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.”