms.
    - Retric 9y ago
      You misreading it, 1 mile diameter = F(density). You can convert that into a formula aka x mile diameter = x ^ 3 * f(density), but it's just a solution not every solution.
      - barrkel 9y ago
        No, I didn't misread it; the formula he gave was for calculating the mass of a sphere, then he calculated the mass of a sphere with a mile diameter. My point was that was the wrong conclusion to come to for finding a conversion from miles to mass: because each additional mile doesn't add the same amount of mass. That is, he used the right formula to draw the wrong conclusion. The conclusion, which is what I quoted, is flatly incorrect for each mile beyond the first (and in fact it's only correct for the first mile, exactly, and will be wrong for any other fraction of a mile, if not corrected for using a squared factor of the radius).
        Retric 9y ago
        But, he is answering a question about a single mile, making it reasonable to actually answer that question. I mean if I say what's a cubic mile of the ocean's mass, I don't want a formula for a cube of arbitrary size I want you know an actual answer. Not that they are going to actually be perfect spheres, but yada yada. PS: I accept you really want to feel superior about this, but more often than not people actually know what they are taking about so using the reasonable interpretation is probably correct.
        barrkel 9y ago
        It's not about feeling superior - it's more about correcting people being Wrong on the Internet! > A mile of diameter weights 7 * 10^8 * density_of_the_asteroid kilograms This sentence, in so far as it can be understood in English, makes a wrong assertion. Only the first mile of diameter approximates to that; "the" mile, not "a" mile. In the context of the conversation - long lost in this subthread - it's the wrong answer without further clarification. It was in reply to the question "How much does a mile weigh?" - again, note "a", not any specific mile. Someone who takes the reply as an answer to that question would be even more misled, irrespective of how well rimliu understands the problem. To be really specific: I think 90+% of people would think that an asteroid with a diameter of two miles would weigh 14e8 * density, given this answer - and they'd be wrong, and increasingly wrong the larger and larger an asteroid they're calculating for. Because mathematical intuition is not common. I added the clarification. Then you came in with your intervention, for reasons that aren't yet clear to me.
        Retric 9y ago
        'I think 90+% of people would think that an asteroid with a diameter of two miles would weigh 14e8 * density' If this where YouTube then you might be right, but I would assume the vast majority of people here understand the r^3 part of the formula for a sphere especially when it was included in the same comment. Though they may forget about the 4/3. And again, it's perfectly valid English to say a mile when you mean exactly 1 mile. AKA "> How much does a mile weigh?" replace that with "How many feet are in a mile." and someone saying 5280 is being reasonable by answering the question. PS: Now if the original question was per mile then I would agree with you.

by rimliu 9y ago

barrkel 9y ago

Every mile extra adds more mass than the previous mile, in a squaring proportion, because it wraps around a larger volume and thus has a larger area.

Retric 9y ago
The ^3 takes care of that. His answer is for 1 mile, but you can easily substitute 37.23 or whatever miles in the formula. 4/3(x 1609.344/2)^3 = cubic meters.
- barrkel 9y ago
  The formula he gave for a mile doesn't include a cubic term: > A mile of diameter weights 7 * 10^8 * density_of_the_asteroid kilograms.
  - Retric 9y ago
    You misreading it, 1 mile diameter = F(density). You can convert that into a formula aka x mile diameter = x ^ 3 * f(density), but it's just a solution not every solution.
    - barrkel 9y ago
      No, I didn't misread it; the formula he gave was for calculating the mass of a sphere, then he calculated the mass of a sphere with a mile diameter. My point was that was the wrong conclusion to come to for finding a conversion from miles to mass: because each additional mile doesn't add the same amount of mass. That is, he used the right formula to draw the wrong conclusion. The conclusion, which is what I quoted, is flatly incorrect for each mile beyond the first (and in fact it's only correct for the first mile, exactly, and will be wrong for any other fraction of a mile, if not corrected for using a squared factor of the radius).
      - Retric 9y ago
        But, he is answering a question about a single mile, making it reasonable to actually answer that question. I mean if I say what's a cubic mile of the ocean's mass, I don't want a formula for a cube of arbitrary size I want you know an actual answer. Not that they are going to actually be perfect spheres, but yada yada. PS: I accept you really want to feel superior about this, but more often than not people actually know what they are taking about so using the reasonable interpretation is probably correct.
        barrkel 9y ago
        It's not about feeling superior - it's more about correcting people being Wrong on the Internet! > A mile of diameter weights 7 * 10^8 * density_of_the_asteroid kilograms This sentence, in so far as it can be understood in English, makes a wrong assertion. Only the first mile of diameter approximates to that; "the" mile, not "a" mile. In the context of the conversation - long lost in this subthread - it's the wrong answer without further clarification. It was in reply to the question "How much does a mile weigh?" - again, note "a", not any specific mile. Someone who takes the reply as an answer to that question would be even more misled, irrespective of how well rimliu understands the problem. To be really specific: I think 90+% of people would think that an asteroid with a diameter of two miles would weigh 14e8 * density, given this answer - and they'd be wrong, and increasingly wrong the larger and larger an asteroid they're calculating for. Because mathematical intuition is not common. I added the clarification. Then you came in with your intervention, for reasons that aren't yet clear to me.
        Retric 9y ago
        'I think 90+% of people would think that an asteroid with a diameter of two miles would weigh 14e8 * density' If this where YouTube then you might be right, but I would assume the vast majority of people here understand the r^3 part of the formula for a sphere especially when it was included in the same comment. Though they may forget about the 4/3. And again, it's perfectly valid English to say a mile when you mean exactly 1 mile. AKA "> How much does a mile weigh?" replace that with "How many feet are in a mile." and someone saying 5280 is being reasonable by answering the question. PS: Now if the original question was per mile then I would agree with you.