# The Inferior planets - Venus

As we now know, Venus rotates around the Sun inside the Earth's orbit. From Earth, it therefore appears to oscillate either side of the Sun with a period of about 19 months and a maximum elongation of about 46º. From Ptolemy's point of view, it rotates on a deferent with a period of 1 year (i.e. the Suns' orbit) and an epicycle whose period is about 7 months. (Because of the way things work, the period of oscillation is equal to p / (1 - p) where p is the period of the epicycle in years.) In addition, the epicycle has a radius equal to 72% of the deferent.

When you run the program in this mode, the following window appears and if you watch it closely you will see that the above relationships hold.

Now the eccentricity of Venus' orbit (effectivelky the epicycle) is 0.7% while the eccentricity of the Earth's orbit (the deferent) is 1.6%. Ptolemy assumed that all epicycles were circular and only applied offsets and equants to the main deferent.

Try adding a 3.2% offset to the deferent. Alternatively try a 1.6% offset plus equant. Is the latter significantl;y better?

It is worth pointing out that the maximum angular discrepancy always ocurs when Venus is passing right in front of the Sun - during which time it is impossible to observe anyway.