non-duplicates that should be duplicates

[Jon Schoenfield]

If I'm remembering correctly, while historians generally use "1 B.C." as the 
year immediately prior to "A.D. 1" (so that no "year 0" exists, and, e.g., 
the expression "the first century B.C." is the 100-year period from 100 B.C. 
through 1 B.C., and "the first century A.D." is the 100-year period from 
A.D. 1 through A.D. 100), astronomers _do_ generally use a "year 0" and use 
negative numbers for dates before their "year 0."  In other words, for dates 
in years prior to A.D. 1,

the historian's "YYYY B.C." = the astronomer's "1-YYYY."

(As I understand it, the rationale for the historian's approach is 
consistency with traditional usage, while the rationale for the astronomer's 
approach is ease of calculation, e.g., of time intervals between events, 
such as comet sightings.)

The dates listed in A072235 and A100748 agree except at

    -87 vs. -86
    -12 vs. -11
    374 vs. 347
and
    1986 vs. 1985.

The comment on A072235 points out that the author doesn't know whether the 
years of observation necessarily coincide with actual years of perihelion, 
so I suppose some of the discrepancies could be accounted for as possible 
differences between a perihelion date and an observation date.

As it turns out, the perihelion dates at the web address Brendan gave agree 
completely with A072235, if we interpret the four negative numbers

    -240, -164, -87, -12

as indicating (the historian's) B.C. dates, i.e., as 240 B.C., 164 B.C., 87 
B.C., and 12 B.C., rather than (the astronomer's) years with a negative 
sign.

It's known that the period of Comet Halley varies somewhat (I think the 
variation is mostly attributed to the gravitational influence of the larger 
planets), but the "347" entry in A100748 is not credible.  Even if I weren't 
further biased by the spelling "Recoreded" <g>, I'd be inclined to trust 
A072235 where the two differ.   :-)

-- Jon

----- Original Message ----- 
From: "Brendan McKay" <bdm at cs.anu.edu.au>
To: "Tanya Khovanova" <tanyakh at TanyaKhovanova.com>
Cc: <seqfan at ext.jussieu.fr>
Sent: Wednesday, May 30, 2007 8:46 PM
Subject: Re: non-duplicates that should be duplicates


> http://www.aerith.net/comet/catalog/0001P/index.html
> might help.  The meaning of negative numbers needs to be
> considered, since our BC/AD numbering system avoids 0.
>
> Brendan.
>
>
> * Tanya Khovanova <tanyakh at TanyaKhovanova.com> [070531 11:39]:
>> These two sequences should be the same:
>>
>> A072235  Years of recorded observations of Comet Halley.
>>
>> -240, -164, -87, -12, 66, 141, 218, 295, 374, 451, 530, 607, 684, 760, 
>> 837, 912, 989, 1066, 1145, 1222, 1301, 1378, 1456, 1531, 1607, 1682, 
>> 1759, 1835, 1910, 1986
>>
>> A100748  Years of recorded appearances of Halley's Comet
>>
>> -240, -164, -86, -11, 66, 141, 218, 295, 347, 451, 530, 607, 684, 760, 
>> 837, 912, 989, 1066, 1145, 1222, 1301, 1378, 1456, 1531, 1607, 1682, 
>> 1759, 1835, 1910, 1985
>>
>>
>> _________________________________________________________________
>> Need personalized email and website? Look no further. It's easy
>> with Doteasy $0 Web Hosting! Learn more at www.doteasy.com
>
>