Solar anomaly and the Antikythera Mechanism

[Bobhare]

I'm building a replica of the Antikythera Mechanism; a device that was conceived and manufactured around 50BC.

it is an orrery and amongst other things it shows the motion of the five known planets, the sun and the moon when viewed from the earth.
I've managed to calculate the motion of the planets and the mechanism I have built follows the theory.

However, according to the many publications on the subject, particularly "The Cosmos in the Antikythera Mechanism -
Tony Freeth and Alexander Jones" there is a set of gears to allow for The Solar Anomaly. This I just don't understand despite many hours of searching.

This anomaly, if appendix 4.1 information is used, causes the observed sun to vary from the mean sun by around 5 degrees on a one year calendar disk equivalent to about 5 days.
The only anomaly I'm aware of is that from the equation of time which is in minutes rather than days and would not show on a one year calendar ring.

All the publications refer to this anomaly but none of them give the logic or maths that develops it. In the Antikythera mechanism the anomaly is generated by a pin and slot arrangement.
I've attached an image of Sun, Mercury and Venus Assembly showing the arrangement of the sun bottom left.

I may have the same problem with the moon but I'd like so solve the sun issue.
Any help would be much appreciated.

 

[WernerQH]

In celestial mechanics "anomaly" usually refers to the angular distance of a planet from its perihelion, as seen from the sun: $$
v \approx M + 2e \sin M + \frac 5 4 e^2 \sin 2 M+ \dots
$$ where $e$ is the eccentricity of the orbit and $M = { 2 \pi \over T } t$ the mean anomaly (which increases linearly with time).

For Earth we have $e = 0.0168$, which would lead to a variation of up to about 2 degrees. So I'm not quite sure if it refers to the same quantity as in your book. It is the reason why the seasons don't have the same length. The maximum deviation would occur near the beginning of April and the beginning of October.

 

[Bobhare]

Thanks for the reply.
I'm beginning to think that the Greeks merely wanted to show the effect of the equation of time rather than the exact values and the value of 2 degrees you quote would hardly be visible on a 365 day dial.
I'm sure the anomaly referred to in the book is the maximum angular difference between the actual sun's position and that resulting from the sun moving in a circular orbit.
From further reading this seems to tie in with your 2 degrees.
I'll modify the gear arrangement to get as closed as possible to your number.

 

[WernerQH]

I'm beginning to think that the Greeks merely wanted to show the effect of the equation of time rather than the exact values and the value of 2 degrees you quote would hardly be visible on a 365 day dial.

The equation of time is connected to the anomaly (eccentricity of Earth's orbit), but has another effect superimposed on it due to the tilt of Earth's axis with respect to the orbit plane. That can amount to 4 degrees, or 16 minutes in the diurnal motion. But I doubt that the Greeks worried about the unevenness of the time displayed by a sundial.

I was quite impressed by the Wikipedia article:

Due to advances in imaging and X-ray technology, it is now possible to know the precise number of teeth and size of the gears within the located fragments. Thus the basic operation of the device is no longer a mystery and has been replicated accurately. The major unknown remains the question of the presence and nature of any planet indicators.

I'll modify the gear arrangement to get as closed as possible to your number.

Good luck!

 

[Bobhare]

The image of the gear arrangement in Wikipedia was invaluable and gives the number of teeth on all the gears but nothing related to pin positions in the pin and slot arrangements.
My understanding of the equation of time is that it is made up of two elements, eccentricity and obliquity. Both are sinusoidal but with a phase shift one to the other. The difference in peak to trough is around 30 minutes which is 7.5 degrees.
Perhaps this is the angle that the Greeks were using?
I've managed to modify the design to produce a difference in angle between mean and true sun of 9.5 degrees which is sufficiently close.
I'm an engineer with a reasonable understanding of physics and I'm amazed that the Greeks could conceive the design and equally amazed that they could make it. For example one of the gears has 223 teeth, a prime number, and is only 110mm diameter. That was after they had understood the motion of the heavenly bodies.

 

[WernerQH]

My understanding of the equation of time is that it is made up of two elements, eccentricity and obliquity. Both are sinusoidal but with a phase shift one to the other. The difference in peak to trough is around 30 minutes which is 7.5 degrees.

Yes, that's my understanding, too.

Perhaps this is the angle that the Greeks were using?

I have no idea.

I'm an engineer with a reasonable understanding of physics and I'm amazed that the Greeks could conceive the design and equally amazed that they could make it. For example one of the gears has 223 teeth, a prime number, and is only 110mm diameter. That was after they had understood the motion of the heavenly bodies.

Yeah, it is amazing. And it was made long before Ptolemy. (He is most famous for his astronomy "textbook", but there must have been excellent astronomers before him.)

 

[Nugatory]

A short digression into the raving crackpottery of Immanuel Velikovsky has been removed from this thread. All posters are reminded that the forum does not host discussions of pseudo-science, not even to debunk it. Please, if you see it, report it instead of engaging.