Seasons, Latitude and Climate Science

We are facing a suite of interrelated personal and public policy decisions that are extraordinarily consequential and for which sound decisions require a deep understanding of many fields. The video above,  A Private Universe (Video Source: YouTube), shows that even many graduates of famous institutions lack the requisite understanding. How can our fellow voters make wise decisions involving, for example, the sources, magnitude, and consequences of climate change and the potential of solar energy when they don't even understand what causes the seasons? 

This simulation can be used to address the very common misconception highlighted in this video. It can also be used in the study of climate science. In particular we include a unit that can help understand why the Earth has experienced ice ages.


In the running simulation, the Earth is spinning on its axis and the instantaneous rate in watts per square meter at which solar energy is arriving at three different points -- the North Pole, a point on the equator, and a point whose latitude can be changed by the "player" -- is displayed using digital meters. As the Earth spins the points pass in and out of the sunlight and students can see the connections between the numbers displayed by the meters and the geometry of the Earth and the sun. They can see why the day is longer toward the north than at the equator during the (northern hemisphere) summer. They can see why summer in the northern hemisphere occurs at the same time as winter in the southern hemisphere. They can change the location of the Sun relative to the Earth and see the geometry behind the seasons and behind solar power. Another meter visually integrates the rate at which solar energy arrives to compute the daily energy in watt hours per square meter.

Students can learn a great deal by experimenting with simulations like this and they can learn even more by building such simulations themselves. This isn't easy, because the mathematics and science isn't easy, but because students put their effort where it belongs on the math and science, the payoff is large.

You can use this simulation in four ways:

  • Your students can work with one of the pre-built simulations included here.
  • You can modify one of the pre-built simulations for your students.
  • Your students can modify one of the pre-built simulations.
  • Your students can build their own simulations.

How you decide to use this simulation depends on your course goals, the level of your students, and your time constraints. 



  • A step-by-step quide to building this simulation
  • A file seasons-skeleton.xml that is the starting point for this simulation. You should save this file in a convenient place. Usually we begin building a simulation by placing a "camera" that transmits a view of the three-dimensional simulation to the screen and by adding lighting that illuminates the scene. By starting with this skeleton you can skip those steps. In this particular unit, the lighting comes from the Sun.
  • A file seasons-mark.xml that is one of several completed simulations that you might use, modify, or build. This one shows three arrows marking three points along the prime meridian. Meters display the rate at which energy from the Sun is reaching those three points in watts per square meter.
  • A file seasons-integral-24.xml that is another of several completed simulations that you might use, modify, or build. This simulation adds a digital meter that computes and displays the energy received from the Sun over the course of a 24 hour day in watt hours per meter.
  • A file seasons-integral-annual.xml that is another of several completed simulations that you might use, modify, or build. In this simulation a digital meter computes and displays the energy received from the Sun over the course of a year in watt hours per meter.
  • Two excerpts, excerpt-1 and excerpt-2, from a forthcoming book, Mathematical Modeling for a Real and Complex World, provide some background and use this simulation in an introduction to climate sclience.
  • A sample test question -- this question asks students to compare the climate on the Earth with that of a newly discovered planet using their own modification of the seasons simulations.




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