The Heliocentric Model
Justin Walega
In The Beginning…
Geocentric Model
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Symmetry
Ptolemy
Imagery
Why?
Appeared all planets orbited regularly
Earth is stable
Issues
Dancing planets
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Epicycles – Apollonius
Early Names
Philolaus
Aristarchus
Archimedes – a larger universe
Change?
Regiomontanus
Christianity
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Calendar issues - Easter
Copernicus
De revolutionibus orbium celestium - 1543

(On the Revolutions of the Heavenly Spheres)
Gave mathematical description with
moving Earth
Spheres
What’s gravity?
Simplest solution
Copernicus
Ptolemy’s methods
100,000 instead of 60
Chords
Methods of solving
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Plane and spherical triangles
Spherical Triangles
“If in the same sphere two triangles have
right angles and another angle equal to
another angle and one side equal to one
side – whether the sides be adjacent to
the equal angles or lie opposite one of the
equal sides – they will have the remaining
sides and the remaining angle equal to the
remaining angle.”
New Issues
Copernicus – Sun not quite center
Protestant vs. Roman Catholic

Chronicles 16:30: "the world also shall be
stable, that it be not moved."
Used for calculations rather than accurate
17th Century
Ancient India
Aryabhata – Aryabhatiya
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Spinning axis
Relation to Sun
Nilakantha Somayaji
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Aryabhatiyabhasa - commentary
Planets around Sun around Earth
Same as Tycho Brahe’s model
Islamic Views
Alhazen’s Doubts on Ptolemy
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Questioned his details
Proposed axis rotation
Heliocentric concept abandoned multiple
times
Tusi & Qushji – moving Earth
Never reached heliocentric model
Advancing Through Time
Galileo – Starry Messenger (1610)

Telescope
Galileo’ dialogue
Kepler – elliptical orbit

Eccentricity
Earth’s Eccentricity
(π/4) x ( (186-179)/(186+179) ) ≈ 0.015
186 days: March equinox -> Sept. equinox
179 days: Sept. equinox -> March equinox
The planetary orbit is an ellipse
The Sun is a focal point, not the center
Neither the linear speed nor the angular speed of
the planet in the orbit is constant, but the area
speed is constant.
The square of the sidereal period is
proportionate to the cube of the mean
between the maximum and minimum
distances from the Sun.
P is the orbital period of planet and a is the
semimajor axis of the orbit
Recent Times
Not center of universe
Infinite? Position?