[color=#999999][color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/dm9prd7h]Attractive projects.[/url][/color][/color][b][br][br]2D Project[/b]: [i]model the terrestrial orbital movement.[/i][br][br]We place the point S (Sun) in the center of the coordinates and a point E (Earth) with the initial velocity the vector [b]v[/b]. If [b]d[/b] is the distance ES, and [b]k[/b] is a constant, we have the vector of gravitational force:[br][list][*]g = k / d² UnitVector(Vector(E, S))[/*][/list]Now you have to enter an auxiliary slider so that, each time it is updated, executes the simple script:[br][list][*]SetValue(E, E + 0.01 v)[/*][*]SetValue(v, v + 0.01 g)[/*][/list]And we already have the elliptical movement! (Note that we have not used any equation or locus).

In the following construction we can see a wider version, with the escape velocity and the conservation of mechanical energy.[br]

Note: These two constructions were made thanks to the help of my department colleague Julio Valbuena, who adapted the idea put forward by Richard Feynman in his famous work [i]The Feynman Lectures on Physics[/i] (1963, volume I, 9-7, [i]Planetary Movements[/i]) .

[color=#999999]Author of the construction of GeoGebra: [color=#999999][url=https://www.geogebra.org/u/rafael]Rafael Losada[/url][/color][/color]