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Solar Geometry and Kepler's Laws
Johannes Kepler (1571-1630) led science to make a complete break with the
Ptolemaic tradition that held to a geocentric view of the universe. He discovered
several very important principles that describe the motion of the planets around the
sun. Known as Kepler's laws, they are:
| (1) |
All planets' orbits are ellipses with the Sun at one focus. |
| (2) |
Planets in their orbits sweep out equal areas in equal time regardless of where in
their orbits they are. |
| (3) |
The square of a planet's orbital period is proportional to the cube of its average
distance from the Sun. If the period (P) is in years and distance or radius (R) is
in Astronomical Units, then the constant k = 1, and P squared = k times R cubed for all
planets. |
Compare the application of Kepler's Third Law to the data published by NASA and that
derived from Solar Geometry:
Kepler's 3rd Law
using published data shows inaccuracies |
| Planet |
Orbital
period
around
the
Sun
in days |
Distance
from
Sun
in AU |
Relative
orbital
period
where
Mercury
= 1 |
Relative
distance
where
Mercury
= 1 |
Period
squared |
Distance
cubed |
Error
per
Kepler's
3rd
Law |
| Mercury |
87.97 |
0.3870989 |
1.00000 |
1.00000 |
1.000 |
1.000 |
0.000 |
| Venus |
224.70 |
0.7233320 |
2.55428 |
1.86860 |
6.524 |
6.524 |
0.000 |
| Earth |
365.26 |
1.0000001 |
4.15210 |
2.58332 |
17.240 |
17.240 |
0.000 |
| Mars |
686.98 |
1.5236623 |
7.80925 |
3.93611 |
60.984 |
60.982 |
0.003 |
| Jupiter |
4,332.71 |
5.2033630 |
49.25213 |
13.44195 |
2,425.772 |
2,428.770 |
-2.998 |
As you can see, the published data doesn't even conform exactly to
Kepler's Third Law, and thus cannot be totally accurate.
Kepler's 3rd Law
using Solar Geometry |
Here are the relationships from Kepler's Third Law as derived from Solar Geometry:
| Planet |
Predicted
orbital
period
around
the
Sun
in days |
Distance
from
Sun
in AU |
Relative
orbital
period
where
Mercury
= 1
(Dist^1.5) |
Relative
distance
where
Mercury
= 1 |
Period
squared |
Distance
cubed |
Error
per
Kepler's
3rd
Law |
| Mercury |
87.97 |
0.3871010 |
1.00000 |
1.00000 |
1.000 |
1.000 |
0.000 |
| Venus |
224.24 |
0.7223402 |
2.54904 |
1.86603 |
6.498 |
6.498 |
0.000 |
| Earth |
365.26 |
1.0000001 |
4.15206 |
2.58331 |
17.240 |
17.240 |
0.000 |
| Mars |
687.06 |
1.5238067 |
7.81013 |
3.93646 |
60.998 |
60.998 |
0.000 |
| Jupiter |
4,334.44 |
5.2026014 |
49.27135 |
13.43991 |
2,427.666 |
2,427.666 |
0.000 |
Because the orbital periods are derived here, there is no deviation in
the relationships per Kepler's Third Law when using Solar Geometry, yet the results are
amazingly close to those published by NASA.
| In a time when most astronomers were attempting to explain planetary motion through a
complicated set of circular orbits within orbits, or epicycles, Kepler sought simplicity
and order that he assumed by faith would be there, and said that he was merely
"thinking God's thoughts after Him." |
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