ולמשול ביום ובלילה. "and to rule by day and by night.⁠" The sun rules by day, the moon at night. Remember that God not only enabled these luminaries to provide light, but He also equipped them with the ability to exercise dominion over the creatures in the "lower" regions, i.e. they can cause damage to creatures on earth or their influence may enable creatures on earth to continue to exist. The sun contributes to our continued existence by means of its power to promote growth by day, whereas the moon has similar influence on certain plants which grow at night. Moreover, the moon controls the ebb and tide of the oceans exercising influence over wells and fountains.

From a kabbalistic point of view the words למשול ביום ובלילה also are an allusion to the powers which guide these two great luminaries in turn, i.e. the signs of the zodiac. These exercise a great deal of power over the fate of mankind unless countermanded by God' s personal intervention, השגחה פרטית.
You will note that the two daily communal offerings presented on the altar of the Temple by the priests on a daily basis corresponded to the powers exercised by sun and moon by day and by night respectively.(compare Numbers 28,4) The Torah writes in Deut. 4,19 אשר חלק להם ה' אלוהיך אותם לכל העמים, "which the Lord your God has assigned to all the (other) nations.⁠" This is a reference to the fate of the Gentiles who are governed by forces of the planetary system (and accounts for the preoccupation of people with astrology). Instead, the Jewish people offer two daily sacrifices in order to neutralize these forces presided over by sun and moon. The Torah continues in the same passage we quoted from Deuteronomy 4,19 to contrast the factors governing the fates of the Jews by writing (verse 20) ואתכם לקח ה' ויוצא אתכם מכור הברזל ממצרים להיות לו עם נחלה כיום הזה. "You, however, the Lord your God took and removed you from the iron crucible, from Egypt, in order to for you to become a people for Him, and inheritance as of this day.⁠" This verse sums up the difference between the forces governing the fates of the Gentiles and God's personal providence in supervising the fate of the Jewish people. When the Torah (Deut. 17,3) wrote the words אשר לא ציויתי "which I did not command,⁠" this referred to the sun and the moon whom God did not command to exercise this control over the people's fates. He did however, command the צבא השמים, "the host of the heaven", i.e. the stars "the guiding forces of sun and moon" to exercise such control. I plan to write more about this in my commentary on the respective verse in Deuteronomy 17,3.
This also explains to you the reason why fasting is effective in warding off negative influences on man. It is similar to an animal sacrifice and requires that one prepares for it beforehand, similar to a sacrificial animal which has to be checked out prior to its becoming offered on the altar. The act of fasting reduces the person's blood, fat and flesh, and the time (late afternoon) when one must officially prepare to observe a fast is the one when both sun and moon exercise their control on earth jointly. This is why Shmuel said (Taanit 12) that any fast-day which the person who observes it did not so designate before nightfall on the previous day is useless. He also said that any fast-day which did not include a sunset is not called a fast-day. Conversely, the tears shed by the supplicant as part of his fast also rank as part of an animal sacrifice as the latter was usually accompanied by a libation of water. We have a long-standing tradition that the gates of tears are never locked, i.e. that even when God has deliberately turned aside from our entreaties because of our sins, He did not turn away from our tears (Berachot 32). Tears are a derivative of the power of water, which itself is a derivative of the emanation חסד, "love" which is on the right (positive) side of the diagram representing the ten emanations. [The "left" side represents negative spiritual attributes. Ed.] The "right" side of God's emanations is always ready to welcome repentant sinners. This is such an important principle that everyone would do well to keep it in mind.

ולהבדיל בין האור ובין החשך, "and to separate between the light and between the darkness.⁠" The verse mentions three distinct functions of these luminaries. 1) To give light; 2) to exercise dominion; 3) to provide separation. God assigned three lofty purposes to these luminaries. It is clear, of course, that behind these apparent causes of what moves the universe is the real Ruler, i.e. the Creator. It is this idea which is expressed in Isaiah 55,10 where the prophet speaks of God as ונתן זרע לזורע ולחם לאוכל "and provides seed for the farmer and bread for those who eat it.⁠" Although the prophet in that verse describes the rain, it is clear that there is a more basic force behind the rain. What the verse tells us is that the rain is an instrument of God at work just as the sun and the moon are manifestations of God their Creator at work controlling His universe This idea is elaborated on in Hoseah 2, 23-24 where the prophet writes concerning the future: אענה נאום ה' אענה את השמים והם יענו את הארץ.והארץ תענה את הדגן ואת התירוש ואת היצהר והם יענו את יזרעל, "I will respond declares the Lord, I will respond to the sky, and it shall respond to the earth, and the earth shall respond with new grain and wine and oil, and they shall respond to Jezreel.⁠" The thrust of the whole verse it that although these various forces of nature all contribute their best to successful life on earth and they each fulfill their appointed task, they do not possess independent powers but are agents of the Creator without whose input none of this would take place. Similarly here. The Torah describes the visible functions of the luminaries; this does not mean that God had abrogated His power in favor of His agents. Had He done so, these luminaries would indeed be deities as, unfortunately, many idol worshipers believe. It is precisely in order to forestall such mistaken ideas that the Torah warns us in Deut. 4,19 "lest you raise your eyes heavenwards and behold the sun, the moon and the stars, the heavenly hosts and be lured into bowing down to them or serving them.⁠" Had God wanted to invest these agents with independent powers the Torah would have described this by having God order them" האירו, משלו, הבדילו! "provide light!, exercise dominion! Establish separations!

You may recall that the sages of Israel had to write to King Talmai that the meaning of the words חלק להם אשר (compare the quote of Deut. 4,19. 4,19) does not mean that they have the powers of deities but that their function is merely to provide light (compare Megillah 9). This was a warning to the Gentiles not to be misled into paganism through the wording of the Torah. [King Talmai of Egypt third century BCE forced 72 Jewish scholars to translate the Torah while sitting in separate cubicles each unable to consult with the other. According to tradition they miraculously rendered the Torah into Greek using exactly the same words. Ed.] The word חלק could otherwise have been understood by Talmai and other Gentiles as meaning that God "engaged in power-sharing" with such heavenly bodies as the sun the moon and the stars. The fact is, however, that God did give the Gentiles the choice to either serve Him or to serve what they perceived to be deities. This did not, however, mean that He ever agreed that these phenomena were deities or had separate, independent powers. The Jewish people were not given such a choice at all. Proof that this is so is found in Ezekiel 20,33 where the prophet had debated this issue with Jews who had felt abandoned by God in exile claiming their "Master" had sold them, i.e. "freed them from the obligation to serve Him.⁠" Ezekiel threatened them saying חי אני נאום ה' אלוהים אם לא ביד חזקה ובזרוע נטויה ובחמה שפוכה אמלוך עליכם .⁠"As I live, says the Lord God, with a strong hand and an outstretched arm and with outpoured fury will I rule over you.⁠"

The reason the luminaries were created (made functional) on the fourth day is because the fourth day is precisely in the middle of the seven days of the מעשה בראשית our chapter deals with. Another reason is that the sun and moon undergo four changes daily in the periods of time allocated to their respective dominance. [Both day and night are divided into four time-periods each known as a משמרת in the language of our sages. Ed.] Similarly, the month [period of lunar orbit (roughly)] is divided into four weeks. The solar year is divided into four seasons. For these and other reasons it was appropriate that the functions of sun and moon commenced on the fourth day of creation.
They had to be created following the emergence of vegetation on earth which became manifest on the third day so that we would have incontrovertible proof that God had preceded creation and not vice versa. If, for instance, the Torah would have reported the directive: "let there be luminaries" on the third day and the directive: "let the earth produce herbs, etc.⁠" on the fourth day, we would have concluded that not God but the celestial forces had been responsible for the universe as we know it. This concept was known in ancient times as קדמת העולם, "the eternal existence of the world.⁠" People would have had reason to believe that the existence of vegetation had been due to the respective influence of sun and moon on the ability of plants to grow. Now that the Torah had reported the directive תדשא הארץ דשא as having preceded the command יהי מאורות there is no room for misunderstanding. This proves that earth had not existed from times immemorial but had come into existence as a result of a directive of its Creator. If there had not yet been any celestial bodies such as sun, moon, the stars, who could have promoted the growth of vegetation if not God?

Please note that in this paragraph the expression מאור, "luminary" occurs five times. This corresponds to the five kinds of light there are. 1) The light of the day. 2) the light of the sun; 3) the light of the moon; 4) the light of the stars; 5) the light of the zodiac constellations. Only the planet sun was created in order to provide light for earth (compare Bereshit Rabbah 6,1).

וירא אלוהים את האור כי טוב, "God saw the light that it was good.⁠" The belief that the system of luminaries was beneficial for the creatures on earth is based on the availability of light and darkness. We read in Job 9,9 עושה עש כסיל וכימה וחדרי תימן, "the One who makes the Bear and the Orion, Pleiades and the chambers of the south wind.⁠" The constellation Pleiades supposedly cools, whereas the constellation Orion supposedly causes warmth on earth. The constellations each fulfill opposite roles and are matched one against the other. Each of them helps the growth and ripening of a variety of plants and fruit in its own fashion. This is also what God had in mind in Job 38,31 when He had asked Job: "can you tie cords to Pleiades?⁠" People on earth obtain an insight into God's power by observing the operation of the forces of nature and marveling at the intelligence which created such a system. As a result of their appreciation of God's intelligence and power they praise Him. This is what Isaiah 40,26 spoke of when he urged the people שאו מרום עיניכם וראו מי ברא אלה, "raise up your eyes to the heavens and behold who has created all these?⁠" All of this is meant when our verse reports that God took a look at how His directive had been carried out and concluded that the results were good.
Another reason God referred to all this as טוב, "good,⁠" is that He foresaw already the great miracle which would be invoked in the future when Joshua would bid the sun and the moon to stop orbiting until he had completed his pursuit of the Canaanites (Joshua 10,12). The wording there is שמש בגבעון דום וירח בעמק אילון, "stand still sun at Gibeon and moon in the valley of Ayalon.⁠" Another reference to a similar miracle is found in Judges 5,20 where the prophetess Devorah describes the stars as having changed their orbit to help Barak fight Siserah.