Posted: Fri Apr 02, 2010 1:51 pm
Both can be right. I'll have to give it a closer look but it's possible that in Lilly's days and in the centuries before and after these max/mins were of these values. I indeed did take the ecliptic into consideration. In the picture you see the purple dotted line of the planetary nodal axis (with the usual node glyph) and the red dotted/little stripes line of the planetary apsides axis. These lines too have a rotation around the Sun of less than a degree per century, hence a period of many centuries. It means that these lines also move with respect to each other. In Martin's picture we see that perihelion of Mars' orbit is in the southern part. In several hundreds of years or more, the perihelion can be close to the ascending node and hundreds of years later in the highest part between the ascending and descending node. These have to be taken into account.
So in brief the differences given by Lilly probably are right but these are correct for a certain period of several centuries. If we wait long enough the other extremes will occur on the north side of the ecliptic.
Further the extreme declinations depend on the precession. Imagine for a moment that the apsides and the nodes axes wouldn't move but only precession would occur. If in Martin's picture the Earth's position on the right would be in the (northern hemisphere) Winter, then Mars would be -23.5?-6.8? = -30.3. Half a precession period (13,000years) later the Earth's position on the right would be the Summer. Then it would be 23.5?-6.8?=16.7?. The effect is 'flattened' and much less extreme.
However the periods when these three (and even more possible) occur in the same time will happen only once (during a several centuries) in the so and so many centuries/millennia or even longer. So theoretically (with the ideal apsides and node position) Venus can be an extreme 9.7? above the ecliptic and only at inferior conjunction with the Sun and when this occurs exactly at the same time as Summer solstice (which is necessarily for the extreme declination) then it will be 23.5?+9.7?=33.2?. If we take the change of obliquity into account (like 24? some 2.5 millennia ago) then this could even be more 33.7?. But this is an extremely rare event.
So in brief the differences given by Lilly probably are right but these are correct for a certain period of several centuries. If we wait long enough the other extremes will occur on the north side of the ecliptic.
Further the extreme declinations depend on the precession. Imagine for a moment that the apsides and the nodes axes wouldn't move but only precession would occur. If in Martin's picture the Earth's position on the right would be in the (northern hemisphere) Winter, then Mars would be -23.5?-6.8? = -30.3. Half a precession period (13,000years) later the Earth's position on the right would be the Summer. Then it would be 23.5?-6.8?=16.7?. The effect is 'flattened' and much less extreme.
However the periods when these three (and even more possible) occur in the same time will happen only once (during a several centuries) in the so and so many centuries/millennia or even longer. So theoretically (with the ideal apsides and node position) Venus can be an extreme 9.7? above the ecliptic and only at inferior conjunction with the Sun and when this occurs exactly at the same time as Summer solstice (which is necessarily for the extreme declination) then it will be 23.5?+9.7?=33.2?. If we take the change of obliquity into account (like 24? some 2.5 millennia ago) then this could even be more 33.7?. But this is an extremely rare event.
