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Homework Help: Need some help about a Steradian

  1. Jan 31, 2006 #1

    hmm I am just a liitle confused in this Steradian. Now I know that this works only with 3D.

    Now a radian is = arc of the size of a radius/radius
    So that
    2*22/7*r/r = 360'
    2*22/7rad = 360'
    22/7rad = 180'

    Now that's how a radian is counted in 2D
    Is there any connection like this in a steradian? I mean can it be converted into degrees and measure the angle of 3D objects.

    I just need to know this because I am realy confused :confused: of this Steredian. Please guy if you got any links about it post here.

  2. jcsd
  3. Jan 31, 2006 #2

    Doc Al

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    Just like the 2D angle can be measured using the radius of a circle (1 radian equals the angle subtended by an arc length of 1 radius), so can the 3D solid angle: 1 steradian equals the solid angle subtended by an area of one radius squared on the surface of a sphere.

    http://www.usd.edu/~schieber/trb2000/sld021.htm [Broken]
    Last edited by a moderator: May 2, 2017
  4. Jan 31, 2006 #3

    Meir Achuz

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    Degrees only work for angles where 180 degrees=pi radians.
    Degrees do not connect to steradians.
    An entire sphere covers 4pi steradians.
    Just forget about degrees and steradians are easy.
  5. Jan 31, 2006 #4
    Oh that's right

    So steradians do not connect with degrees?
    I see. But then in what unit do they measure the angle. Is it just Steredian and then make the sums.
  6. Feb 6, 2006 #5

    Meir Achuz

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    The unit is "steradian". For instance, a hemisphere has 2\pi steradians.
  7. Feb 6, 2006 #6


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    Well, they might not be able to forget entirely about degrees. In astronomy, for example, angular areas are often quoted in "square degrees". Converting is just a matter of multiplying by the square of the conversion from radians to degrees:

    Angular Area of sphere = [itex]4\pi[/itex] steradians = [itex]4\pi(\frac{360}{2\pi})^2[/itex] square degrees [itex]\simeq[/itex] 41,000 square degrees

    The important thing to remember is that it's a unit of angle squared. Conversion should then be easy.
  8. Feb 7, 2006 #7
    hey thanks that's very useful. Thanks alot
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