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.

This is a comparing table of several ancient tables taken from

Ptolemy, Bianchini, and Copernicus: Tables for Planetary Latitudes in Archive for History of Exact Sciences (ISSN 0003-9519), Vol. 58, No. 5, p. 453 - 473 (2004)
Alf.T. is obviously the princeps edition of Alfonsine Tables, Ratdolt 1483.

In every case in the modern list given by Tuckerman I have Mars 4.38 N - 6.53 S latitude.


margherita

Very useful Margherita - thank you. And thankyou too Eddy, for the further post, explaining how the values change, but only over very great periods of time.

extreme north and south declinations of planets and the Moon:

AD 1 to AD 1000 (obliquity AD 1 = 23,42')

Moon 28n59 / 28s59 (AD 1 to AD 500)
Mercury 25n39 / 25s48
Venus 27n22 / 27s38
Mars 27n49 / 29s51
Jupiter 24n16 / 24s15
Saturn 23n49 / 23s47
Uranus 24n05 / 24s04
Neptune 23n07 / 23s09
Pluto 30n20 / 30s48

AD 1001 to 2020 (obliquity AD 1000 = 23,34')

Moon 28n45 / 28s45 (1800 to 2020)
Mercury 25n39 / 25s52
Venus 27n49 / 28s05
Mars 27n32 / 29s26
Jupiter 23n52 / 23s51
Saturn 23n16 / 23s17
Uranus 23n53 / 23s53
Neptune 23n07 / 22s59
Pluto 30n20 / 29s59

Source: Riyal max/min declination output sorted with a word processor.

Juan

Deb wrote: Hence I'm confused again - why are these figures saying that there is a difference and you are saying there is not ??

Eddy is correct in that the longitudes of Mars perihelion and node do precess

However the rates are slow so make a small difference over the centuries.

Peri = 1.84?/cent
Node = 0.772?/cent

Since the time of Lilly's C.A. publication (1647) perigee has advanced 6.67? and node 2.8? in longitude. The difference 3.87? in longitude is the total offset of the framework in 363 years!

This makes only minor difference to the extreme geo lats.

Current arc between peri and node is 73.49?. As this is increasing the extreme lats are also increasing whereby they will reach maximum in 16 centuries time.

Martin

@Martin,

I have lost the Astrolab Companion files and the download link in my mail has expired .

Pankaj