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Encyclopedia > Small angle formula

The small-angle formula is a mathematical approximation, used in astronomy. It relates the linear size (D) of an object to its angular size (α) and its distance from the observer (d) and is a valid approximation if α is small.


The approximate formula is:

D = α d / 206,265

Here, α has to be measured in arcseconds.


The number 206,265 is approximately equal to the number of arcseconds in a circle (1,296,000), divided by .


The exact formula is

D = 2 d tan(απ/1,296,000)

and the above approximation follows from this because tan(x) is approximately equal to x if x is small.


  Results from FactBites:
 
Angle - Wikipedia, the free encyclopedia (1429 words)
Angles provide a means of expressing the difference in slope between two rays meeting at a vertex without the need to explicitly define the slopes of the two rays.
The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection.
This angle is equal to π/2 radians minus the angle between the intersecting line and the line that goes through the point of intersection and is perpendicular to the plane.
  More results at FactBites »

 

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