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Nomenclature
from the Copernican Model:
Copernicus
required two types of planets in the Heliocentric Model.
-
Inferior
Planets: Planets Closer to the Sun than
the Earth.
-
Superior
Planets: Planets Farther from the Sun
than the Earth.
He
also determined that this led to many special orientations of the planets
that were useful for determining the characteristics of their orbits.
The important position for
inferior planets is
-
Elongation:
Here
the planet is separated as far from the Sun as it gets.
For Superior Planets, the
significant positions are
-
Opposition
(overhead at midnight)
-
Quadrature
(a 90° separation of the Superior Planet and the Sun)
Copernicus used simple geometry
to get the relative distances of the planets in Astronomical
Units, AU, (the distance from the Sun to the Earth--a quantity
he
did not know!)
-
Measurements of the angle
of the greatest elongation can be used to measure
the radius of an inferior
planet orbit.
-
The time between quadrature
and opposition provides enough information to derive
the radius of a superior planet orbit.
Using measurements of planetary
positions he was able to determine the distance to the planets with excellent
precision.
Finally, Copernicus was
able to develop a formula that could determine the Sidereal
(with respect to the stars) orbital period of a planet using
the time between successive inferior conjunctions
(also
known as its Synodic period).
-
For a Superior Planet: 1/P
= 1/E - 1/S
-
For an Inferior Planet: 1/P
= 1/E + 1/S
-
Where:
P = Planet Sidereal
Period
E = Earth Sidereal
Period (a year!)
S = Planet Synodic
Period
One
thing about these formulae; they are general.
That is to say you can apply them to any
system, for example the Moons of Jupiter,
and get the same quality results.
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