On the status of plane and solid angles in the International System of Units (SI)
Abstract
The article analyzes the arguments that have become the basis for the 1980 CIPM recommendations declaring plane and solid angles as dimensionless derived quantities. This decision was the result of an incorrect interpretation of mathematical relationships that connect the ratio of two lengths with the plane angle, and the ratio of area to square of length with the solid angle. The analysis of these relationships, presented in the article, showed that they determine neither the dimensions of the angles nor their units, but only the numerical values of the angles expressed in radians and steradians. It is shown that the series expansions of trigonometric functions sometimes used to prove the dimensionless character of the plane angle is also incorrect because in this case the trigonometric functions of two different types, independent of each other, are offen confused. It is established that the plane angle is an independent quantity and therefore should be assigned to the base quantities and its unit, the radian, should be added to the base SI units. It is shown that the solid angle is the derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.
- Publication:
-
Metrologia
- Pub Date:
- December 2019
- DOI:
- arXiv:
- arXiv:1810.12057
- Bibcode:
- 2019Metro..56f5009K
- Keywords:
-
- plane angle;
- solid angle;
- radian;
- steradian;
- Physics - Classical Physics
- E-Print:
- Correction of error in the calculation of the ratio between the steradian and the radian. 13 pages, 3 figures