lundi 5 mai 2008

Trigonometry, principles, astronomic applications

A What Sine, Cosine, Tangent mean and how they are calculated. The S, C or T for any angle is constant even in obtuse or acute triangles. But their values are calculated using "name of Indian chief" SOH-CAH-TOA (watching Tipi shapes, I do not know more of the story, since I was "reminded" of it in tenth grade without ever having heard it in earlier grades) for hypotenuse = radius of unity circle = 1. Some key values of side relations: O = A @ 45° (half of 90°) ; H = 2A @ 60° ; H = 2O @ 30 °.





















Sorry for marking sides in capital letters and angles in minuscules. It is the other way round usually.

B What you can use them for and what you need to do that. I've forgotten the formulas.























C Application in Solar System - I calculating distance to Moon - II using distance of Moon (known from calculation I) with angle of Sun shining on Moon to calculate distance to Sun - III using distance to Sun (known from calculation II) with angle of Sun shining on any other planet (Venus in this example) to calculate distances to that planet from Sun as well as Earth. (source: forgotten consultations of astronomical encyclopedias or school lessons). Note this gives you distance and angles at different times, hence relative movements, but no clue as to which way movement is absolutely going, nor where, if anywhere, there is absolute rest. The results are compatible with Heliocentrism as well as Tycho Brahe-style Geocentrism. They are also confirmed by unmanned space travel with cameras and so on, so far.























D Application or misapplication in parallactic distance calculations: I observations as observed: Star alpha Centauri wavers same way and same time as Sun, but a far shorter distance, between Summer and Winter Solstices - II the heliocentric reinterpretation allows distance calculations, because it gives us one known distance and two known angles (source: any book/article in astronomy, redrawn by me) - III but without that reinterpretation, we have only one angle (less than 00° 00' 01" of a circle) and no known distances.






















That being so, parallax seems to depend on heliocentric assumptions.

Hans Lundahl
Aix en Provence
22 April/5 May 2008

3 commentaires:

Hans Lundahl a dit…

Physics can be Phun

Anonyme a dit…

If you do not see second, third and fourth images, protest!

HGL a dit…

And yes, in picture four the earth is seen as point of a cone in relation to sun. Here is a better diagram, but text in French.