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Daily motion of the sun --- Part1

Introduction

Path of the daily motion of the sun changes with seasons.

How does the Sun move due to the earth's rotation?
Check out the path of the sun. Watch the movie of daily motion of the sun that was taken with a digital camera with a 180-degree field of vision lens and plot the path on a worksheet or a clear plastic hemisphere.
Is the path the same all year long?
Length of day and night changes with seasons. This is because the path of the sun changes with seasons.Watch the movies which are taken by the whole sky camera in the same place in each season. Plot the motion of the sun on a worksheet or a clear plastic hemisphere from the movie of each season and ceck out how the path changes over the year. Think of the difference in length of day and night in different seasons from the results.
The sun rises everyday. It is always there, but do you knonw where it rises, reaches its highest point in the sky, and sets?
The time the sun rises is the morning. Does the morning begin at same time? How about the evening? Think of the daily motion of the sun in each season.

Imagine the motion of the sun!

The Whole Sky Camera system is composed of the digital camera, the fisheye lens, and the a level.
Because the fish-eye lens has 180-degree field of view, Whole sky scenery from the place where the camera was set up can be taken in one photograph by turning the camera with the fish-eye lens to the zenith.

The whole sky camera

Over view image of the Whole Sky Camera	Pattern diagram seen from side

The Whole Sky Camera system is composed of the digital camera, the fisheye lens, and the a level.
Because the fish-eye lens has 180-degree field of view, Whole sky scenery from the place where the camera was set up can be taken in one photograph by turning the camera with the fish-eye lens to the zenith.

The view through the fisheye lens

A picture taken by normal lens	A picture taken by fisheye lens at the same place

How are the movies made?

From sunrise to sunset, a whole sky photograph is taken at regular intervals by the Whole Sky Camera system. This image data is downloaded onto a computer, the directions and the images are processed, and coordinates of direction and altitude are added to them using Adobe graphic soft Illustrator. Moreover, each image is edited with the passage of time to make movies by using the software Movie Maker to edit Microsoft-based animations.

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Experimental Method

Things to prepare

The movies of daily motion of the sun, taken at two hour intervals, Worksheet ( You can download them.), PC, Application for seeing movies
※If you have any chance to make a movie of daily motion of the sun at school that contains landscape with which you are familiar, that is the best one.

If you want to make a movie by yourself, go to Making movies by The Whole Sky Camera

Let's watch the movie!

Watch the movie and check out the path of the sun. From where to where is it moving?

Record the position of the sun at two hour intervals.

Next, watch the movie, note the position of the sun at each two hour interval and plot it on your worksheet.
The left is one of the images in the movie of daily motion of the sun taken at 11:43 a.m. (Culmination) on June 21, 2005 at Sendai Japan (latitude 38 degrees north).A light white circle is the sun. The right diagram is the worksheet with the position of the sun plotted by reading the direction and the altitude of it from the left image.
In the same way, record the path of the sun over a whole day in your worksheet by watching the image every two hours.

Record the path of the sun in other seasons.

Watch another movie taken in the other season and find out if there are any differences between the seasons.
In the same way, read the position of the sun from the images every two hours and record the path of the sun during a day.

Discussion

The pictures above are plotted by the movie taken on June 21, 2005 at Sendai Japan (Latitude 38 degrees north). They show the path of the sun during a day.

The pictures above are plotted by the movie taken on March 15, 2005 at Sendai Japan (Latitude 38 degrees north). They show the path of the sun during a day.

Let's Compare them.

Compare the paths of the sun that recorded in June and March.
Can you find out the differences between them in Culmination altitude, position of sunrise, position of sunset and length of daytime? How different are they?

Practical Description

Describe what you understood from the observation.
The sun rises in the east and sets in the west reaching its highest point in the south.
The culmination altitude in June is higher than March.
The position of sunrise and sunset in June becomes more northern than March.
Daytime in June is longer than March.

Discussion

Why do the culmination altitude or length of day change with seasons?
To find out the answer, imagine the motion of the sun in the Celestial Sphere that shows the position of the earth and the sun from the universe

Understanding the Celestial Sphere(1)

The earth revolves around the sun on a path that's called an orbit. It takes a year to complete the trip.
Check out the paths of the daily motion of the sun when the earth is in (a)~(d) of the figure below by the Celestial Sphere.

Let's start from position (a).
To make it easier to understand the motion of objects in our skies, depicting the heavens as a sphere surrounding the earth; "The Celestial Sphere" is helpful. The Celestial Sphere
Every object we see in space is drawn on the Celestial Sphere. The sun is also one of them, so you can draw it on it. The picture below shows the sun and the earth at position (a). The plane in which the earth revolves around the sun (= orbital plane) is tilted at approximately 23.4 degrees to the earth's rotation plane. So, the sun in the position (a) can be drawn at 66.6 degrees from the earth's axis on the Celestial Sphere as the next figure.

Next, make the earth small in the centre of the Celestial Sphere, draw the ground for the observer and draw the path of the motion of the sun. It will be as shown in the next figure.

Remember that the direction where Polaris is is north and where the sun rises is east, write each direction in.

How about position (b)? In the (b), the underside of the screen is daytime, so you can not see the observer who is also on the underside. Then, the figure will represent the view from the earth's surface. Because the direction the sun rises is east, each direction will be as shown in the next figure.

In the same way, think about the path of the sun in the position (c) and (d).
Here is the path of the sun in the position (c).

Here is the path of the sun in the position (d).

天球で確かめよう(2)

Here, draw those paths of the sun on a Celestial Sphere which is tilted to make the observer stand vertical. Be aware of the direction.
It will be as in the next figure.

Understanding the Celestial Sphere(3)

How about the seasons of the Northern Hemisphere in each position (a), (b), (c) and (d).

Describe the length of day and night and the Culmination altitude comparing position (a), (b), (c) and (d).

Understanding the Celestial Sphere(4)

If the earth's axis were vertical to the orbital plane, what would the path of the sun on a Celestial Sphere be?
The orbital motion of the earth and the path of the sun in the position (a), (b), (c) and (d) would be as the next figures.

Draw those paths of the sun on the Celestial Sphere which is tilted to make the observer stand vertical. Be aware of the direction.
It will be as in the next figure.

The path of the sun in the position (a), in (b) or (d) and in the (c) are all different when the earth's axis is tilted. However, if the earth's axis weren't tilted, the path of the sun would always be the same in any position and there would be no difference in the length of day or the culmination altitude.
Thus, the tilt of the earth's axis is the reason for the seasons.

Challenge

Uranus' axis is tilted at approximately 90 degrees to the orbital plane. This tipped rotational axis gives rise to extreme seasons on Uranus. In summer, 21 years of daytime in the Northern Hemisphere and in winter, 21 years of nighttime. Think about which position, (a), (b), (c) or (d) shows summer or winter for Uranus.

Download

Movie of Daily Motion of the Sun taken at Miyagi University of Education (Latitude 38 degrees 15'31.5'' north, Longitude 140 degrees 49'47'' east, 160 m high) / Every 2 hours

Around Vernal Equinox　March 15, 2005. sunrise 5:47, culmination 11:46 sunset 17:44

wmv (4.58MB)

Around Summer Solstice　June 21, 2005. sunrise 4:12, culmination 11:38, sunset 19:04

wmv(12.07MB)

Around Autumnal Equinox 　September 29, 2005. sunrise 5:29, culmination 11:27, sunset 17:24

wmv(10MB)

Around Winter Solstice　December 20, 2005. sunrise 6:47, culmination 11:34, sunset 16:21

wmv(8MB)

Worksheet

WORD159KB

Related paper

Space experiments in classrooms-7: Development of movies of solar diurnal motion imaged by solar camera Bulletin of Miyagi University of Education Vol.40