Pt2 The Celestial Spheres According to Maimonides’ Mishneh Torah (Laws of Foundations of the Torah 3:1-9)
This is the second and final part of a two-part series. Part 1 is here; the outline for the series can be found there.
Division of the Ninth Sphere Into the Zodiac Constellations
The ninth sphere1 was divided by “early sages”2 into twelve parts, naming each part after the star patterns visible beneath it.
These are the twelve signs of the zodiac (מזלות): Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces.3
גלגל התשיעי, שהוא מקיף את הכל, חלקוהו החכמים הקדמונים לשנים עשר חלקים.
כל חלק וחלק העלו לו שם, על שם צורה זו שתראה בו מן הכוכבים שלמטה ממנו שהם מכונים תחתיו.
והם המזלות, ששמותם
טלה.
שור.
תאומים.
סרטן.
אריה.
בתולה.
מאזנים.
עקרב.
קשת.
גדי.
דלי.
דגים
The ninth sphere, which encompasses all the others, was divided by the Sages of the early generations into twelve sections.
They gave each of these sections a name, based on the shapes that appeared to be formed by the stars below it which correspond to it.
These are the mazalot, which are called
the lamb,
the ox,
the twins,
the crab,
the lion,
the virgin,
the scales,
the scorpion,
the bow,
the goat,
the bucket,
and the fish.
Star Movements, Sizes, and Ancient Divisions
Part 1
The ninth sphere has no divisions, shapes, or celestial bodies (=planets/stars) of its own; instead, the larger stars in the eighth sphere appear in specific forms or resemble them.
These twelve forms corresponded to divisions at the time of the biblical Flood (המבול) and received their names then,4 but their positions have since shifted slightly due to the slow movement of stars in the eighth sphere.5
גלגל התשיעי עצמו אין בו לא חלוקה, ולא צורה מכל הצורות האלו, ולא כוכב.
אלא בחבור הכוכבים שבגלגל השמיני הוא שיראה בכוכבים גדולים שבו תבנית הצורות האלו או קרוב מהן.
ואלו השנים עשר צורות לא היו מכונות כנגד אותן החלקים אלא בזמן המבול,
שאז העלו להן שמות אלו,
אבל בזמן הזה, כבר סבבו מעט.
לפי שכל הכוכבים שבגלגל שמיני, כלם סובבים כמו השמש והירח, אלא שהן סובבין בכבדות.
The ninth sphere itself has no division, nor does it possess any of these shapes or any stars.
Rather, the larger stars of the constellations of the eighth sphere are seen in the shape of these forms, or [in a form] resembling them.
These twelve forms corresponded to these divisions only at the time of the Flood
and then, they were given these names.
However, at present, they have already moved slightly,
because all the stars in the eighth sphere move, as the sun and the moon do. It is just that [these stars] move more slowly.
Part 2
These stars (in the 8th sphere) take about 70 years to cover the distance that the sun or moon travels in one day.
Among visible stars, some are smaller than Earth, while others are much larger.
Earth is approximately 40 times larger than the moon, while the sun is about 170 times larger than Earth, making the moon about 1/6800th the size of the sun.
No other star is as large as the Sun or as small as Mercury, the planet in the second sphere.6
וחלק שיתהלך השמש והירח כנגדו ביום אחד, ילך כנגדו כל כוכב מהן בקרוב משבעים שנה
כל הכוכבים הנראים,
יש מהן כוכבים קטנים -- שהארץ גדולה מאחד מהן.
ויש מהן כוכבים גדולים -- שכל אחד מהן גדול מן הארץ כמה פעמים.
והארץ גדולה מן הירח כמו ארבעים פעמים.
והשמש גדולה מן הארץ כמו מאה ושבעים פעמים.
נמצא: הירח אחד מששת אלפים ושמונה מאות מן השמש, בקרוב.
ואין בכל הכוכבים כוכב גדול מן השמש, ולא קטן מכוכב שבגלגל השני
It would take any of these stars approximately seventy years to move the [same] distance which the sun and the moon move in one day.
[Among] all the stars we see
are small ones which the Earth surpasses in size
and large ones which are several times larger than the Earth.
Our Earth is approximately 40 times larger than the moon,
and the sun is approximately 170 times larger than the Earth.
Thus, the moon is approximately one 6800th the size of the sun.
None of the other stars is as large as the sun, nor is one as small as [the planet] Kochav, in the second sphere.
Consciousness of Spheres and Celestial Bodies
Celestial bodies (=planets/stars) and spheres possess intellect (דעה / השכל) and a soul (נפש), praising their Creator according to their level.
They are alive (חיים) and sentient, aware7 of God, themselves, and the angels above them. “Each one praises (משבחים) and glorifies (מפארים) their Creator (יוצרם) as the angels do.”
The intellect (דעת) of celestial bodies and celestial spheres surpasses human understanding but is less than that of angels.
כל הכוכבים והגלגלים כלן בעלי נפש ודעה והשכל הם.
והם חיים ועומדים, ומכירין את מי שאמר והיה העולם.
כל אחד ואחד לפי גדלו ולפי מעלתו משבחים ומפארים ליוצרם כמו המלאכים.
וכשם שמכירין הקדוש ברוך הוא, כך מכירין את עצמן, ומכירין את המלאכים שלמעלה מהן.
ודעת הכוכבים והגלגלים מעוטה מדעת המלאכים, וגדולה מדעת בני אדם
All the stars and spheres possess a soul, knowledge, and intellect.
They are alive and stand in recognition of the One who spoke and [thus brought] the world into being.
According to their size and level, each one praises and glorifies their Creator as the angels do.
Just as they are aware of the Holy One, blessed be He, they are also aware of themselves and of the angels which surpass them.
The knowledge of the stars and the spheres is less than the knowledge of the angels, but greater than that of men.
Appendix #1 - The Angelic Hierarchy (MT, Laws of Foundations of the Torah, 2:7)
Mishneh_Torah%2C_Foundations_of_the_Torah.2.7
Maimonides states that angels are categorized into a hierarchy of ten levels, as follows:
Holy Living Creatures (Hayyot) - The highest level, situated just below God (האל) and the Throne of Glory (כסא הכבוד), representing unparalleled closeness to God.8
Malakhim
Sons of God (B’nei Elohim)
Ishim - The lowest level, consisting of angels who communicate with prophets and are perceived in prophetic visions.9 Their name, meaning "men," signifies their proximity to human understanding.
Each name reflects the corresponding spiritual rank, with Hayyot at the pinnacle and Ishim closest to human cognition.10
שנוי שמות המלאכים על שם מעלתם הוא.
ולפיכך נקראים חיות הקדש, והם למעלה מן הכל
ואופנים
ואראלים
וחשמלים
ושרפים
ומלאכים
ואלהים
ובני אלהים
וכרובים
ואישים.
כל אלו עשרה השמות -- שנקראו בהן המלאכים -- על שם עשר מעלות שלהן הן,
ומעלה שאין למעלה ממנה -- אלא מעלת האל ברוך הוא -- היא מעלת הצורה שנקראת חיות.
לפיכך נאמר בנבואה שהן תחת כסא הכבוד.
ומעלה עשירית היא מעלת הצורה שנקראת אישים
והם המלאכים המדברים עם הנביאים, ונראים להם במראה הנבואה.
לפיכך נקראו "אישים", שמעלתם קרובה למעלת דעת בני אדם
The different names with which the angels are called reflect their [spiritual] levels (מעלתם).
Thus, they are called: the Holy Living Creatures (Hayyot), who are above all the others;
and Ophanim;
the Erelim;
the Hashmalim;
and Seraphim;
the Malakhim;
the Elohim;
the Sons of God (B’nei Elohim);
the Cherubim;
the Ishim
These ten names which are used to refer to the angels reflect their ten [different spiritual] levels.
The level above which there is no higher level except that of God (האל), blessed be He, is that of the form called “Living Creatures” (Hayyot).
Therefore, the prophets state that they [=the Living Creatures] are below the Throne of Glory.
The tenth [and lowest] level is that of the form called Ishim.
They are the angels who communicate with the prophets and are perceived by them in prophetic visions.
Therefore, they are called “Ishim” (“men”), because their level is close to the level of human knowledge.
Appendix #2 - The Complexity of Lunar Calculations and the Universality of Astronomical Truth (MT, Laws of Sanctification of the New Month, 17:23-24)
Mishneh_Torah%2C_Sanctification_of_the_New_Month.17.23-24
The Challenge of Lunar Calculations
The moon's irregular (עקלקלות) orbit (מעגלותיו) requires complex calculations, involving frequent adjustments through additions and subtractions. These refinements ensure accuracy while avoiding excessively complicated methods.
The talmudic sages highlighted this complexity by stating (Rosh_Hashanah.25a.8): "The sun knows its setting; the moon does not know its setting," and (ibid., 25a.7) “Sometimes [the moon] comes by a long [path] and sometimes it comes by a short [one]“ emphasizing the moon's unpredictable nature.
Consequently, the arc of sighting for the moon varies, sometimes being long and sometimes short, reflecting the necessary adjustments.
וכבר ראית מן המעשים האלו, כמה חשבונות יש בו, וכמה תוספות, וכמה גרועין, אחר שיגענו הרבה.
עד שהמציאנו דרכים קרובים שאין בחשבונם עמק גדול.
שהירח עקלקלות גדולות יש במעגלותיו.
ולפיכך אמרו חכמים
(תהילים קד יט): "שמש ידע מבואו"
ירח לא ידע מבואו.
ואמרו חכמים: פעמים בא בארכה, פעמים בא בקצרה.
כמו שתראה מחשבונות אלו
שפעמים תוסיף, ופעמים תגרע
עד שתהא קשת הראיה.
ופעמים תהיה קשת הראיה ארוכה, ופעמים קצרה
כמו שבארנו
From all the above, you have seen the extent of the calculations, and the additions and the subtractions that required much effort
to present a method that comes close [to being exact] without necessitating extremely complicated calculations.
[This process is necessary] because the moon has major incongruities in its orbit.
In this vein, our Sages said,
"'The sun knows the time of its setting';
the moon does not know the time of its setting."
Similarly, our Sages said, "At times, its setting is prolonged, and at times, it is hastened."
This is reflected in these calculations, where at times it is necessary to add, and at times it is necessary to subtract
until we arrive at the arc of sighting.
And as explained,
at times the arc of sighting is great, and at times it is small.
Sources of Astronomical Wisdom
The foundations of these calculations lie in the sciences (חכמת) of seasons (תקופות) and geometry (גימטריות), extensively documented by Greek scholars (חכמי יון) in books that remain accessible today.
Texts authored by Jewish sages (חכמי ישראל) during the era of the Prophets, particularly from the tribe of Yissachar,11 have been lost.
וטעם כל אלו החשבונות
ומפני מה מוסיפים מנין, זה ומפני מה גורעין
והיאך נודע כל דבר ודבר מאלו הדברים
והראיה על כל דבר ודבר
היא חכמת התקופות והגימטריות
שחברו בה חכמי יון ספרים הרבה
והם הנמצאים עכשו ביד החכמים.
אבל הספרים שחברו חכמי ישראל — שהיו בימי הנביאים מבני יששכר — לא הגיעו אלינו.
The rationales for all these calculations,
and the reasons why this number is added, and why that subtraction is made,
and how all these concepts are known,
and the proofs for each of these principles
are [the subject] of the wisdom of astronomy and geometry,
concerning which the Greeks wrote many books.
These texts are presently in the hands of the sages.
The texts written by the Sages of Israel in the age of the prophets from the tribe of Yissachar have not been transmitted to us.
Reliance on Evidence, Not Authority
The validity of these calculations rests on clear, indisputable proofs, making their origin—whether from prophets or non-Jews12—irrelevant.
Once a concept's rationale and truth are established through rigorous evidence, reliance shifts from the authority of its source to the veracity of its reasoning and proof.13
ומאחר שכל אלו הדברים בראיות ברורות הם, שאין בהם דפי
ואי אפשר לאדם להרהר אחריהם,
אין חוששין למחבר,
בין שחברו אותם נביאים, בין שחברו אותם האמות.
שכל דבר שנתגלה טעמו, ונודעה אמתתו, בראיות שאין בהם דפי
אנו סומכין על זה האיש שאמרו או שלמדו
על הראיה שנתגלתה והטעם שנודע
Nevertheless, since these concepts can be proven in an unshakable manner,
leaving no room for question,
the identity of the author is of no concern,
be he a prophet or a gentile,
For a matter whose rationale has been revealed and has proven truthful in an unshakable manner,
we do not rely on [the personal authority of] the individual who made these statements or taught these concepts,
but on the proofs he presented and the reasons he made known.
Referred to as Primum Mobile in the Greek astronomical tradition, as mentioned in my note in Part 1.
החכמים הקדמונים.
From a critical historical perspective, this was the Babylonians, see Wikipedia, “Zodiac”, section “Early history”:
Around the end of the fifth century BC, Babylonian astronomers divided the ecliptic into 12 equal "signs", by analogy to 12 schematic months of 30 days each.”)
Some of these zodiac names are mentioned in the Talmud, with the same Hebrew names used by Maimonides here, see my “Pt2 Celestial Phenomena: Comets and Constellations in the Talmud (Mishnah Berakhot 9:2; Berakhot 58b-59a)”, and my footnote there, f. 7.
In traditional Jewish chronology, the biblical Flood is dated to around 2105 BCE. [See the table “Comparative Jewish Chronology”, row “Great Deluge (in time of Noah)”, in Wikipedia, “Traditional Jewish chronology”, section “Josephus's timeline of events”]
However, from a critical historical perspective, the divisions were made by the Babylonians much later than that; around 400 BCE, see my earlier footnote.
From a scientific perspective, this shift is called the precession of the equinoxes, an astronomical phenomenon caused by the gradual wobble of Earth's axis, which changes the apparent positions of the stars over thousands of years.
Comparison of these measurements with modern scientific measurements:
Stars in the eighth sphere move more slowly than the sun and moon, taking about 70 years to cover the same daily distance
This refers to the idea of the fixed stars in the eighth sphere having a much slower apparent motion compared to the sun and moon. The "70 years" estimate does not align with the scientific calculation; the slow motion is due to the precession (mentioned in my previous note); this is a 26,000-year cycle).
The Earth is 40 times larger than the moon
The Earth’s diameter is about 3.7 times that of the moon, and its volume is roughly 50 times greater.
The sun is 170 times larger than the Earth
The sun’s diameter is about 109 times that of Earth, and its volume is approximately 1.3 million times greater.
The moon is 1/6800th the size of the sun
The moon’s diameter is about 1/400th that of the sun, and its volume is significantly smaller than 1/6800th. So significant underestimate; was logically derived from previous ratios.
No star is as large as the sun, nor as small as Mercury
Many stars are much larger than the sun. For example, Betelgeuse and UY Scuti are vastly larger.
The claim about Mercury being the smallest celestial body is incorrect; there are smaller celestial objects like some moons and dwarf planets.
מכירין - literally: “recognizing”.
Maimonides’ statement here is based on the Talmudic passage analyzed in my recent piece here, section “Part 3: the Ophanim, Seraphim, Holy Living Creatures (Ḥayyot), ministering angels, and the Throne of Glory”.
On Prophecy: Its Nature, Preparation, and the Unparalleled Prophecy of Moses, see MT, Laws of Foundations of the Torah, Chapter 7.
See there (ibid., 7:6), especially, how for all prophets' other than Moses, the medium of prophecy is via angels, manifesting as metaphors (משל) or allegories/riddles (חידה; as opposed to Moses, who received direct communication from God, without intermediaries or metaphors):
כל הנביאים על ידי מלאך.
לפיכך רואים מה שהם רואים במשל וחידה.
[Divine insight is bestowed upon] all the [other] prophets through the medium of an angel.
Therefore, they perceive only metaphoric imagery and allegories
I made adjustments to here the default Sefaria translation, as needed.
Compare the various hierarchies listed in Wikipedia, “Angels in Judaism”, section “Angelic hierarchy”.
בני יששכר.
See Hebrew Wikipedia, שבט יששכר, section השבט במדרש, my translation:
The members of the tribe were renowned for their great wisdom and became particularly famous for their knowledge of the "Secret of Intercalation" (סוד העיבור; i.e. the intercalation of the Hebrew calendar). Rava (in the Talmud) praises the wisdom of the members of the tribe and their ability "to establish halakhic rulings in accordance with the law" (אסוקי שמעתתא אליבא דהלכתא):
"You will not find a Torah scholar (צורבא מרבנן) who teaches unless he comes from the tribe of Levi or the tribe of Issachar... Issachar, as it is written (1 Chronicles 12:33): 'And of the sons of Issachar, those with understanding of the times (יודעי בינה לעיתים), to know what Israel ought to do.'”
The author of the book Sefer HaYuchasin also mentions in Chapter 6 that one of the books lost to the Jewish people is The Book of Astronomy (ספר התכונה) by the Sons of Issachar, along with The Book of Remedies (ספר הרפואות) by King Solomon, and others.
According to the Blessing of Moses and the Midrash, the tribes were divided between Torah study (Issachar) and earning a livelihood (Zebulun). This division gave rise to the Issachar-Zebulun Agreement (הסכם יששכר וזבולון), a partnership between a financially capable individual and a poor Torah scholar.
Compare Sarah Pessin, “The Influence of Islamic Thought on Maimonides”, in Stanford Encyclopedia of Philosophy, First published Thu Jun 30, 2005; substantive revision Wed May 28, 2014:
Sensitive to this contextual approach, Pines begins his edition and translation of the Guide with a consideration of myriad Islamic (and Greek) philosophical sources, and while Hyman notes that “it should not…be inferred that medieval Jewish philosophy was a branch of Islamic philosophy,” he goes on to note that “by and large Jewish philosophy was a continuation of the philosophy which flourished in the Islamic world” (Hyman 1996, 678-679).
Sensitive to the impact of the Islamic context, Stroumsa reminds us that “…Maimonides was an avid reader, who took pains to remain abreast of contemporary scholarship in general and philosophical scholarship in particular… ” (Stroumsa 2009, 173, n. 69), and “that Maimonides, who only rarely cited his sources, read all he could find, and that he had no qualms about perusing the theological or legal works of non-Jews…” (Stroumsa 2009, xii).
Responding to Davidson’s more conservative approach to reading sources into the text, Stroumsa adds, “Maimonides’ philosophical erudition was no doubt far broader than would seem to be the case only on the basis of his explicit references. We must therefore be alert to the possibility that Maimonides’ words reflect, whether by way of acceptance or by way of reaction and criticism, his knowledge of the works of thinkers whose names are not explicitly mentioned” (Stroumsa 2009, 24-5).