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Thread: Random Cosmic Numbers

  1. #1
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    Random Cosmic Numbers

    Proxima Centauri is 4.2 light years away. That is 24,673,274,438,400 miles. Going at the speed of the Sun through the Milky Way, 492,150 miles per hour, it would take 5,723 years to get there. In 100 years the Sun has only gone 431,123,400,000 miles, or 7 percent of 1 light year (5,874,589,152,000 miles).

    https://i.imgur.com/RUZFo0S.jpg

    All objects, plus Earth-Moon distance are to scale. You could fit the rest of the planets between the Earth and Moon at apogee, and put that inside the sun with room to spare.

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    Unless that figure of 4.2 light years is assumed to be exact, it is meaningless to give the number of miles with that sort of precision. I don't think we are even close to that sort of precision in determining cosmic distances and speeds for these objects.

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    The number of astronomical units in a light year, 63241.077, is very close to the number of inches in a mile, 63360.

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    Are my numbers accurate?

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    Quote Originally Posted by cjackson View Post
    Are my numbers accurate?
    As Hornblower said - they are misleadingly precise. Rule of thumb - for calculations involving multiplication/division your answers should be given to the same number of significant figures as your least precise input. In this case you have a distance to 2sf so you shouldn't be quoting your other results to more than that. From the numbers you have given your answers should be:

    That is 25,000,000,000,000 miles
    It takes 5700 years to get there

    More precision that this is not particularly meaningful without some kind of error analysis on the measurements (since 4.2 could be 4.15 - 4.24 in this example)

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    I was always very suspicious of the conversion from inches to centimtres 2.54, as those two systems of measurement derive from such different sources.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    If this Wiki source is correct, the inch is by law exactly 2.54 cm as per the international yard and pound agreement of 1959. That agreement defined the yard as exactly 0.9144 meter, and the inch follows from dividing by 36.

    https://en.wikipedia.org/wiki/Intern...yard_and_pound

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    Quote Originally Posted by Hornblower View Post
    If this Wiki source is correct, the inch is by law exactly 2.54 cm as per the international yard and pound agreement of 1959. That agreement defined the yard as exactly 0.9144 meter, and the inch follows from dividing by 36.

    https://en.wikipedia.org/wiki/Intern...yard_and_pound
    That's correct. The inch and the centimeter have a relatively round number relating them because they've been defined that way, pretty much for convenience.
    Conserve energy. Commute with the Hamiltonian.

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    The problem is that conversion can introduce false precision, like when an aircraft flying at an altitude of 5000 meters is reported as flying at 16404 feet making it look like its altimeter is incredibly precise.

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    Quote Originally Posted by Grey View Post
    That's correct. The inch and the centimeter have a relatively round number relating them because they've been defined that way, pretty much for convenience.
    It means that thumbs have lost their precision in carpentry since 1959. A lot of carpentry in Britain predates 1959. And my school ruler, in inches, is wrong even at standard T and P.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by Shaula View Post
    From the numbers you have given your answers should be:

    That is 25,000,000,000,000 miles
    No. That has the same degree of accuracy: 14 sig digs.

    The correct answer is: 25x10^12 miles

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    Quote Originally Posted by DaveC426913 View Post
    No. That has the same degree of accuracy: 14 sig digs.

    The correct answer is: 25x10^12 miles
    https://en.wikipedia.org/wiki/Signif...ules_explained
    As these conventions are not in general use, it is often necessary to determine from context whether such trailing zeros are intended to be significant.
    I'm lazy and ambiguous, not wrong.

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    Quote Originally Posted by Shaula View Post
    OK, but in a discussion specifically about precision and significant figures, ambiguous is as good as wrong, particularly when your goal is to correct someone else's error.

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    False precision also comes up when computing areas and volumes. If you measure a cube to be 125 mm on a side and report its volume to be 1,953,125 cubic mm but it's actually 124.99 mm on a side then your last 4 digits would be wrong.

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    Quote Originally Posted by Chuck View Post
    False precision also comes up when computing areas and volumes. If you measure a cube to be 125 mm on a side and report its volume to be 1,953,125 cubic mm but it's actually 124.99 mm on a side then your last 4 digits would be wrong.
    When I was a graduate student in physics, I had an entire course dedicated to data analysis, which included a fairly lengthy section on error propagation: understanding how a given range of error in your initial measurements (like 125.00 +/- 0.01 mm, if your measurement precision was really 0.01 mm) would effect the error in your final result. In the case of a calculation that depends on the cube of a measured value, the relative error (the error expressed as a fraction of the value) of the result will be 3 times the relative error of the measurement, so you'd end up with something like 1,953,125 +/- 469 mm3, likely reported as 1,953,100 +/- 500 mm3.
    Conserve energy. Commute with the Hamiltonian.

  16. #16
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    I remember an amusing display of false precision on the outfield fence at Riverfront Stadium in Cincinnati. They displayed the distance from the plate to the nearest foot, and then the metric equivalent in meters to two decimal places, as in centimeters.

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