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# Kepler's Laws of Planetary Motion

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Kepler's Laws of planetary motion
First law: The planetary orbits are conic sections. The kind
and the shape of the conic section depend on the initial parameters of the planet's trajectory. One may vary the
absolute value of the initial velocity keeping its direction and the solar distance constant. Here,
the sun is in the left focus of a small ellipse. A certain velocity results
in a circular orbit. These
examples show that, even if all motions follow from one differential equation, each single trajectory is dependent on the initial
position and initial velocity of
the planet. Scale variation 1:2 Here, a somewhat elongated ellipse develops with the sun in the focus on the right. It can clearly be seen
that the planet moves faster near-the sun than far from
it. Starting with still higher
velocity the planet eventually leaves the solar system on a hyperbolic trajectory, here compared to
an ellipse. Again, the starting direction makes a right angle
with the line connecting sun and planet. However, this angle
may be also acute, for instance +60 degrees. In this case a much more elongated
ellipse results. Here, both can be compared. Obviously the same is true in the other direction, i. e. -60 degrees.
The absolute value of the velocity is still the same,
only the directions vary. Again a flat ellipse results. Here compared to the first one. The third parameter to be
varied is the initial solar distance. In this and the following examples the initial velocity vector is kept constant. In
the first example the sun is in the right focus. The next orbit is circular. If one starts the trajectory
at a still greater distance, again an ellipse results, but the sun is now in the left focus. Increasing the initial distance further eventually results
in a hyperbolic trajectory. Kepler's second law: The angular momentum
with respect to the sun is constant. This means that the position vector of a planet relative to the sun sweeps out equal areas of the ellipse in equal times. These areas are shown here. momentum of the planet with respect to the sun is A modern physicist generally formulates constant. This follows from the existence of a central force this law differently: The angular between sun and planet. Kepler's
third law tells us something about the periods of planetary revolution: The squares of the
periods of revolution are proportional to the cubes of the semimajor axes of planetary orbits. Here, the ratio of the two periods is two. For the ratio of the semimajor axes one gets two to the two-thirds power or cubic root of two squared. The planets are moving with corresponding velocities. To make the situation clearer in the picture they are stopped after each revolution.
Kepler-Gesetze
Kepler-Gesetze
Computeranimation
Umlaufbahn
Planet
Computeranimation
Brennpunkt <Optik>
Gleichstrom
Sonnenstrahlung
Fahrgeschwindigkeit
Computeranimation
Umlaufbahn
Trajektorie <Meteorologie>
Computeranimation
Brennpunkt <Optik>
Sonnenstrahlung
Maßstab <Messtechnik>
Fahrgeschwindigkeit
Initiator <Steuerungstechnik>
Planet
Computeranimation
Sonnenstrahlung
Planet
Computeranimation
Gleichstrom
Sonnensystem
Fahrgeschwindigkeit
Planet
Computeranimation
Proof <Graphische Technik>
Planet
Übungsmunition
Leitungstheorie
Anstellwinkel
Computeranimation
Fahrgeschwindigkeit
Computeranimation
Gleichstrom
Längenmessung
Fahrgeschwindigkeit
Initiator <Steuerungstechnik>
Computeranimation
Umlaufbahn
Brennpunkt <Optik>
Längenmessung
Sonnenstrahlung
Trajektorie <Meteorologie>
Computeranimation
Trajektorie <Meteorologie>
Computeranimation
Zentralkraftfeld
Atomphysiker
Umlaufzeit
Umlaufbahn
Sonnenstrahlung
Planetarischer Nebel
Planet
Computeranimation
Array
Rotationszustand
Umlaufbahn
Umlaufzeit
Fahrgeschwindigkeit
Planet
Rootsgebläse
Leistungssteuerung
Computeranimation
Computeranimation

 Titel Kepler's Laws of Planetary Motion Alternativer Titel Keplersche Gesetze der Planetenbewegungen Autor Schlier, Christoph Benz, Alois Mitwirkende Gotthard Glatzer (Redaktion) Gerhard Matzdorf (Kamera) L. Rüppel (Schnitt) Lizenz Keine Open-Access-Lizenz:Es gilt deutsches Urheberrecht. Der Film darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. DOI 10.3203/IWF/C-1286eng IWF-Signatur C 1286 Herausgeber IWF (Göttingen) Erscheinungsjahr 1978 Sprache Englisch Produzent IWF Produktionsjahr 1977