Talk:Solid angle

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Possible correction (I'm not sure): Under Tetrahedron, the definition of "Theta sub a" should perhaps be angle BOC instead of OBC and similarly for the others. Could the author or someone confirm this?Tap17 (talk) 07:14, 23 February 2008 (UTC). Yes it is a correction. Page now updated. Thanks Frank M Jackson (talk)

The solid angle is not an angle!! it's a surface area of a projection!! check Wolfram's mathworld. —Preceding unsigned comment added by 200.119.3.210 (talk) 22:36, 18 December 2007 (UTC)

"To get an angle, imagine two lines passing through the center of a unit circle. The length of the arc between the lines on the unit circle is the angle, in radians."

this definition would make the angle dependent on radius. this definition definition gives the angle units of length, absurd. this should be "length of arc divided by the radius"

Unit circle = circle with radius 1. EJ 19:29, 6 Jun 2005 (UTC)

Can someone explain the notation on the equation at the bottom of the page? Is Omega the solid angle? Do the italics represent the magnitude of the vectors? What do the brackets at the top mean?

Contents

[edit] explanation

brackets = triple scalar product. italics = magnitude of vector. Omega= solid angle.

152.78.98.1 15:53, 7 April 2006 (UTC) Somehow, this formula seems to be wrong. Let's ignore the minor detail that we get positive or negative solid angles, depending on the orientation of the vertices. The problem is as follows:

Let's take a triangle whose center is very close to the observer. The angle omega then should be close to 4pi/2 = 2pi, and omega/2 should be close to pi. Now, taking the arctangent of the fraction will give something in the range -pi/2..pi/2. So, this cannot work - or can it?

[edit] Solid angles in higher dimensions?

Does anyone know formulas for solid angles (aside from the surface (d-1)-volume of the d-dimensional ball) in higher dimensions? Especially appreciated would be an analogue of the tan(Omega/2) formula (the one using the triple product and the 3 dot products) in an arbitrary number of dimensions.

i dont think its likely. the cross product is only defined for the r3 euclidean vector space, so i dont expect its in that form. btw might they define it as (in r4) (surface volume)/r^3? I got scammed 10:09, 5 September 2006 (UTC)
There must be a way. I'm not a mathematician (just a physicist). The 3D version can be derived from the Levi-Civita tensor (see Levi-Civita symbol) using 3 indices. Perhaps a similar tensor can be defined in N-space? If any pair of indices are equal, the element is zero. If the indices are permuted evenly, the element is 1, and if they are permuted oddly, the element is -1. Summation of the LC Density over N-1 dimensions with N-1 vectors might give you a N-dimensional cross-product. Can anyone confirm this or play with it? --MxBuck 05:58, 2 November 2007 (UTC)
  • There is a recurrence formula for "surface" and "volume", Sn and Vn, respectively, of n-D spheres; namely, Sn=2πR×Vn−2 and Vn=[R×Sn]/n. If the n-D solid angle is defined as: Ωn=Sn/Rn−1, I wonder if we could determine Ωn subtended at the center of the "sphere" in this manner. If so, we would have the following results: Ω1=2, Ω2=2π, Ω3=4π, Ω4=2п2, Ω5=8п2/3, Ω6=п3, etc. Zymogen (talk) 14:18, 19 May 2008 (UTC)

"The Sun and Moon both subtend a solid angle of 5.11×10-6 sr in the sky of Earth, or about 1/2,500,000th of the celestial sphere."

Could this be wrong? Using the formula provided an answer of 5.98×10-5 is given.

Another web based article appears to be correct -

"The sun and moon are both seen from Earth at a fractional area of 0.001% of the celestial hemisphere or 5.98×10-5 steradian [1]."

[edit] Solid angle formulas

I've updated the page with a formula for the solid angle subtended by a rectangular pyramid. If you'd like to know where this somewhat messy-looking formula comes from I've posted a derivation here (pdf file): [1].

Bgerke 20:50, 1 February 2007 (UTC)

Excellent job. I always wondered where that pyramid formula came from, which was originally in the article. Thanks for generalizing it to a rectangular pyramid. -Amatulic 22:28, 1 February 2007 (UTC)

[edit] Confused Definition of Subtend

At the top of the article, it is said that "The solid angle, Ω, is the angle in three-dimensional space that an object subtends at a point." In other words, an object subtends an angle. But further down in the article under Tetrahedron, it says, "The solid angle at O that subtends the triangular surface ABC..." This implies that an angle subtends an object. I believe Wolfram uses the former definition, although in the body of their own article on solid angle, there is one instance of the reverse, I think. Could someone please rectify this confusion? I've seen the former definition being used most frequently, so this article should match this for both consistency and accuracy, if indeed that is the correct definition.Firth m (talk) 00:13, 25 February 2008 (UTC)

Yes I agree, it is the object that subtends the solid angle. So the solid angle either extends the object or is subtended by the object. Tetrahedron page updated accordingly Frank M Jackson (talk) 15:10, Tuesday June 10, 2008 (UTC)