To what end did Hashem take Avraham outside and show him the stars?
Rashi #1: Literally, to impress upon him that he would be the father of a nation who would be as numerous as the stars.
Rashi #2: A hint that he should stop reading the stars
See Ramban. He adds that Yishmael would be born before Avram's name was changed to Avraham, but Yishmael was not destined to inherit him, and what Hashem was promising him in this Pasuk was a son who would inherit him.
As the Gemara says in Rosh Hashanah 16b, "A change of name brings about a change of Mazal." Refer to 15:5:1.3:1.
Peninim mi'Shulchan ha'Gra: This is if they are Tzadikim; if not, they descend to the earth. Haman could not find a time that is a bad Mazal for Yisrael, for they are above Mazal. He cast lots "Lifnei Haman," i.e. to find when he himself has a good Mazal.
The Gemara (Shabbos 156b) says that Hashem moved the planet Tzedek from the west to the east, thus changing Avraham's Mazal. How is this to be understood?
Maharal #1 (Chidushei Agados Vol. 1, p. 89, to Shabbos 156a): Avraham's Mazal had been in the west, i.e., about to set below the horizon, for he would not be leaving a son to inherit him. This may have been true in the natural order of the world, but Hashem had just begun to put Avraham's destiny into motion, like the beginning of a planet's trajectory is rising in the east.
Maharal #2 (ibid; Gevuros Hashem, Intro #2): The planet did not move backwards in its orbit in the physical sense. Miraculously, it appeared to be so. This was visible to those at that time and location alone, while in other locations the planets remained visible at their normal positions.
What are the implications of "Koh Yiy'heh Zar'echa"?
Rashi (in Zecharyah, 11:12, citing a Midrash): From the word "Yih'yeh" (Gematriya thirty) we learn that there is no generation that contains less than thirty Tzadikim.
Why does it say twice in the verse, "He said"?
Lev Eliyahu (Shemos p. 128): It says "He said" also about Avraham's seed, to teach that not only will they be numerous like the stars, but also they will be above Mazal, like Avraham himself.
QUESTIONS ON RASHI
Rashi writes: "According to the Midrash, Hashem told Avraham, 'Leave go of your astrology!'" What did Rashi find difficult with the simple explanation
Gur Aryeh: If so, Hashem could have merely told Avraham, "go outside," without actually bringing him out.
Rashi writes: "'Avram' shall not have children, but Avraham is destined to have this constitute a change in the Mazal?
Gur Aryeh: The stars indicated that "Avram" would not have children, but indicated nothing at all about "Avraham." Hashem now informed him that He would change his name, and thus bring about a new Mazal.
Rashi writes: "... but Avraham is destined to have children." What is the significance of changing a person's name?
Gur Aryeh, Maharal (Chidushei Agados Vol. 1, p. 107, to Rosh Hashanah 16b): The Gemara (ibid.) teaches that a change in name is one of four things that can tear up a Heavenly decree. A name teaches about one's essence. A change in name changes a person fundamentally, and he becomes a different person. Any previous decree is thus nullified. 1
Maharal (ibid.) adds that a change in name is third on this list of four. It is parallel to the Berachah of "Kedushas Ha'Shem," and to the third Midah (Tif'eres), represented by Yaakov Avinu. We may add that the promise to Avraham, "I shall make your name great" (12:2), refers to Yaakov; refer to 12:2:2.2:2. (EK)
Rashi writes: "The Mazal shall change." However, the Gemara teaches (Shabbos 156a) that Mazal does not apply to Yisrael at all! Why then was there a need to change Avraham's name?
Maharal (Chidushei Agados Vol. 1, p. 89, to Shabbos 156a): While Yisrael is not completely under the influence of Mazal (as are the other nations), they do need merits to overcome it, and if they sin they do revert to its influence. So too regarding Avraham; although he was above Mazal, he was still liable to become affected by it. It all depends on the strength of the decree, and upon the person. 1
Certainly, Tefilah is effective in changing one's Mazal. The point the Gemara is making is that Klal Yisrael as a whole is over and above Mazal, and likewise for any individual who performs a Mitzvah.
Rashi writes: "This would explain the expression 'Habatah,' [which means] looking [down] from above to below." Mizrachi asks
Mizrachi: Rashi refers only to the term "Habatah" found in this Pasuk.
Gur Aryeh:"Habatah" (beginning with the letter Hei) is related to the word "Chabatah" ("beating," beginning with 'Ches'). When the eye focuses on its subject, one's vision can be described as "beating down" and capturing that object. Focusing on any object that can be viewed from above can be described as "Habatah," whereas the stars cannot possibly be viewed from "above;" therefore the term needs to be explained.