The planetary increase of brightness during retrograde motion: An explanandum constructed ad explanantem

May combine two claims.

The change in brightness of Jupiter and Saturn is hardly detectable to the naked eye; Saturn's magnitude difference is only 0.6 and Jupiter's around 0.8.

“The situation is, however, different for the other two superior planets: their change in brightness is hardly detectable for the necked eye.Saturn's magnitude difference is only of 0.6 and Jupiter's around 0.8.”

• AssumptionRests on an assumption: Brightness is proportional to the apparent area of the planet's disk, and a change in brightness is inversely proportional to the square of a change in distance.
• AssumptionRests on an assumption: The more complete the phase is, the brighter the planet appears.
• AssumptionRests on an assumption: A magnitude difference of 1 is detectable to the naked eye when comparing celestial bodies at the same time.

May combine two claims.

The change in brightness of Venus is only around 0.8 magnitudes, a difference hardly detectable and similar to Jupiter.

“The change in brightness of Venus is only of around 0.8, a magnitude difference hardly detectable, similar to that of Jupiter.”

• Also stated in: § 2. Do the planets increase their brightness during retrograde motion? · boosted

  “The fact that Venus does not change significantly in brightness is a very well-known fact today (see Goldstein, 1996: 1).”

• cites Goldstein, 1996: 1 sourceNot checked — no full text of the source

• AssumptionRests on an assumption: Brightness is proportional to the apparent area of the planet's disk, and a change in brightness is inversely proportional to the square of a change in distance.
• AssumptionRests on an assumption: The more complete the phase is, the brighter the planet appears.
• AssumptionRests on an assumption: A magnitude difference of 1 is detectable to the naked eye when comparing celestial bodies at the same time.

May combine two claims.

The only planet with a clearly perceivable change of brightness during retrograde motion is Mars; the other planets do not significantly change their brightness.

“As I have already noted, the only planet with a clearly perceivable change of brightness is Mars.”

• Also stated in: § 2. Do the planets increase their brightness during retrograde motion? · hedged

  “In conclusion, Venus's changes of brightness are hardly detectable to the naked eye, but even if they were, we would only see that it diminishes its brightness during retrograde motion, exactly the opposite of Mars.”

• cites Goldstein, 1996: 1 sourceNot checked — no full text of the source

• AssumptionRests on an assumption: The arc visionis is around 10° for all planets, but only 5° for Venus.
• AssumptionRests on an assumption: A magnitude difference of 1 is detectable to the naked eye when comparing celestial bodies at the same time.

May combine two claims.

Venus's brightness shows relatively little change because the enormous variation in its distance from Earth is largely canceled by the effect of the phases, arriving at new phase at its minimum distance.

“Venus's brightness also shows relatively little change, because the enormous variation in its distance from the Earth is largely canceled by the effect of the phases: the more Venus increases its size, the more its phase decreases, arriving at new phase at its minimum distance.”

• AssumptionRests on an assumption: Brightness is proportional to the apparent area of the planet's disk, and a change in brightness is inversely proportional to the square of a change in distance.
• AssumptionRests on an assumption: The more complete the phase is, the brighter the planet appears.

May combine two claims.

Mercury is only visible at greatest elongation, so there is not much variation in distance during intervals of visibility; its small apparent size prevents detection of any variance in apparent size.

“Mercury is only visible on greatest elongation so there is not much variation in distance during the intervals of visibility.Moreover, the small apparent size of Mercury prevents the detection of any variance in its apparent size.”

• AssumptionRests on an assumption: The arc visionis is around 10° for all planets, but only 5° for Venus.

May combine two claims.

There are five observations of Mars in the Almagest, three of them are oppositions at years 130, 135 and 139, which Ptolemy used for determining the values of eccentricity and apogee of Mars model, but without mentioning its brightness.

“There are five observations of Mars in the Almagest, three of them are oppositions at years 130, 135 and 139, which Ptolemy used for determining the values of eccentricity and apogee of Mars model, but without mentioning its brightness (Almagest X, 7; Toomer, 1998: 484).”

• cites Almagest X, 7; Toomer, 1998: 484Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

In Ancient times, leaving Simplicius aside, Proclus and Theon of Smyrna are the only other authors who referred to changes of planetary brightness or apparent sizes, both after Ptolemy.

“In Ancient timesdleaving Simplicius asidedProclus and Theon of Smyrna are the only other authors who referred to the changes of planetary brightness (or apparent sizes), both after Ptolemy.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The values in Figure 4 correspond to one synodic period starting at 1995.

“The values correspond to one synodic period starting at 1995.”

May combine two claims.

The difference between the maximum and minimum apparent diameter of the Moon during 1995-1998 is 247.5 arcseconds, with maximum 2010.7'' and minimum 1463.2''.

“I took the difference between the maximum and minimum apparent diameter of the moon during years 1995e1998 and it is 247.5 00 , being the maximum diameter 2010.7 00 and the minimum 1463.200 .”

May combine two claims.

Simplicius is right about Mars but doubly wrong about Venus: Venus cannot be seen in the middle of its retrograde motion because of the Sun's glare, and even if visible it would be at new phase and not at maximum brightness.

“Simplicius is right about Mars, but doubly wrong about Venus: first it is impossible to see Venus in the middle of its retrograde motion because of the glare of the Sun, and second because, even if the sunlight would not make it disappear, it would still be at a new phase and so not in its maximum brightness!”

• AssumptionRests on an assumption: The arc visionis is around 10° for all planets, but only 5° for Venus.

May combine two claims.

The retrograde motion of an outer planet is produced when the planet is in opposition, at its minimum distance from Earth and in full phase, having maximum possible brightness.

“The retrograde motion of outer planet is produced when the planet is in opposition (M 1 ), i.e., when the planet is both at its minimum distance from the Earth and in a full phase, having the maximum possible brightness.”

Probably not a substantial claim: may not pass S1 (asserted).

Many scholars affirm that the main reason for the rejection of Eudoxus' homocentric spheres in favor of the epicycle and deferent system was the impossibility of the former to explain the planetary increase of brightness during retrograde motion.

“So, it is usually affirmed that the main reason for the rejection of Eudoxus' homocentric spheres in favor of the epicycle and deferent system was that the first cannot explain the manifest planetary increase of brightness during retrograde motion, while the second can.”

• Also stated in: § 1. Introduction · plain

  “Many scholars who made important contributions to the history of Ancient astronomy, such as Thomas Heath, Giovanni Schiaparelli or John L. Dreyer, agree with this assertion.”

• cites Heath (1913: 221)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Schiaparelli ([1926], 1998: 122)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Dreyer (1953: 141)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

During retrograde motion, inner planets are in new phase, reaching their minimum possible brightness.

“Even more important, during retrograde motion, they are in new phase, reaching their minimum possible brightness.”

• AssumptionRests on an assumption: Brightness is proportional to the apparent area of the planet's disk, and a change in brightness is inversely proportional to the square of a change in distance.
• AssumptionRests on an assumption: The more complete the phase is, the brighter the planet appears.

May combine two claims.

The maximum-to-minimum distance ratios from Earth are roughly Mercury 2.2, Venus 6.1, Mars 4.8, Jupiter 1.5, and Saturn 1.2.

“The proportions are roughly (Van Helden, 1985: 44), Mercury: 2.2; Venus: 6.1; Mars: 4.8; Jupiter: 1.5 and Saturn: 1.2.”

• cites Van Helden, 1985: 44Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

In Ptolemy's epicycle and deferent model, Mars and Venus are the planets with the bigger epicycles, and therefore the planets that vary their distance from Earth the most.

“In Ptolemy's epicycle and deferent model, Mars and Venus are the planets with the bigger epicycles, and, therefore the planets that vary their distance from the Earth the most.”

Classified as probably not a substantial claim.

Simplicius affirms that the observed change in brightness of Venus and Mars was one of the reasons for the rejection of the homocentric spheres in favor of epicycle models.

“Simpicius affirms that the observed change in brightness of Venus and Mars was one of the reasons for the rejection of the homocentric spheres in favor of epicycle models.”

• cites De Caelo 2.12, Bowen, 2013: 165Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Venus's changes of brightness are hardly detectable to the naked eye, and if visible, Venus would only be seen to diminish its brightness during retrograde motion, opposite to Mars.

“In conclusion, Venus's changes of brightness are hardly detectable to the naked eye, but even if they were, we would only see that it diminishes its brightness during retrograde motion, exactly the opposite of Mars.”

• AssumptionRests on an assumption: Brightness is proportional to the apparent area of the planet's disk, and a change in brightness is inversely proportional to the square of a change in distance.
• AssumptionRests on an assumption: The more complete the phase is, the brighter the planet appears.
• AssumptionRests on an assumption: A magnitude difference of 1 is detectable to the naked eye when comparing celestial bodies at the same time.

May combine two claims.

Venus's small brightness change is partially due to its atmosphere: sulfuric acid droplets scatter light, so even at new phase it is still shining.

“This very small change is partially due also to Venus's atmosphere: the presence of sulfuric acid droplets in the high atmosphere of the planet scatters an important amount of light (Mallama, Wang, & Howard, 2006: 10), so even at a new phase is still shining.”

• cites Mallama, Wang, & Howard, 2006: 10 sourceNot checked — no full text of the source

• AssumptionRests on an assumption: Brightness is proportional to the apparent area of the planet's disk, and a change in brightness is inversely proportional to the square of a change in distance.
• AssumptionRests on an assumption: The more complete the phase is, the brighter the planet appears.

Probably not a substantial claim: may not pass S4 (based).

Even by Ptolemaic times, when references to change of brightness started to appear, the homocentric sphere model had been abandoned many centuries before.

“Furthermore, even by Ptolemaic times when these references started to appear, the homocentric sphere model had been abandoned many centuries before.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Proclus gives the list of planetary phenomena that had to be explained by Ancient astronomers, including motion in longitude, latitude, and retrogradations.

“Proclus gives the list of planetary phenomena that had to be explained by Ancient astronomers (the motion in longitude, in latitude, the retrogradations, etc.).”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Proclus's observation is certainly true for Mars and Jupiter.

“Proclus's observation, however, is certainly true for Mars and Jupiter.”

May combine two claims.

The observation of Mars's brightness change re-appears in Copernicus, who asserts that when Mars shines all night it seems to equal Jupiter in size, distinguished only by its reddish color, while in other configurations it is barely among second-magnitude stars.

“This observation re-appears in Copernicus, who asserts that when Mars “shines all night, seems to equal Jupiter in size, being distinguished only by its reddish color.Yet in the other configurations it is found barely among the stars of the second magnitude, being recognized by those who track it with assiduous observations” (Copernicus I, X; Rosen, 1992: 22).”

• cites Copernicus I, X; Rosen, 1992: 22Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Aristarchus of Samos put the empirical data he used as input in his calculation of the sizes and distances of the Sun and Moon among the hypotheses and never explained how he obtained these values.

“Aristarchus of Samos puts the empirical data that he used as input in his calculation of the sizes and distances of the Sun and Moon among the hypotheses and he never explains how he obtained these values (Heath 1913: 352-353).”

• cites Heath 1913: 352-353Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim.

The certainty of the claim that the main reason for the rejection of the homocentric spheres in favor of the epicycle and deferent system was the change in brightness of the planets during retrograde motion is unfounded.

“I will aim to show in this paper that the certainty of this claim, i.e., that the main reason for the rejection of the homocentric spheres in favor of the epicycle and deferent system was the change in brightness of the planets during retrograde motion, is unfounded.”

Classified as probably not a substantial claim. May combine two claims.

Calcidius described the solar anomaly and said the Sun appears to move slower and be smaller when in Gemini (apogee), and biggest and fastest when in Sagittarius (perigee).

“Calcidius, in his Commentary to the Timaeus, described the solar anomaly and said that the “Sun appears to move slower and be smaller to our eye when it is in Gemini [its apogee], and the biggest and fastest when it is in Sagittarius [its perigee]” (I, 82; Moreschini, 2003: 271-274).”

• cites I, 82; Moreschini, 2003: 271-274Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

This condition is precisely what happens with Venus (1 turn in the deferent in 1.598 turns in the epicycle) and Mars (1 turn in the deferent in 1.135 turns in the epicycle).

“But this is precisely what happens with Venus (1 turn in the deferent in 1.598 turns in the epicycle) and Mars (1 turn in the deferent in 1.135 turns in the epicycle).”

Classified as probably not a substantial claim.

In the Almagest, Ptolemy said the apparent increase in sizes at horizons is caused not by a decrease in distances but by exhalations of moisture surrounding the earth interposed between the observer and the heavenly bodies.

“In the Almagest (I,3, Toomer, 1998: 39) he said that “the apparent increase in their sizes at horizons is caused, not by a decrease in their distances, but by the exhalations of moisture surrounding the earth being interposed between the place from which we observe and the heavenly bodies, just as objects placed in water appear bigger than they are, and the lower they sink, the bigger they appear””

• cites Almagest I,3, Toomer, 1998: 39Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

Ancient Greeks granted a much more important role to theory in detriment of observation than we do today, both in building and confirming their models.

“This is particularly true in Simplicius's case, because ancient Greeks granted a much more important role to theory in detriment of observation than we do today, both in the building and confirming of their models.”

May combine two claims.

The first clear testimonies about change of brightness are contemporary to Ptolemy, in the case of Theon, or around three centuries after him, in the case of Proclus.

“The first clear testimonies that we have are contemporary to Ptolemy, in the case of Theondeven it seems a theory-laden observationdor around three centuries after him, in the case of Proclus.”

May combine two claims.

Proclus introduces a new fact: Mars and Jupiter on one hand, and Venus and Mercury on the other, sometimes have the same apparent size.

“Proclus introduces a new fact: Mars and Jupiter on the one hand, and Venus and Mercury on the other, sometimes have the same apparent size.”

May combine two claims.

Unlike the same-sense epicycle model, the opposite-sense model has important restrictions for producing retrograde motion; in particular, it cannot make Venus and Mars move in retrograde motion at the periods that they actually do.

“Unlike the same-sense epicycle model, the opposite-sense has important restrictions for producing retrograde motion.In particular, it cannot make Venus and Mars to move in retrograde motion at the periods that they actually do.”

May combine two claims.

Ptolemy observed that for the planets it takes more time to go from maximum speed to mean than from mean to maximum; therefore the same-sense model must be chosen.

“Ptolemy says that he observed that for the planets, it takes more time to go from maximum speed to mean, than from mean to maximum.Therefore, the same-sense model must be chosen.”

May combine two claims.

The crucial point for Proclus was the observation that the planets are sometimes observed bigger, sometimes smaller, as if moving in depth and sometimes closer and sometimes further away.

“The crucial point for Proclus was the observation that the planets “are sometimes observed bigger, sometimes smaller, as if they were moving in depth and sometimes they were closer to us and sometimes further away.”

• cites i.18; Manitius, 1909: 10-11Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

It is possible to produce retrograde motion by inverting the sense of the planet's motion on the epicycle; in that case retrograde motion is produced when the planet is at its maximum distance from the center of the deferent.

“It is also possible, however, to produce retrograde motion inverting the sense of the motion of the planet on the epicycle.In this case, the retrograde motion is produced when the planet is at its maximum distance from the center of the deferent.”

May combine two claims.

When Mars retrogrades close to its perigee, because of its large eccentricity, it becomes as bright as Jupiter, making it very difficult to distinguish them, if not for Mars's color.

“Nevertheless, when Mars retrogrades close to its perigee, because of its large eccentricity, it becomes as bright as Jupiter, making it very difficult to distinguish each other, if not for Mars color.”

May combine two claims.

Theon does not distinguish between the Sun and Moon and the planets, nor among the planets which have a perceivable change in size (Mars) and which do not (the rest).

“Taking into account that Theon does not distinguish between what happens with the Sun and Moon (which do not retrograde) and the planets (which retrograde) and, among them, which one have a perceivable change in size (Mars) and which ones not (the rest)”

May combine two claims.

There exist opposite-sense epicycle models in which the epicycle and deferent rotate in opposite directions; in these, retrograde motion is produced when the planet is farther from Earth and it should appear less bright.

“In Section 5, I will draw the reader's attention to the existence of what I shall call 'oppositesense epicycle models', i.e., planetary models in which the epicycle and the deferent rotate in opposite directions.In these well attested models, the retrograde motion is produced when the planet is farther away to the Earth and, consequently, they should appear to be less bright.”

May combine two claims.

The Moon is farther away when it is close to the horizon than when it is at zenith by around one Earth radius, so it should be smaller.

“Moreover, the Moon is farther away when it is close to the horizon than when it is at zenith by around one Earth radius, so it should be smaller.”

May combine two claims.

Pliny the Elder referred to this mixed model, although his discussion of planetary motion is very muddled and it is doubtful how much he really understood of it.

“The third evidence comes from Pliny the Elder, also contemporary to Ptolemy, who in his Natural History (II, 64-75;Neugebauer, 1975: 802-805) referred to this mixed model, although his discussion of planetary motion is very muddled and it is doubtful how much he really understood of it (see Neugebauer, 1975: 802).”

• cites Neugebauer, 1975: 802-805 sourceNot checked — no full text of the source
• cites Neugebauer, 1975: 802 sourceNot checked — no full text of the source

May combine two claims.

Simplicius claimed he observed Venus to be bigger at the middle of retrograde motion, which is patently false; Pliny affirmed he observed the outer planets, including Mars, to be smaller at retrograde motion, which is also patently false.

“So, while Simplicius, who defended the same-sense model, claimed that he observed Venus to be bigger at the middle of the retrograde motion (which is patently false), Pliny, commenting the opposite-sense model, affirmed that he observed the outer planets (including Mars) to be smaller at retrograde motion (which is also patently false)!”

Classified as probably not a substantial claim.

Bowen affirms that no one before Ptolemy appears to have paid any attention to the fact that stars differ in size or brightness, if they noticed it at all.

“Bowen affirms that “no one before Ptolemy appears to have paid any attention to the fact that the stars (both fixed and wandering) differ in size (brightness), if they noticed it at all” (Bowen, 2013: 289)”

• cites Bowen, 2013: 289 sourceNot checked — no full text of the source

May combine two claims. The quote only partly states this claim.

In the Keskintos inscription, the speed of the epicycle of Mars is triplicated presumably to make it faster than double the speed of the deferent, so the model can produce retrograde motion for Mars but produces three retrograde loops when Mars actually has only one, generating two spurious loops in each synodic cycle.

“It seems that the opposite-sense model defenders were aware of this problem, for, in the Keskintos inscription (Jones, 2006: 31), which shows parameters of the speeds of the planets, the speed of the epicycle of Mars is triplicated presumably in order to making it faster than the double of the speed of the deferent (3 > 1.135*2 ¼ 2.27).6 In this way, the model is able to produce retrograde motion”

• cites Jones, 2006: 31Not checked — no full text of the source

May combine two claims.

In his later Optics, Ptolemy abandoned this incorrect physical explanation and claims the phenomenon is due to a psychological illusion.

“In his later work Optics (59; Smith, 1996: 151), however, he abandoned this incorrect physical explanation and claims that the phenomenon is due to a psychological illusion.”

• cites Optics 59; Smith, 1996: 151Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Theon does not explicitly mention the change of brightness during retrograde motion, but he does so implicitly when relating change of sizes to change of distances and change of distances to change of speeds.

“Theon does not explicitly mention the change of brightness during retrograde motion, but he does it implicitly when relating the change of sizes to the change of distances and the change of distances to the change of speeds.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Theon of Smyrna sometimes describes arguments based on observations but very often mixes theoretical inferences and observational data.

“He sometimes describes arguments based on observations (for example, for proving the spherical shape of the Earth), but very often he mixes theoretical inferences and observational data in these descriptions.”

Classified as probably not a substantial claim.

Pliny affirmed that when the outer planets are at opposition and in the middle of retrograde motion, they appear very small because they are at the distance of their greatest altitude and moving with their smallest velocity.

“In particular, Pliny affirmed that when the outer planets are at opposition and, therefore, in the middle of retrograde motion, “they appear very small because they are at the distance of their greatest altitude and are moving with their smallest velocity” (Pliny II, 70;1962: 216).”

• cites Pliny II, 70;1962: 216Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The mixed system shows that at least in this case the change in brightness is not related to the selection of the epicycle direction: inner planets do not show change in brightness and are carried in the same-sense model, making them closer during retrograde; outer planets are carried in the opposite-sense model making them farther during retrograde, even if one of them shows a clear increase of亮度

“This is especially relevant to our topic for it shows that at least in this case the change in brightness is not related to the selection of the epicycle direction: the inner planets do not show change in brightness and, nevertheless, are carried in the same-sense epicycle model, making the planets to be closer to the Earth during their retrograde motion; the outer planets are carried in the”

Probably not a substantial claim: may not pass S3 (load-bearing).

Proclus is not explicitly relating the fact of equal apparent sizes to a change in speed, as Theon did.

“Of considerable importance, he is not explicitly relating this fact to a change in speed, as Theon did.”

May combine two claims.

Levi ben Gerson emphasized that the observed difference in size of Mars is just 1:2, while the Ptolemaic model requires 1:7, and that he could not perceive any changes of brightness in Mercury, Jupiter or Saturn.

“Levi ben Gerson goes further and emphasizes that the observed difference in size of Mars is just 1:2, while the Ptolemaic model requires 1:7, and that he cannot perceive any changes of brightness in Mercury, Jupiter or Saturn (Goldstein, 1985: 105-106), as required by Ptolemaic models.”

• cites Goldstein, 1985: 105-106Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionRests on an assumption: A magnitude difference of 1 is detectable to the naked eye when comparing celestial bodies at the same time.

Classified as probably not a substantial claim. May combine two claims.

For correctly understanding Ptolemy's text, when he talks about the eccentric hypothesis he is talking also about the opposite-sense model, because they are equivalent, and when he talks about the epicyclic hypothesis, he is talking about the same-sense model.

“For correctly understanding Ptolemy's text it is important to realize that when he talks about the eccentric hypothesis he is talking also about the opposite-sense model, because they are equivalent, and when he talks about the epicyclic hypothesis, he is talking about the same-sense model (see Almagest III, 3, Toomer, 1998: 146).”

• cites Almagest III, 3, Toomer, 1998: 146Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Theon is not talking of a real observation but of a deduced observation: if change of speed corresponds to change in distance, then there would also be a change in apparent size.

“it seems reasonable to suppose that he is not talking of a “real” observation but of a “deduced observation”: if the change of speed corresponds to a change in distance, then there would be also a change in apparent size.”

May combine two claims.

One clear example is the observation of the lunar parallax: the value obtained is clearly wrong but extraordinarily good for obtaining the lunar distance he is looking for at syzygies.

“One clear example is the observation of the lunar parallax: the value obtained is clearly wrong but extraordinary good for obtaining the lunar distance he is looking for at syzygies (Almagest V,12; Toomer, 1998: 61-62).”

• cites Almagest V,12; Toomer, 1998: 61-62Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The most obvious change in apparent size in both the Sun and Moon is the sometimes huge increase of size observed when they are near the horizon, at rising or setting.

“The most obvious change in the apparent size in both the Sun and Moon is the sometimes huge increase of size that is observed when they are near the horizon, at rising or setting.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

We do not really know what reasons forced the abandonment of the homocentric spheres in favor of the epicycle and deferent system.

“We do not really know what reasons forced the abandonment of the homocentric spheres in favor of the epicycle and deferent system.”

May combine two claims.

When Ptolemy introduced the planetary models in the Almagest, he explicitly said there are two possibilities for producing retrograde motion (same-sense and opposite-sense), and he chose the same-sense model, making his reason explicit, without making any reference to the change in brightness of the planets at all.

“When Ptolemy introduced in the Almagest the planetary models, he explicitly said that there are two possibilities for producing retrograde motion (i.e., same-sense and opposite-sense models), and that he chose the same-sense model, making his reason explicit, without making any reference to the change in brightness of the planets at all.”

Classified as probably not a substantial claim. May combine two claims.

Bowen states there is no evidence that anyone before Ptolemy noticed a variation in the size or brightness of any star, or thought such variation important.

“there is no evidence that anyone noticed a variation in the size or brightness of any star, or that they thought such a variation important”.(Bowen, 2002: 161).”

• cites Bowen, 2002: 161 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

It is impossible to see Venus in the middle of its retrograde motion because it is in conjunction with the Sun.

“it should not be difficult to realize (at least for scholars) that it is impossible to see Venus in the middle of its retrograde motion because it is in conjunction with the Sun.”

May combine two claims.

According to the same-sense epicycle and deferent model, the planets approach the Earth when they retrograde, and an increase of brightness would naturally be interpreted as a decrease of distance.

“One can easily show that according to homocentric spheres the planets cannot change its geocentric distance, and that according to (same-sense) epicycle and deferent model the planets approach the Earth when they retrograde and that an increase of brightness would be naturally interpreted as a decrease of distance that it is hard to resist to such an explanation.”

May combine two claims.

Simplicius and Pliny are both wrong.

“And they are both wrong.”

May combine two claims.

For the Sun, the change of speed is observable; the change of size due to change of distance is theoretical.

“This is another case of mingling theory with observation: the change of speed is observable; the change of size (due to the change of distance) is theoretical.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The author of the Ars Eudoxi papyrus claims that all total solar eclipses are annular.

“The author of the papyrus claims, therefore, that all total solar eclipses are annular.”

Probably not a substantial claim: may not pass S2 (checkable).

This is a case of theory-laden observation.

“Second, this is a fascinating case of theory-laden observation, which could be used for illustrating this idea in textbooks.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Plutarch, in On the Face in the Moon, said that even if the moon sometimes covers the sun entirely, a kind of light is visible about the rim which keeps the shadow from being profound and absolute.

“Plutarch, in his On the Face in the Moon, discussing why during a total solar eclipse the sky was not as dark as during night, said that “even if the moon, however, does sometimes cover the sun entirely, .a kind of light is visible about the rim which keeps the shadow from being profound and absolute.”(Cherniss & Helmbold, 1957: 122).”

• cites Cherniss & Helmbold, 1957: 122Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The evidence points in the opposite direction: the change of brightness during retrograde motion has been a theoretical observation-a fact first derived from the theory and then introduced in the set of phenomena that the theory successfully explained.

“Rather, the evidence points in the opposite direction: it seems that the change of brightness during retrograde motion has been a theoretical observation: i.e., a fact first derived from the theory and then introduced in the set of phenomena that the theory successfully explained.”

May combine two claims.

There are not enough elements to be certain that Ancient astronomers actually observed annular eclipses, because the Ancient observer cannot be expected to distinguish simply by observation an annular eclipse from a total-with-corona eclipse, and there is not enough data for identifying the particular eclipses mentioned in some ancient texts.

“There are not enough elements to be certain that Ancient astronomers actually observed annular eclipses, 11 because the Ancient observer cannot be expected to distinguish simply by observation an annular eclipse from a total-with-corona eclipse, and there is not enough data for identifying the particular eclipses mentioned in some ancient texts.”

• AssumptionRests on an assumption: The Ancient observer cannot be expected to distinguish simply by observation an annular eclipse from a total-with-corona eclipse.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

The values in Figure 4 are representative; they could vary from one synodic month to the next, but not significantly.

“These values are representative, they could vary from one synodic month to the next, but not significantly.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Proclus referred to annular and total eclipses just after his mention of the changes of sizes of the planets, in his list of phenomena.

“Proclus referred to annular and total eclipses just after his mention of the changes of sizes of the planets, in his list of phenomena.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Philostratus, in Life of Apollonius of Tyana, said that the death of the emperor had been previously announced by a remarkable portent in the heavens: the orb of the sun was surrounded by a wreath resembling a rainbow, but dimmed the sunlight.

“Philostratus, in the Life of Apollonius of Tyana, said that the death of the emperor had been previously announced by a “remarkable portent . in the heavens.The orb of the sun was surrounded by a wreath which resembled a rainbow, but dimmed the sunlight.”(VIII, chap. 23;1912: 387).”

• cites VIII, chap. 23;1912: 387Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

The Ars Eudoxi papyrus states that solar eclipses can never be total but must remain at most annular, because the apparent size of the Sun is always greater than the apparent size of the Moon.

“The papyrus refers that solar eclipses can never be total but must remain at most annular, because the apparent size of the Sun is always greater than the apparent size of the Moon (Tannery, 1893: 292-293; Blass, 1887: 23-24; see also Neugebauer, 1975: 668, 688-687).”

• cites Tannery, 1893Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Blass, 1887Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Neugebauer, 1975 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The acknowledgment of changes of lunar apparent size and distance could have been used against Eudoxus's homocentric spheres and in favor of epicycles and deferents.

“This, in turn, could have been used against Eudoxus's homocentric spheres and in favor of epicycles and deferents.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

There is no agreement about which historical eclipse Plutarch is referring to, but it seems clear that he is describing a real eclipse.

“There is no agreement about to which historical eclipse Plutarch is referring, but it seems clear that he is describing a real eclipse.12”

Classified as probably not a substantial claim. May combine two claims.

If we interpret a change of apparent size as a change in distance, we can conclude that the Moon changes its distance from the Earth.

“If we interpret a change of apparent size as a change in distance, we can conclude that the Moon changes its distance from the Earth.”

May combine two claims.

The change in apparent size of the Sun could not be detected by the naked eye, because the change is very small (variation between maximum and minimum distance of 0.016) and mainly because the brightness of the Sun would prevent any clear observation of its circumference.

“This change in size could not be detected by the naked eye, not only because the change is very small (a variation between maximum and minimum distance of 0.016foot_6 ), but mainly because the brightness of the Sun would prevent any clear observation of its circumference.”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

Usually, when the eclipse is total, the Moon covers the totality of the Sun, showing both luminaries have precisely the same apparent size.

“Usually, when the eclipse is total, the Moon covers the totality of the Sun, showing that both luminaries have precisely the same apparent size.”

May combine two claims.

The homocentric spheres cannot make Venus and Mars have retrograde loops at the correct period, while the same-sense epicycle and deferent model can.

“First, while the homocentric spheres cannot make Venus and Mars have retrograde loops at the correct period, this is possible for the (same-sense) epicycle and deferent model, which turns to be a very strong empirical reason.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

There are ten more annular eclipses during these seven centuries that were visible from somewhere in Greece or close to it.

“There are ten more annular eclipses during these seven centuries that were visible from somewhere in Greece or close to it.”

May combine two claims.

Sometimes there are annular eclipses, i.e., some rim of the Sun shines around the Moon, implying that in those eclipses the apparent size of the Moon is a bit smaller than the apparent size of the Sun.

“Sometimes, however, there are annular eclipses, i.e., some rim of the Sun shines around the Moon, implying that in those eclipses, the apparent size of the Moon is a bit smaller than the apparent size of the Sun.”

May combine two claims.

Athens saw, from its foundation (508 BCE) to the death of Ptolemy, two annular eclipses, one in 478 BCE and the other in 164 CE, leaving more than 640 years without annular eclipses.

“Athens saw, from the date of its foundation (508 BCE) to the death of Ptolemy, as well two annular eclipses, one in 478 BCE and the other in 164 CE, leaving more than 640 years without annular eclipses.10”

May combine two claims.

Pliny affirms that the outer planets are seen less bright at the middle of their retrograde motion, exactly as the opposite-sense epicycle and deferent model asserts.

“On the other hand, Pliny affirms that the outer planets are seen less bright at the middle of their retrograde motion, exactly as the theory he is defending, the opposite-sense epicycle and deferent model, asserts.”

• cites PlinyNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

The first eclipse unequivocally asserted to have been annular was the eclipse of April 9, 1567 observed by Clavius at Rome.

“According to Grant (1855: 371) the first eclipse that”

• cites Grant (1855: 371)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Ptolemy's Almagest implies that annular eclipses are impossible, because the lunar and solar apparent sizes are the same only when the Moon is at its greatest distance from the Earth.

“Actually, according to Ptolemy, the lunar and solar apparent sizes are the same only”

• cites Almagest V, 14Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Toomer, 1998: 252Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

For the Moon, changes of apparent size are highly more significant, with a variation of 0.157 between maximum and minimum apparent size, around 10 times bigger than solar variation.

“First of all, its changes of apparent size are highly more significant, with a variation of 0.157 between maximum and minimum apparent size, around 10 times bigger than solar variation.9”

Probably not a substantial claim: may not pass S3 (load-bearing).

Proclus also says that some astronomers reported annular eclipses.

“Proclus also says that”

• cites Proclus, Hyp.I,19Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Manitius, 1909: 10,11Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Grant affirms that Philostratus is describing a solar total-with-corona eclipse, but it is really doubtful even whether he is talking about an eclipse or not.

“Grant (1852: 376-377) affirms that Philostratus is describing a solar total-with-corona eclipse, but it is really doubtful even whether he is talking about an eclipse or not (see Newton, 1970: 114).”

• cites Grant, 1852: 376-377Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Newton, 1970: 114Not checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Even if annular eclipses are more common than total eclipses, they are not too frequent and one particular city might not have seen an annular eclipse for centuries.

“Even if annular eclipses are more common than total eclipses, they are not too frequent and one particular city might not have seen an annular eclipse for centuries.”

May combine two claims.

The same-sense epicycle and deferent system was not conceived for explaining the change of brightness, and nevertheless it successfully explains the changes of brightness of Mars.

“Finally, this case could be used against some scientific realism positions, because the (same-sense) epicycle and deferent system was not conceived for explaining the change of brightness, and nevertheless it successfully explains the changes of brightness of Mars.”

May combine two claims.

None of the three candidate eclipses for Plutarch's reference was an annular eclipse, so Plutarch must have seen a total eclipse.

“Moreover, according to NASA Eclipse web site (http://eclipse.gsfc.nasa.gov/SEcat5/SE1501-1600.html), none of the three candidates was an annular eclipse, so he must have seen a total eclipse.”

• cites NASA Eclipse web siteNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

There are some testimonies in Ancient times that astronomers were probably aware of annular eclipses.

“In addition, there are some testimonies in Ancient times that astronomers were probably aware of annular eclipses.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Sosigenes is usually attributed with the observation of an annular eclipse.

“Sosigenes is usually attributed with the observation of an annular eclipse (Neugebauer, 1975: 104, n. 4;668).”

• cites Neugebauer, 1975: 104, n. 4;668 sourceNot checked — no full text of the source

May combine two claims.

Up to the time discussed, there is only one ancient testimony affirming that all total eclipses are annular, and two saying that annular eclipses are impossible.

“So far, thus, there is only one testimony affirming that all total eclipses are annular, and two saying that annular eclipses are impossible.”

May combine two claims.

One cannot be sure that the change in apparent size of the Moon played a role as an objection against homocentric spheres, but there is no doubt that annular eclipses were an attested fact in Ancient times.

“One cannot be sure, for there is no testimony (except, again, that of Simplicius himself), that the change in the apparent size of the Moon played a role as an objection against homocentric spheres, but at least there is no doubt that annular eclipses were an attested fact in Ancient times.”