Some seventeen observations of Timocharis are reported by Ptolemy which fall into three different types: stellar, lunar and planetary. First, we have a list of twelve stellar declinations which he adduces in support of his analysis of precession (these are interspersed with six observations by Aristyllos which are excluded here):
| Star | Reference | Reported Dec | Actual Dec (273 BCE) |
|---|---|---|---|
| α Aql (Altair) | H2.19 | +5.8° | +5.666° |
| η Tau (mid Pleiades) | H2.19 | +14.50° | +14.600° |
| α Tau (Aldebaran) | H2.20 | +8.75° | +9.079° |
| γ Ori (Bellatrix) | H2.20 | +1.20° | +1.293° |
| α Ori (Betelgeuse) | H2.20 | +3.83° | +3.839° |
| α CMa (Sirius) | H2.20 | −16.33° | −16.191° |
| α Leo (Regulus) | H2.21 | +21.33° | +21.088° |
| α Vir (Spica) | H2.22 | +1.40° | +1.347° |
| α Boo (Arcturus) | H2.22 | +31.50° | +32.179° |
| α Lib (Zubenelgenubi) | H2.23 | −5.00° | −4.853° |
| β Lib (Zubeneschamali) | H2.23 | +1.20° | +1.008° |
| α Sco (Antares) | H2.23 | −18.33° | −18.441° |
A least squares analysis using the VCW model for these declinations shows a minimum discrepancy for the year 273 BCE with an average error of 0.251°, a pretty good level of accuracy. We don't know, of course, that they were all made in the same year, but at least we have a date around which we know that Timocharis was active.
Second, there are four observations of Lunar occultations. Each is given a fairly detailed account by Ptolemy, and I give the first in full:
[1] Timocharis, who observed in Alexandria, records the following. In the 47th year of the First Kallippic 76 year period, on the 8th of Anthesterion, which is Athyr 29 in the Egyptian calendar, towards the end of the third hour [of night], the southern half of the Moon was seen to cover exactly either the rearmost third or [the rearmost half] of the Pleiades. That moment is in the 465th year from Nabonassar, Athyr [III] 29/30 in the Egyptian calendar [January 29th 283 BCE], 3 seasonal hours before midnight or 3⅓ equinoctial hours before midnight. At that moment, according to the hypotheses we demonstrated previously, the position of the Moon was as follows:
| True longitude: | Taurus 0;20° | True latitude: | 3;45° north of the ecliptic |
| Apparent longitude: | 29;20° | Apparent latitude: | 3;35° north of the ecliptic |
(for the culminating point was two-thirds through Gemini). Therefore, at that time the rearmost end of the Pleiades was about 29½° towards the rear from the spring equinox (for the Moon's centre was still in advance of it), and was about 3⅔° north of the ecliptic (for again, it was a little north of the Moon's centre).
At the stated date (November 29th, 283 BCE), modern calculation shows that the Moon was in waxing crescent phase (44% illuminated) and it was the rearmost (easterly) part of the Pleiades that was occulted, including the brightest star η Tau (Alcyone) in the southwestern sky. The occultation of the stars lasted from 18:10 to 20:50 local time (that is, about 3⅙ hours before midnight). At mid-occultation (approximately 19:30) the actual coordinates of the Moon were:
| Coordinate System | Longitude | Latitude | |
|---|---|---|---|
| Ecliptic | λ = 28° 14' | β = 3° 51' | (Ptolemy: 29°20', 3°35' at 19:30) |
| Equatorial | α = 1h 39m | δ = 14° 33' | |
| Horizontal | A = 247° 41' | a = 56° 21' |
Ptolemy goes on to list three more lunar observations by Timocharis. These are given in summary form in comparison with modern calculation below.
[2] An occultation of the star Spica (α Vir) on March 9th, 294 BCE 'at the beginning of third hour' which Ptolemy states to be about four hours before midnight (7.3; H2.28−29). By modern calculation the occultation began at 20:50 and lasted until 22:10. The Moon was full with 99.5% illumination and its position at mid-occultation (21:30) was:
| Coordinate System | Longitude | Latitude | |
|---|---|---|---|
| Ecliptic | λ = 172° 00' | β = −1° 53' | (Ptolemy: 172°05', −2°00' at 20:00) |
| Equatorial | α = 11h 28m | δ = 1° 29' | |
| Horizontal | A = 114° 22' | a = 36° 38' |
Sunset was at 18:00, so the occultation began towards the end of the third hour of the night if that is how we are to understand the words of Timocharis (as reported by Ptolemy).
[3] A further occultation of Spica (7.3; H2.29−30) on November 9th, 283 BCE at '3½ seasonal hours after midnight'. In this case, the Moon was a waning crescent (18% illuminated) and just grazed Spica with its northern limb at 03:10 according to modern calculation.
| Coordinate System | Longitude | Latitude | |
|---|---|---|---|
| Ecliptic | λ = 172° 12' | β = −2° 13' | (Ptolemy: 172°30', −2°15' at 02:30) |
| Equatorial | α = 11h 27m | δ = 1° 05' | |
| Horizontal | A = 93° 45' | a = 08° 22' |
[4] An occultation of β Sco (7.3; H2.32−33) on December 21st, 295 BCE at '3 seasonal hours after midnight'. Modern calculation shows that the grazing occultation of the star by the northern limb took place at 05:30. The Moon was a waning crescent (21% illuminated) and its position was:
| Coordinate System | Longitude | Latitude | |
|---|---|---|---|
| Ecliptic | λ = 211° 27' | β = +0° 52' | (Ptolemy: 212°00', +1°05' at 03:24) |
| Equatorial | α = 13h 58m | δ = −11° 18' | |
| Horizontal | A = 129° 35' | a = 31° 21' |
From these tables it can be seen that, not only were Ptolemy's calculations for nearly 450 years before his time pretty good, but also that the observations of Timocharis were themselves fairly reliable.
Third, we have one observation of Venus made by Timocharis and analysed by Ptolemy (10.4; H2.310−315). This was made on October 12th, 272 BCE a couple of hours before dawn, and describes Venus as occulting the star η Vir ('the star opposite Vindemiatrix'). In fact, Venus did not occult the star, but passed by on the southern side at an angular distance of 13 minutes of arc around 04:00, about two hours before sunrise. However, given the brightness of Venus at the time (magnitude −4.16, 70% illuminated) compared with that of the star (magnitude 3.85), and that the event occurred at an altitude of just 15° above the eastern horizon, the star would have become invisible owing to the glare of the planet, and consequently it would have seemed that an occultation had taken place.
Timocharis, then, despite Hipparchos' partial censure and the small sample of his work presented by Ptolemy, deserves to be credited as a careful observer and perhaps the first to make and record systematic observations of the stars and planets.
Lunar crater: Timocharis (diameter 34 km).
Last updated 28/04/20
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