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Given a planet and a point $P$, is there an existing name for the angle $\theta$ as seen in the diagram below? If not, what would you call it? ("Angle of elevation"?)

Mystery angle diagram


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Question not clear. Where's the planet in the diagram? Where's the point? Where's the observer? What does $r$ mean? – Gerry Myerson Jun 14 '12 at 5:41
@Gerry: Sorry! The circle represents the planet. $P$ is the point (which is the location of the observer). $r$ is the radius, and doesn't really add to the question at all. – Cameron Jun 14 '12 at 5:42
I think you're asking about the "angular radius" of the planet, although a more commonly used concept is the "angular diameter". – Gerry Myerson Jun 14 '12 at 5:42
up vote 3 down vote accepted

I think you want the "angular radius" of the planet, although people more commonly use the "angular diameter" instead.

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So I do! Amazing, thanks! – Cameron Jun 14 '12 at 5:47
Not that it makes any practical difference when we are far away, but I think the angular diameter is marginally different, and is the largest angle subtended at the eye. Thus it would be the angle between tangent lines. – André Nicolas Jun 14 '12 at 6:00
@André, I don't mean the two terms are synonymous, indeed, the angular diameter is twice the angular radius. I just mean that OP is asking about the first concept, but the second concept gets used a lot more. – Gerry Myerson Jun 14 '12 at 6:58
@GerryMyerson: Sorry if I wasn't clear. The angular diameter would be $2\arcsin(r/D)$, where $D$ is the distance from the observer to the centre of the sphere. The OP's angle is $\arctan(r/D)$, so it is a (very) little smaller than $\arcsin(r/D)$. – André Nicolas Jun 14 '12 at 7:17
@André, yes, I see your point now, distinguishing between lines to the poles and tangent lines. OP has drawn the line to the pole, whereas angular radius applies when instead one draws the tangent line. As you say, no practical difference when both numbers are small. – Gerry Myerson Jun 14 '12 at 7:34

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