a simple calculation for earth spin projected onto sun-earth orbit plane.

( — 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 %.