Kepler: Determination of the Earth's Orbit
Once one accepts the heliocentric model, it becomes important to
determine the precise shape of the Earth's orbit about the Sun and
how the Earth proceeds along that orbit. This Kepler did by supposing
that Mars returns to the same location relative to the Sun each Martian
year (1.88 Earth years). From his vantage point on Earth, he could
observe directly the angle SEM between the Sun and Mars.
It might be supposed that one would need an observer on Mars to
determine the angle SME between the Sun and Earth as it would be
seen on Mars. However, this is not the case, for one can determine
the angle SME by observing how Mars moves against the background of
stars, which are so far away that they exhibit almost no parallax.
In our simulation, we treat SM as a fixed (but unknown) distance.
Using the angles SEM and SME, observed once each Martian year, a little
trigonometry yields the locations of Earth relative to the same scale.
As you run the simulation, you will see the successive positions of
the Earth for a total of 50 Martian years. For conceptual clarity the
eccentricity of Earth's orbit has been exaggerated in the simulation.
Instead of the actual eccentricity 0.0167, we have employed Mercury's
eccentricity 0.2056. We have also neglected the slight difference of
inclinations of the orbits of Earth and Mars. At the end of the
simulation, the major and minor axes of the elliptical orbit are
displayed.