Steradian

Steradian . Is the solid angle unit of measure of the International System of Units . The name steradian is made up of the Greek “stereos” which means “solid” and radian , it is the three-dimensional equivalent of radian . Its symbol is mr .

Summary

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  • 1 Definition
  • 2 Formulations
  • 3 Sphere and steradian
  • 4 Equivalence with another SI unit
  • 5 Utility
  • 6 Note on terminology
  • 7 See also
  • 8 Reference
  • 9 Source

Definition

Steradian 1 is defined as a solid angle that, having its center in that of a sphere , has an area (on the sphere) equal to the square of the radius . The solid angle of a full sphere is 4π steradians.

Formulations

sr = a = r 2

A stereoradian marks an area on a sphere equal to (radius) 2 .

Ω = S / r 2

Where S is the surface covered by the object in an imaginary sphere of radius r, whose center coincides with the vertex of the angle .

1 sr = r 2 / r 2

A steradian is the angle that a surface r 2 covers at a distance r from the vertex.

Sphere and steradian

  • The area of ​​a sphere is 4πr 2
  • The surface area of ​​a sterradian is r 2

So a sphere measures 4π steradians, plus or minus 12.57 steradians. In the same way a steradian is 1 / 12.57, plus or minus 8% of a sphere. When measuring angles , no matter the size of the sphere , it always measures 4π steradians.

Equivalence with another SI unit

Name Symbol Steradian equivalence
square angle Π ° 3,046 2 x 10 -4 sr

Utility

In the practical field, angles are measured in degrees (unit of measure for plane angle). The relationship between the value of a flat angle expressed in radians and that expressed in degrees (angular) is as follows:

  • 1 rad = 180 ° / p (angular degrees)
  • The value of a radian is approximately 57 ° 17 ’44’ ‘.
  • Steradian can be expressed mathematically as:

sr = 2 p (1 – cos a / 2)

Where a = plane angle at the vertex of the cone of the solid angle.

Steradian is used in theoretical calculations, but not for measurements in the practical field, because in this case it has the same limitations as radian .

Terminology Note

This unit derived from the International System of Units known by the initials SI does not come from the proper name of a person, so its name (steradian), and its symbol (sr), are written with lowercase except in the case that a phrase or title.

 

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