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Kepler's Laws of Planetary Motion


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Formal Metadata

Title Kepler's Laws of Planetary Motion
Alternative Title Keplersche Gesetze der Planetenbewegungen
Author Schlier, Christoph
Benz, Alois
Contributors Gotthard Glatzer (Redaktion)
Gerhard Matzdorf (Kamera)
L. Rüppel (Schnitt)
License No Open Access License:
German copyright law applies. This film may be used for your own use but it may not be distributed via the internet or passed on to external parties.
DOI 10.3203/IWF/C-1286eng
IWF Signature C 1286
Publisher IWF (Göttingen)
Release Date 1978
Language English
Producer IWF
Production Year 1977

Technical Metadata

IWF Technical Data Film, 16 mm, LT, 56 m ; SW, 5 min

Content Metadata

Subject Area Physics
Abstract The film demonstrates Kepler's three laws of planetary motion. In addition the first part shows that a trajectory is determined not only by the forcefield but also by the initial condition of the motion.
Keywords Kepler's laws of planetary motion
planetary motion
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.
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