&intro=Everyone knows that it's warmer in the summer than in the winter, but why is that?  Is it because the Earth is closer to the Sun in the summer?  Does it have something to do with the tilt of the Earth's axis of rotation?  And why does summer in Paris happen at the same time as winter in Perth? 
With this interactive, you can examine three factors which are all linked together: the position of the Earth in its orbit around the Sun,  the tilt of the Earth's axis of rotation, and the path of the Sun in the sky over the course of day.  You can also see how the average daily temperature changes in response to these factors.

&howto=You should see four items on your screen.  At the top, there is a view of the Earth's position in its orbit around the Sun.  A white "X" shows your location on the Earth: in the northern hemisphere near latitude 45 degrees.  Just to the right of the orbit is a thermometer which indicates the average temperature at your location. The bottom of the screen is divided into two panels.  The panel on the left shows a view of the landscape from your location on Earth, looking South.  The panel on the right allows you to modify the tilt of the Earth's axis of rotation with respect to the plane of its orbit.  You can choose any angle with the Inclination Angle slider, or pick an angle corresponding to that of a real planet.  You can also speed up, slow down, or pause the passing of time using the controls in this panel.
Let the interactive run for one complete orbit while you watch; if you become impatient, click the upward arrow to increase the speed of the action.  Watch the path of the Sun in the sky as the Earth moves from one side of its orbit to the other.  Is there any change?  What does the thermometer indicate?  After the Earth has made one complete orbit, try increasing the tilt of its rotation axis to 20 degrees or so, and watch over another orbit.  What happens now?

&inter=Interactive

&exer=1. If the inclination angle is 0 degrees, how does the path of the Sun in the sky change as the Earth moves from the right side of its orbit to the left?  What is the longest duration (in hours) of sunlit time during the year?  What is the shortest duration of sunlit time?  What is the change in average temperature?
2. Modify the inclination angle to 23 degrees and watch for a complete revolution.  What is the length of the longest and shortest duration of sunlit times now?  What is the change in average temperature now?
3. Modify the inclination angle to 60 degrees.  Watch the position of the Sun and the brightness of the sky over the landscape carefully.  What are the longest and shortest durations of sunlit time now?  What is the change in average temperature over the course of a year?
4. What is the smallest inclination angle which leads to a 24-hour period without sunlight?
5. The rotation axis of the real Earth is tilted by 23.5 degrees with respect to its orbital plane.  Suppose you wanted to experience 24 hours of darkness, during which the Sun would never rise above the horizon.  Where could you go to make it happen?  During which month should you go there?
6. The planet Uranus is tilted nearly on its side, so that its axis of rotation is only 8 degrees away from its orbital plane. If you lived at latitude 45 degrees on Uranus, for what fraction of a Uranian year would the longest winter night last?

&solu=1. When the inclination angle is zero, there is no change in the path of the Sun through the sky as the Earth orbits around the Sun.  Both the longest and shortest days of the year contain 12 hours of sunlight.  There is no change in average temperature during the year. 
2. When the inclination angle is 23 degrees, the longest sunlit period is about 15 hours, and the shortest is about 9 hours.  There is a modest increase in temperature from winter to summer.
3. When the inclination angle is 60 degrees, the longest sunlit period lasts for more than 24 hours (i.e., the Sun never sets during the height of summer) and the shortest sunlit period is zero hours (i.e. the Sun never rises in the depths of winter).  The change in average temperature from winter to summer is larger than that for a 23-degree tilt.
4. The smallest inclination angle which leads to 24 hours of night is about 50 degrees.
5. In general, if one goes to a latitude which is [90 degrees minus inclination angle], one will experience no sunlight in winter and no darkness in summer.  Any region closer to the North Pole is called "arctic", and any region closer to the South Pole is called "antarctic."
6. An observer at latitude 45 degrees on Uranus would experience a winter night which lasts for about one-third of the entire Uranian year!