Kepler's Laws of Planetary Motion
37 views
Formal Metadata
Title 
Kepler's Laws of Planetary Motion

Alternative Title 
Keplersche Gesetze der Planetenbewegungen

Author 

Contributors 

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. 
Identifiers 

IWF Signature 
C 1286

Publisher 
IWF (Göttingen)

Release Date 
1978

Language 
English

Producer 

Production Year 
1977

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

Content Metadata
Subject Area  
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
astrophysics
astronomy

Related Material
00:00
Computer animation
00:09
Computer animation
00:23
Computer animation
00:50
Computer animation
01:17
Computer animation
01:34
Computer animation
01:42
Computer animation
01:59
Computer animation
02:14
Computer animation
02:32
Computer animation
02:58
Computer animation
03:25
Computer animation
03:34
Computer animation
04:12
Computer animation
04:44
Computer animation
00:05
Kepler's Laws of planetary motion
00:10
First law: The planetary orbits are conic sections. The kind
00:18
and the shape of the conic section depend on the initial parameters of the planet's trajectory. One may vary the
00:27
absolute value of the initial velocity keeping its direction and the solar distance constant. Here,
00:43
the sun is in the left focus of a small ellipse. A certain velocity results
00:55
in a circular orbit. These
01:05
examples show that, even if all motions follow from one differential equation, each single trajectory is dependent on the initial
01:18
position and initial velocity of
01:21
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
01:36
that the planet moves faster nearthe sun than far from
01:42
it. Starting with still higher
01:45
velocity the planet eventually leaves the solar system on a hyperbolic trajectory, here compared to
01:56
an ellipse. Again, the starting direction makes a right angle
02:02
with the line connecting sun and planet. However, this angle
02:09
may be also acute, for instance +60 degrees. In this case a much more elongated
02:17
ellipse results. Here, both can be compared. Obviously the same is true in the other direction, i. e. 60 degrees.
02:29
The absolute value of the velocity is still the same,
02:35
only the directions vary. Again a flat ellipse results. Here compared to the first one. The third parameter to be
02:47
varied is the initial solar distance. In this and the following examples the initial velocity vector is kept constant. In
03:00
the first example the sun is in the right focus. The next orbit is circular. If one starts the trajectory
03:11
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
03:27
in a hyperbolic trajectory. Kepler's second law: The angular momentum
03:35
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
04:06
third law tells us something about the periods of planetary revolution: The squares of the
04:15
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 twothirds 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.