Talk:Solid angle

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"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?

[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)

"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]."

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