Seasons and the sun
Duration of sunshine and height of sun depending on date and northern latitude
Table of Contents
- Introduction
- Introduction
- Concept and precision
- Concept
- Remarks on precision
- Manual and grafics
- Window 3D Grafics
- Window "Grafics"
- Window Grafics2
- How to
- Timecorrection
- Applets
- Versions
Introduction
1. Introduction
This ggb.-worksheet shows how the height of the sun changes during the day [br]depending on dato and northern latitude. [br]The length of the day between sunrise and sunset is calculated as a function of the dato.[br][br][br][br][br][br] [br] [br] [br] [br][br][br][br][br][br]
Concept
Basics of visualization is [u][i]pure geometrics[/i][/u] .[br][br]In the [u][b]1.step[/b][/u] it's calculated, how the angle between the direction from earth to sun is changing according to inclination of the axis of the earth depending on dato. The result gives a vector connecting the centres of earth and sun. [br]In the [b][u]2. step[/u][/b] this vector is used as normalvector of a [u][b]plane E[/b][/u] containing centre of the earth. [b]E[/b] divides earth in two parts representing day and night. For each [u][b]circle of latitude b[/b][/u][sub][u][b]g[/b][/u][/sub] the ratio between archlength lieing in daypart and length of circle is exactly the same as the percentage of daylength from 24 h.[br]In the [b][u]3. step[/u][/b] we follow an [u][b]observer B[sub]g[/sub][/b][/u] rotating on its circle of latitude togehter with earth, From the postionvector from geocenter to B[sub]g[/sub] and the normalvector of E at every time the angle between ray of sunlight and horizon is calculated.
Window 3D Grafics
It's shown how height of sun at highnoon is changing within the seasons.[br]In the "Graphic"-window the dato and the latitude can be chosen and animated.[br]The rotation of the earth is visualized by rotating an observer B[sub]g[/sub][br] with the slider t[sub]d[/sub] in window "Graphics2".[br][br]
Versions
Ggb-worksheet contains 3 grafics and many input- / output- texts .[br]To handle it some width is necessary so it is not convenient for small screens. [br][br][br]2 versions are added:[br][br]A "big-one": formatted about 16:9 with he title "Seasons and the sun big"[br]and a "smaller" : optimized formatted about ca. 4:3 with he title "Seasons and the sun - small".[br]Both can be downloaded to run as Ggb-file directly in Geogebra-program