How Does a Steradian Relate to Degrees in 3D Measurements?

[dilan]

Hi,

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 really confused of this Steredian. Please guy if you got any links about it post here.

Thanks

 

[Doc Al]

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
http://en.wikipedia.org/wiki/Steradian

 

[Meir Achuz]

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.

 

[dilan]

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.

 

[Meir Achuz]

The unit is "steradian". For instance, a hemisphere has 2\pi steradians.

 

[SpaceTiger]

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 = $4\pi$ steradians = $4\pi(\frac{360}{2\pi})^2$ square degrees $\simeq$ 41,000 square degrees

The important thing to remember is that it's a unit of angle squared. Conversion should then be easy.

 

[dilan]

hey thanks that's very useful. Thanks a lot