[color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/sw2cat9w]GeoGebra Principia[/url].[/color][br][br][br]Let's take a closer look at how simple it is, thanks to the continuously animated slider, to observe the elliptical motion of the Earth around the Sun without the need for infinitesimal analysis [[url=https://www.geogebra.org/m/sw2cat9w#material/er8nf4qt]20[/url]].[br][list][*][color=#808080]Note: This construction was made based on the suggestion of my colleague Julio Valbuena, who adapted the idea presented by Richard Feynman in his famous book [i]The Feynman Lectures on Physics[/i] (volume I, 9-7, [i]Planetary motions[/i]), see [url=https://www.geogebra.org/m/sw2cat9w#material/kajqeqkk]Bibliography[/url].[/color][br][/*][/list]We place the point S (Sun) at the coordinate center and a point T (Earth) with initial velocity vector v. If d is the distance TS and k is a positive constant, we have the gravitational force vector:[br][br] g = k/d² UnitVector(S–T)[br]  [br]Now we just need to introduce an auxiliary slider so that, whenever it is updated, it executes the very simple script:[br][br] SetValue(v, v + 0.03 g)[br] SetValue(T, T + 0.03 v)[br]  [br]¡And we already have elliptical motion! (Note that we haven't used any equations or geometric loci.)

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