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The first several chapters of Mishneh Torah (ch.3-4) include some pseudo-scientific (Aristotelian?) passages, seemingly unrelated to practical Halacha, for example,

"The celestial spheres are called heaven, firmament, habitation and nebula, and there are nine such spheres; ... the spheres are pure and transparent as glass or sapphire, therefore the stars which are in the eighth sphere, seem to be beneath the first sphere."

"All of these spheres which encircle the universe, are round as a globe, and the earth is suspended in the center... All of the stars and spheres are beings, endowed with a soul, intelligence and understanding; they continue a purposeful life and are conscious of the existence of Him Who spoke and the universe sprang forth. "

"These four elements, namely: fire, air, water and earth, are the elements of all the creatures beneath the expanse; all that be whether of man, beast, fowl, creeping thing, fish, vegetation, minerals, precious stones, pearls, structural stones, mountains and glaciers, the body of each and every one is the joint issue of these four elements. "

Why all those explanations are needed in a Halachic compendium? What Biblical Mitzvahs do they relate to?

At first, I thought it to be a part of the Mitzvah of knowing Hashem, but the end of the second chapter suggests that its details are explained only in the first two chapters.

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The Rambam addresses the reason for the first 4 chapters at the end of chapter 4:

וְעִנְיְנֵי אַרְבָּעָה פְּרָקִים אֵלּוּ שֶׁבְּחָמֵשׁ מִצְוֹת הָאֵלּוּ הֵם שֶׁחֲכָמִים הָרִאשׁוֹנִים קוֹרְאִין אוֹתוֹ פַּרְדֵּס כְּמוֹ שֶׁאָמְרוּ אַרְבָּעָה נִכְנְסוּ לַפַּרְדֵּס. וְאַף עַל פִּי שֶׁגְּדוֹלֵי יִשְׂרָאֵל הָיוּ וַחֲכָמִים גְּדוֹלִים הָיוּ לֹא כֻּלָּם הָיָה בָּהֶן כֹּחַ לֵידַע וּלְהַשִּׂיג כָּל הַדְּבָרִים עַל בֻּרְיָן. וַאֲנִי אוֹמֵר שֶׁאֵין רָאוּי לְטַיֵּל בַּפַּרְדֵּס אֶלָּא מִי שֶׁנִּתְמַלֵּא כְּרֵסוֹ לֶחֶם וּבָשָׂר. וְלֶחֶם וּבָשָׂר הוּא לֵידַע הָאָסוּר וְהַמֻּתָּר וְכַיּוֹצֵא בָּהֶם מִשְּׁאָר הַמִּצְוֹת. וְאַף עַל פִּי שֶׁדְּבָרִים אֵלּוּ דָּבָר קָטָן קָרְאוּ אוֹתָן חֲכָמִים שֶׁהֲרֵי אָמְרוּ חֲכָמִים דָּבָר גָּדוֹל מַעֲשֵׂה מֶרְכָּבָה וְדָבָר קָטָן הֲוָיוֹת דְּאַבַּיֵּי וְרָבָא. אַף עַל פִּי כֵן רְאוּיִין הֵן לְהַקְדִּימָן. שֶׁהֵן מְיַשְּׁבִין דַּעְתּוֹ שֶׁל אָדָם תְּחִלָּה. וְעוֹד שֶׁהֵם הַטּוֹבָה הַגְּדוֹלָה שֶׁהִשְׁפִּיעַ הַקָּדוֹשׁ בָּרוּךְ הוּא לְיִשּׁוּב הָעוֹלָם הַזֶּה כְּדֵי לִנְחל חַיֵּי הָעוֹלָם הַבָּא. וְאֶפְשָׁר שֶׁיְּדָעֵם הַכּל קָטָן וְגָדוֹל אִישׁ וְאִשָּׁה בַּעַל לֵב רָחָב וּבַעַל לֵב קָצָר:

The subjects in these four chapters of these five commandments, are the same which the early sages speak of as Vineyard, saying: "Four entered the vineyard" (Haggigah 14), who, though great men in Israel and great scholars, not all of them had the intellectual power to know and grasp all these matters clearly; and I say that no one is deserving to promenade in the Vineyard unless he be filled with intellectual bread and meat, that is to say: one must know what is forbidden and what is permitted and similar to these of the rest of the commandments. And, although these matters were pronounced by the sages as of lesser importance, for they said: "A great matter is the Works of the Chariot, and a small matter is the controversies of Abyia and Raba,3 Nevertheless, they have precedence as a study because they commence to compose man's mind; moreover, they are the store of great good which the Holy One, blessed is He, hath provided for the social existence of this world, so that the life of the world to Come may also be inherited, and be accessible to all, little and great, men and women, to one of broad understanding as well as to one of lesser understanding.

In simple english: Rambam believed these chapters were the subject matter of Pardes (In his terminology this is synonomous with Maaseh Bereshit and Maaseh Merkavah). Leaving aside whether or not Rambam was correct, this is his stated reason for including these chapters in Yesodei Hatorah. Since Rambam viewed this as part of Maaseh Bereshit (ch. 3-4) and Maaseh Merkavah (ch. 1-2), he views them all as falling under knowing Hashem. For a greater understanding of precisely how Rambam understood how this information leads to knowing Hashem, I recommend reading the relevant passages in Moreh Nevuchim.

The five commandments that he is refering to as the purpose of the first 4 chapters, according to the anonymous commentator, are:

חמש המצות הם. לידע שיש שם אלוה. ושלא לעלות במחשבה שיש אלוה זולתו. וליחדו. ולאהבו. וליראה ממנו:

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