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Math Help - Astronomical numbers.

  1. #1
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    Astronomical numbers.

    Teacher gave us this for extra credit. He wants us to convert astronomical objects into money based on their radius. This is how it works. The earth is worth one penny. $.01

    The earth's radius is 6,378 km. So 6,378 km equal one penny in this system.

    Next we move on to the sun, which has a radius of 696,000 km. So we divide that by 6,378. Which is 109 cents. So the sun is worth 1.09

    Solar System is 40 AU. I want this in km. AU is 1.5 x 10^8 km. So do 40 times 1.5 x 10^8 =6,000,000,000km or 6 x 10^9. So then I divide 6 x 10^9 by 6.378 x 10^3. And I get 940,733 cents. Drop 2 decimals to convert to dollars and I get $9,407 for the price of the solar system.

    I know the final answers on those are correct because he helped us with him.

    It is the even bigger ones I am having problems with. Next is Milky Way. It is 50,000 light years across. I want to convert this to km too. A light year is 10 trillion km. So I multiply 50,000 by 10 trillion. Or is there a better way to do this? Anyway, assuming I do multiply them it is 5 x 10^4 x 1 x 10^13. So that is 5 x 10^17. Now I divide this by 6.378 x 10^3 and get .78394481 x 10^14. Now what? Should I get rid of some exponents? Maybe 783 x 10^9? Which is 78,300,000,000,000 cents. Take out to points to convert to dollars and you have $783,000,000,000 as the cost of the Milky Way, Is this correct? Is there a better way to do it?

    thanks
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  2. #2
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    All of your steps look good. You seem to understand scientific notation pretty well.
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  3. #3
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    Quote Originally Posted by LivingMath View Post
    All of your steps look good. You seem to understand scientific notation pretty well.
    I hope this isnt sarcasm. lol. I know this a pretty basic question and feel embarrassed even asking it really. I just havent taken math in years and this stuff is very unintuitive to me and it takes me a long time.
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  4. #4
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    Quote Originally Posted by hansbethe View Post
    I hope this isnt sarcasm. lol. I know this a pretty basic question and feel embarrassed even asking it really. I just havent taken math in years and this stuff is very unintuitive to me and it takes me a long time.
    No sarcasm intended. I'm just relearning a lot of higher math myself, so I understand your feelings.
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  5. #5
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    astronomical numbers

    An AU is the mean distance between the earth and sun.If you want to find the worth of the solar system you need to look up the diameter of the planets and add the sun.


    bjh
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  6. #6
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    Quote Originally Posted by bjhopper View Post
    An AU is the mean distance between the earth and sun.If you want to find the worth of the solar system you need to look up the diameter of the planets and add the sun.


    bjh
    I already have the radius of the solar system. Which is 40 au. It is the milky way one I am concerned about.
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  7. #7
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    What about the milky way ?

    Exactly what are you concerned about regarding the milky way?
    Is it if you calculations are correct?
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  8. #8
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    astronomacal numbers

    originally posted by hansbethe

    My interpretation of the problem was finding the worth of solid bodies in the solar system.Does your teacher value space?

    bjh
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  9. #9
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    Quote Originally Posted by Henryt999 View Post
    Exactly what are you concerned about regarding the milky way?
    Is it if you calculations are correct?
    Yes.
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  10. #10
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    Quote Originally Posted by bjhopper View Post
    originally posted by hansbethe

    My interpretation of the problem was finding the worth of solid bodies in the solar system.Does your teacher value space?

    bjh
    No, it is an exercise in scale. To show how us how big things really are. The questions ask what is the value of the earth, then the sun, then the solar system, then the milky way, then the local group, then the visible universe. The only thing we have to do is divide the radius of each by the radius of the earth. To get the amount in cents. Then convert that to dollars. So, the earth is worth one penny. .01. Sun is worth 1.09. Solar System is worth 9,407. Now I am trying to figure out the milky way. Which I think is 78 trillion after readjusting.

    I have the radius of all given to me on the paper. I just need to divide the radius by 6,378 to get cents.

    Milky Way Radius= 50,000 ly
    Local Group= 1.5 million ly
    visibile universe= 13.7 billion ly

    The way Im doing it is converting the light years into kilometers. A light year is 10 trillion km so I multiply that by 1.5 million in the case of the local group. Is this how it should be done?
    Last edited by hansbethe; February 2nd 2010 at 03:02 PM.
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  11. #11
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    Alright, the final answers I got are:


    milky way- 783 billion dollars
    local group- 23 trillion
    visible universe- 214 quadrillion.
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  12. #12
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    anyone check my work? milky way=50,000 ly across. 10 trillion km in a light year, so:

    5 x 10^4 x 1 x 10^13 = 5 x 10^17.

    5 x 10^17 divided by 6.378 x 10^3 =.783 x 10^14

    I convert that to 78.3 x 10^12 for the total cents. Now to convert that to dollars I divide 78.3 X 10^12 by 10^2. So I get 78.3 x 10^10 dollars. Which is 783 billion.
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