MathCAD Addendum 1
Version: 12 July 2006
1. Angular measurement units and conversions
A degree is probably most familiar angular unit: There are 90 degrees in a right angle and 360 degrees in a circle. A more mathematically natural unit is the radian: There are 2
so
Most computer math languages (including MathCAD) expect that the arguments of trig functions are in radians. Hence, the familiar sin(30deg) = 0.5 doesn't give the expected answer:
unless we specify the angular unit explicitly:
In astronomy, most angles are very small (<<1 deg), so we commonly express angles in either arcminutes (1/60 deg) or arcseconds (1/3600 deg). MathCAD has both units buil-in:
2. Small angle formula
For small angles (
This means that we can approximate either the sine or tangent by the angle itself.
The 'small angle formula' is a relation between the size of an object, its distance, and its angualr size. If the linear size D of an object is given in AU, and the angular size
Example: The planet Neptune is observed to have an angular size
First let's define an astronimical unit: