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Math Help - astronmonical measurement

  1. #1
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    astronmonical measurement

    ok these questions are sort of linked and i really hope this question belongs in this board since it does deal with astronomy

    Question 1 In a scale Universe with the sun the size of a spherical grain of fine sand (diameter= 0.2 millimeters), how big a box (in cubic meters) would you need to hold all the stars in the Milky Way Galaxy. Packing efficiency of sand is a very complex problem, but assume that each grain of sand occupies 0.023 cubic millimeters.

    i believe i got this one right and that the 0.2mm isn't used. here is what i got

    200 billion grains of sand
    Density of a grain of sand = 0.0023 mm3

    200 billion x 0.0023mm3 = 460000000mm3

    460000000mm3 = 0.46m3 (google.com)

    The box would have to be the size of 0.46m3


    ok but the next problem is tricky and I think i am really doing it wrong

    Question 1b How big, in meters, would the Milky Way galaxy be in this scale universe? If the center of the Milky way was centered on Toronto, approximately where would the edge of the galaxy be? (eg, near Kitchner? Near Jupiter?).

    I was told to scale the sun to a grain of sand so i have to use the 0.2mm from Question 1 to help figure this out


    i really dont know if I am doing this right here is what i got

    Milky Way = 100,000 light years in diameter = 9.4605284 ◊ 1020 m
    Sunís diameter = 1,400,000 km (Taken from 100,000 light years = 946,091,000,000,000,000km
    (100,000 x 9.46091E+12)
    Sunís diameter = 1,400,000 km
    0.2mm


    946,091,000,000,000,000km divided by 1,400,000km x 0.2=135155857142.857142

    i really don't know what i did wrong here it seems that what i am doing is correct but this numer seems wrong so i am wondering if any one can help me with this question

    soory again if this question does not belong in this board and in another one here
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by blar View Post
    ok these questions are sort of linked and i really hope this question belongs in this board since it does deal with astronomy

    Question 1 In a scale Universe with the sun the size of a spherical grain of fine sand (diameter= 0.2 millimeters), how big a box (in cubic meters) would you need to hold all the stars in the Milky Way Galaxy. Packing efficiency of sand is a very complex problem, but assume that each grain of sand occupies 0.023 cubic millimeters.

    i believe i got this one right and that the 0.2mm isn't used. here is what i got

    200 billion grains of sand
    Density of a grain of sand = 0.0023 mm3
    Not density but effective volume occupies by a single grain.

    You have 0.0023 cubic mm here but 0.023 cubic mm earlier.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Not density but effective volume occupies by a single grain.

    You have 0.0023 cubic mm here but 0.023 cubic mm earlier.

    RonL
    thank you so much i did not catch that mistake

    did you happen to see what i am doing wrong in Question 1b??
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by blar View Post
    Question 1b How big, in meters, would the Milky Way galaxy be in this scale universe? If the center of the Milky way was centered on Toronto, approximately where would the edge of the galaxy be? (eg, near Kitchner? Near Jupiter?).

    I was told to scale the sun to a grain of sand so i have to use the 0.2mm from Question 1 to help figure this out


    i really dont know if I am doing this right here is what i got

    Milky Way = 100,000 light years in diameter = 9.4605284 ◊ 1020 m
    Sun’s diameter = 1,400,000 km (Taken from 100,000 light years = 946,091,000,000,000,000km
    (100,000 x 9.46091E+12)
    Sun’s diameter = 1,400,000 km
    0.2mm


    946,091,000,000,000,000km divided by 1,400,000km x 0.2=135155857142.857142

    i really don't know what i did wrong here it seems that what i am doing is correct but this numer seems wrong so i am wondering if any one can help me with this question

    soory again if this question does not belong in this board and in another one here
    First lose the excessive precision, at least some of your data is only correct to between 2 and 3
    significant digits.

    Then:

    c ~= 3 10^8 m/s
    1 yr ~= 60*60*25*365.24 s ~=3.2 10^7 s

    1 ly ~= 9.5 10^15 m

    L1=10^5 ly ~=9.5 10^20 m

    L2=Dia of Sun ~= 1.4 10^9 m

    scalled size of Galaxy=L1/L2*0.2 ~= 13.6 10^11 = 1.36 10^12 m

    RonL
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    c ~= 3 10^8 m/s
    1 yr ~= 60*60*25*365.24 s ~=3.2 10^7 s

    1 ly ~= 9.5 10^15 m

    L1=10^5 ly ~=9.5 10^20 m

    L2=Dia of Sun ~= 1.4 10^9 m

    scalled size of Galaxy=L1/L2*0.2 ~= 13.6 10^11 = 1.36 10^12 m

    RonL
    i am sorry but you lost me i am not good at reading this math stuff

    is 10^15 mean 10 to the power of 15?

    is it possble for you to explain this in a simpler way???

    and what is the c??

    thank you so much
    Last edited by blar; March 21st 2007 at 11:22 PM.
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  6. #6
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by blar View Post
    i am sorry but you lost me i am not good at reading this math stuff

    is 10^15 mean 10 to the power of 15?

    is it possble for you to explain this in a simpler way???

    and what is the c??

    thank you so much
    For future reference, the symbol ^ means 'raised to the power of'. So yes, 10^15 means 10 'raised to the power of' 15.

    The way CaptainBlack was writing the numbers is called "Scientific Notation." It's a way of writing very big or very small numbers so that it's easy to see exactly how big or small they are. For example:
    312 000 000 000 000 000 000 just looks like a big number, but exactly how big is it? We can write this number in scientific notiation as:
    3.12 * 10^20 ... The 10^20 means that we would take the decimal in 3.12 and move it to the right 20 spaces.
    Now we can easily see that this number is 20+1 = 21 digits long, and we can start using this number in equations without too much difficulty.

    c is the speed of light. CaptainBlack used this to find out how long 1 light year is in meters.

    I would go more in detail, but I have to go. Hopefully someone else can finish up this explanation.
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    thank you guys
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by blar View Post
    i am sorry but you lost me i am not good at reading this math stuff

    is 10^15 mean 10 to the power of 15?

    is it possble for you to explain this in a simpler way???

    and what is the c??

    thank you so much
    ecMathGeek has answered most of this more than adequately.

    What I do want to say is that using scientific notation makes it much easier
    to keep track of the size of the answer as when the powers of 10 are
    multiplied the exponents (powers) add.

    RonL
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