On a plane, we can measure angles as shown to the left, where P is the center of a circle of radius r and q is the angle between the two radii. A circle is divided into 360 degrees, but 2*p radians. A radian is defined as the angle that subtends an arc

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On solid angles
On a plane, we can measure angles as shown to the
left, where P is the center of a circle of radius
r and q is the angle between the two radii. A
circle is divided into 360 degrees, but 2p
radians. A radian is defined as the angle that
subtends an arc on a circle equal to the radius,
as shown. It is about 57 degrees (360/(2p). The
chord between the two radii has length
C2rtan(0.5 radians).
In a volume, we can measure solid angles as shown
to the right, where P is the center of a sphere
of radius r and q is the solid angle of a cone
that intersects the sphere in a small circle of
circumference pC. A sphere (area 4pr)
contains 4p steradians, where a steradian is the
unit of solid angle. The cone defined to the
right subtends a solid angle of 1 steradian or 1
sr. Most remote- sensing scanners have angular
resolutions that are a small fraction of a sr
airborne scanners are commonly 0.0025 or 0.001
sr, for example. As a rule of thumb, the pixel
size for a 2.5 milliradian instrument is about 1
m for every thousand feet of elevation above
terrain.