Home

Site Map

Search

astronomy,
                      software, applet, java,shareware, sun, rotation
GeoAstro
Applets

Astronomy
physics,astronomy,applet,Java,
Chaos Game
physics,astronomy,applet,Java
Java
physics,astronomy,applet,Java
Miscel-

laneous
physics,astronomy,applet,Java
Physics Quiz
physics,astronomy,applet,Java
Who is
Who ?

Ancient Theories of the Sun:
3.
Eccentric and Equant Model Applet

1. Eccentric Model Applet
2. Epicyclic Model Applet

 data

Select from the Details menu.

e is distance between the center (+) and the Earth, which is equal to the distance between the center and the equant point, both measured in units of the radius.

For e=0 the equant point and the Earth coincide with the center.

time
                  interval
Select the time interval.
equant point
Uncheck the box to remove the equant point (setting it to the center).

Apogee
A
Ptolemy equant point
P
Perigee

In addition to the eccentric position of the Earth there is an equant point - which is opposite to the Earth and sees the planet or the Sun move at a uniform angular speed (angle α) on the black circle (radius r) around the center (+).

rMin=r-e, rMax=r+e
eccentricity=(rMax-rMin)/(rMax+rMin)=e/r

eccentricity earth orbit

duration
              lenghth summer season

Diagram computed by e=1/60

The results are in very good agreement with my Seasons Applet


The following diagrams are showing the between the precise heliocentric longitude (computed by my Planet applet) and the value from the eccentric and equant model:

error longitude sun

longitude sun

The following diagram is showing the between the precise distance of the Sun (computed by my Planet applet) and the value from the eccentric and equant model (e=1/60):

distance
                  of the sun


Web Links

Hipparchus: Orbit of the Sun (Wikipedia)

Ptolemy (Wikipedia)

Jahreszeit (Wikipedia)

Gemini Elementa Astronomiae, editit C. Manitius (PDF, Greek/German)

Des Claudius Ptolemäus Handbuch der Astronomie (Übers. Karl Manitius)

The Fallacy of the Equant

Aside: Eccentric motion vs Equant motion

Books
James Evans: The History and Prctice of Ancient Astronomy,
Oxford University Press, 1998, Chapter Five: Solar Theory.

Hugh Thurston: Early Astronomy, Springer, Berlin/New York 1994.

Jean Meeus: Astronomical Tables of the Sun, Moon and Planets. 2nd ed., Willmann-Bell, Richmond 1995.

Updated: 2012, Jul 15