# The Dynamic Solar System with Elliptical Orbits

Procedure: 1. Construct a slider with parameter n. Interval: (0,2000), increment 0.1; Animation: speed 0.1 to get slow movement of the planets, repeat oscillating. 2. Construct ellipses (orbits) by entering in the Input field their equations, selected in such way that they have in common the Sun in one of their focuses. One orbit belongs to a comet. The Sun is represented by the yellow circle for which is not difficult to provide its equation. 3. Every planet is represented by a small circle which will move along its respective orbit. To provide the movement of the planet use the virtual tool “Angle with Given Size”. Firstly, construct the intersection point of the ellipse with the positive x-axis using the virtual tool “Intersect Two Objects”. Let be this point A, and the coordinative origin O. Select the tool “Angle with Given Size” and use it by choosing the side AO as the first side of the angle. On the table displaced replace the angular measure of 45 grades by the variable n grade. After this will be shown the other side OA’. The measure of the angle is a variable, so it will be changed by the slider when its status is “Animation On”. 4. Define the centre of the planet. Construct the segment OA’ using the virtual tool “Segment between Two Points” or “Ray through Two Points”. Construct the intersection point of the segment with the ellipse. Let be P1. 5. Construct the planet represented by a circle. Use the virtual tool “Circle with Centre and Radius”, click on the intersection point, appears a table in which we put a small value for the radius (for instance 0.3) and click OK. The circle will be displayed. Using Object Properties of the dialog box we select the desired colour and its filling. 6. Test the movement of the planet by selecting in the slider the option Animation On. *** Further, continue in the same way to construct the other planets taking care that the measures of the angles be chosen in such a way that the planets be not in a straight line and they orbit with different angular speeds.

Resource Type
Activity
Tags
dynamic  ellipse  elliptical  exploration  orbits  system
Target Group (Age)
15 – 18
Language
English (United Kingdom)

GeoGebra version
3.2
Views
8124

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