( — written about 3 weeks ago, from 6th November 2011 )

My friend on f-b asked me how to show that “*Earth rotates around sun in a tilt of 23.5 degrees and rotates around itself with spin S* should mean **earth-spin S is 84% along sun’s vertical and 16% along sun’s horizontal**“;

I searched on Google for a **trigonometric calculator** and a **square root calculator** as linked below.

USE the following for quick calculations;

“**Trigonometry Calculator** solves for all **6 trigonometric functions **and for all** 6 trigonometric arc-functions**, the double line display works with **degrees** and **radians** simultaneously;* sine, cosine, tangent, cotangent, secant, co-secant, arc-sine, arc-cosine, arc-tangent, arc-cotangent, arc-secant, arc-co-secant* … ”

**Here is the earth-around-sun and earth-spin situation:**

**Earth rotates around sun in a tilt of 23.5 degrees** and **earth rotates around itself with spin S**. SO S is **84% along sun’s vertical** and **16% along sun’s horizontal**;

**proof:**

cos (square) (23.5 deg) + cos (square) (90-23.5 deg) = 1. ( — basic trigonometry )

So S_z = S.cos ( 23.5 deg ), S_xy = S.sin ( 23.5 deg ), ( — components of the spin vector of earth )

z: **cos (square) ( 23.5 deg )** = ( 0.91706 )(square) = **84.09 %**, xy: **sin (square) ( 23.5 deg )** = ( 0.39875 ) (square) = **15.9 %.**