Astronomical Modelling

Cabri 3D is a good tool for astronomical modelling as it allows dynamic modelling of 3D situations. Here are some of the possible models, presented roughly in oder of complexity. It may seem surprising that something as "esoteric" as the retrograde motion of Mars is simpler to model than something as everyday as the seasons, but there we are! For simplicity, some basic assumptions have been made in all models: orbits are circular, speeds and radii are constant, astronomical objects are points or spheres. Drag the large red points to show the motion.

If you are new to Cabri 3D, you might want to work through this demo before attempting to make the models below.

The Word documents are designed to give you step-by-step instructions for the basic model and are deliberately very narrow so that they can be seen on the screen at the same time as a Cabri 3D file.

Files may be opened or downloaded. To see how to work out how a file was constructed, look at the demo How constructed (related file moving Claude1).

 The Retrograde Motion of Mars

As Mars moves across the sky, it sometimes reverses its direction of travel. In this model variables such as the relative speeds of Earth and Mars, the relative orbital radii and inclination of the orbit may be changed to explore the effect on the apparent motion of Mars.

 Word Document 

 Cabri 3D files: basic model    more precise model

 A Solar Eclipse

As the moon orbits the Earth, part of the Earth's surface may be in its shadow. When this happens, the Sun will not be visible in these areas.

 Word Document 

 Cabri 3D files: basic model   more advanced model incorporating inclination of the Moon's orbit

 The Seasons 1

This model gives a qualitative idea of the way in which daylight changes at different seasons

 Word Document  

 Cabri 3D files: basic model

 The Earth's Rotation

This model shows how you can put a specific location and/or circles of latitude and longitude on a rotating Earth. It can optionally be used to enhance the two previous models, and is necessary for the model The Seasons 2

 Word Document

Cabri 3D files: basic model

 The Seasons 2

This model enables the calculation of hours of daylight on different days of the year at different latitudes


 Cabri 3D files: basic model   model incorporating graph

 The Seasons 3

This model looks at the position of the sun in the sky on different days of the year at different latitudes.


 Cabri 3D files: basic model    model with two views

 The Seasons 4

This model looks at the way light hits the earth's surface on different days of the year at different latitudes.


 Cabri 3D file: basic model


This model uses a variation on the Seasons 3 and 4 models to model a simple sundial.


Cabri 3D files: horizontal sundial    sundial on inclined surface