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Thread: Random math, science, and tech knowledge that doesn't deserve its own thread

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    Member Aurast's Avatar
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    Random math, science, and tech knowledge that doesn't deserve its own thread

    To start with, what the hell is a parsec?



    (it's a right triangle)

    If the angle on the right is one arcsecond (1/3600 of a degree) then d is one parsec. If the angle is two arcseconds, then d is two parsecs. One parsec = (one AU)/sin(1 arcsecond) * sin(pi/2 - one arcsecond) Nevermind the relationship is only true when the angle is 1 arcsecond.

    An astronomical unit is about ninety-three million miles. A parsec turns out to be around 3.26 lightyears. The parsec is the SI unit for astronomical distances so if you were planning to publish any astronomy research using light-years, tough luck.
    Last edited by Aurast; 05-09-2015 at 03:44 AM.

  2. #2
    Quote Originally Posted by Aurast View Post
    If the angle is two arcseconds, then d is two parsecs.
    I don't think that's correct. If the angle on the right gets bigger and the whole thing remains a right triangle then d must become smaller. So two parsecs would be a shorter distance than one parsec.

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    Member Aurast's Avatar
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    Quote Originally Posted by pathogenetic_peripatetic View Post
    I don't think that's correct. If the angle on the right gets bigger and the whole thing remains a right triangle then d must become smaller. So two parsecs would be a shorter distance than one parsec.
    Good catch I think you're right. In that case I suppose perhaps the 1 AU side is actually an arc instead of being straight. Or else the triangle is used to calculate the length of one parsec but no more than one.

    EDIT: Upon further research it does look like you can only represent a distance of ONE parsec this way. That makes me sad somehow.

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    Mens bona regnum possidet ferrus's Avatar
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    Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt. Die Logik ist transcendental. - Wittgenstein

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    Meae Musae Servus Hephaestus's Avatar
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    ^^^No offense to the astro-nerds, but that is really cool!
    --Mention of these things is so taboo, they aren't even allowed a name for the prohibition. It is just not done.

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    Persona Oblongata OrionzRevenge's Avatar
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    Quote Originally Posted by Aurast View Post
    Good catch I think you're right. In that case I suppose perhaps the 1 AU side is actually an arc instead of being straight. Or else the triangle is used to calculate the length of one parsec but no more than one.

    EDIT: Upon further research it does look like you can only represent a distance of ONE parsec this way. That makes me sad somehow.
    It's a convenient unit adopted when astronomical instruments acquired the accuracy to measure the Parallax of the Stars.

    Holding your thumb at arms length and winking each eye in turn, you notice the angle of variance in your thumbs position vis a vis a far distant background.

    With nearby stars we can use the Earth's change in position over a six month period in the same manner we use the distance between our eyes to range nearby objects.



    The reason this is a convenient unit is because 1 arc second being equal to 3.26 ly fits well with the discovery of our nearest neighbor star being 4.2 ly away.

    This equates to Proxima Centauri being 1.29 Parallax Second of Arc (parsec) away.

    Just nice and handy to start our tally very nearly at one and tie it to something as concrete as an arc second.

    Especially given that parallax was the method allowing for these discoveries.
    Creativity is the residue of time wasted. ~ Albert Einstein

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    Member Aurast's Avatar
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    Let's see if I can get something right for a change.

    How many people need to enter a room before it becomes more likely than not that two of them share a birthday? Just 23!

    product((365-x)/365,x,1,22) = .4927

    When the second person walks into the room, the chance of him or her not sharing a birthday with the first is 364/365.
    For the third person, the chance they don't share a birthday with either of the other two is 363/365 (we get to assume the first two people don't share a birthday because we multiply this with the above^ probability)
    For the fourth, it's 362/365
    etc...

    Keep multiplying the probabilities until the product (the probability that no one shares a birthday) drops below 50%.

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    Quote Originally Posted by OrionzRevenge View Post
    It's a convenient unit adopted when astronomical instruments acquired the accuracy to measure the Parallax of the Stars.

    Holding your thumb at arms length and winking each eye in turn, you notice the angle of variance in your thumbs position vis a vis a far distant background.

    With nearby stars we can use the Earth's change in position over a six month period in the same manner we use the distance between our eyes to range nearby objects.



    The reason this is a convenient unit is because 1 arc second being equal to 3.26 ly fits well with the discovery of our nearest neighbor star being 4.2 ly away.

    This equates to Proxima Centauri being 1.29 Parallax Second of Arc (parsec) away.

    Just nice and handy to start our tally very nearly at one and tie it to something as concrete as an arc second.

    Especially given that parallax was the method allowing for these discoveries.
    Also, one attoparsec per microfortnight is about 1 inch per second. Very handy!

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    Persona Oblongata OrionzRevenge's Avatar
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    Quote Originally Posted by Aurast View Post
    Also, one attoparsec per microfortnight is about 1 inch per second. Very handy!
    Yeah it's really just a convenient ruler when measuring interstellar distance within a galaxy.

    Proxima Centauri is 1.29 parsecs away and the Milkyway is about 30.7 Kiloparsecs across.

    Even though it is the SI unit of astronomical distance, it really isn't of much significance beyond that.

    Something as cosmically profound as E=MC2 uses the gram-meter-second units.

    More often in cosmic conversations you'll hear Light Year as a unit of distance because, for example, speaking about the farthest objects seen at around 13.6 Billion Light Years is not only speaking about the vastly distant reaches of space, but also about objects in the vastly distant past. As Light Year units of distance informs us that the information about said objects has taken 13.6 billion years to reach us here & now. From an ancient universe that was vastly smaller in linear measure.
    Creativity is the residue of time wasted. ~ Albert Einstein

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    Member Aurast's Avatar
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    That reminds me of a good one! If the universe is less than 14 billion years old how can the visible universe be over 90 billion light years across? Nothing mystical about this. The universe is expanding and the speed of light is finite. The edge of the visible universe looks like it's close to 14 billion light years away, but the light we see from there is very, very old. A galaxy that we see there is in reality much, much farther away in proper distance.

    But the universe isn't really all that big. If you were to print one novel for each unique 100,000 character-long permutation of the characters of the Roman alphabet, they would fill a volume dozens of orders of magnitude larger than the visible universe. To be fair, that's quite a lot of books: 26^100,000 of them.

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