Orbit

Autor:Rafael Losada Liste

This activity belongs to the GeoGebra book GeoGebra Principia. 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 [20].

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 The Feynman Lectures on Physics (volume I, 9-7, Planetary motions), see Bibliography.

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: g = k/d² UnitVector(S–T) Now we just need to introduce an auxiliary slider so that, whenever it is updated, it executes the very simple script: SetValue(v, v + 0.03 g) SetValue(T, T + 0.03 v) ¡And we already have elliptical motion! (Note that we haven't used any equations or geometric loci.)

Author of the construction of GeoGebra: Rafael Losada.

Orbit

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