Making predictions according to the positions of stars, as explained in the question, is not permissible. If it is believed that this has an effect on the falling of rain, this is Shirk (associating others with Allah in His Divinity or worship) and Kufr (disbelief). But if it is believed that the One who has the effective power is Allah Alone, but He made the rain fall due to the position of the star, this is Haram (prohibited), as it is not permissible for a Muslim to either metaphorically or literally attribute characteristics of Allah to a subjugated being. This is based on the general statement of the Prophet (peace be upon him),
My Ummah (nation) has four (characteristics) belonging to Jahiliyyah (pre-Islamic time of ignorance) that they have not abandoned: pride in their lineage, vilifying other peoples' lineages, seeking rain through the stars, and wailing for the dead.
(Part No. 1; Page No. 623)
Muslim in his Sahih [Book of Authentic Hadith].
The Prophet (peace be upon him) also said to his Sahabah (Companions) one rainy morning:
“Do you know what your Lord said?” They replied, “Allah and His Messenger know best.” He (peace be upon him) said, “He said: ‘Some of My Servants entered the morning as believers and some as unbelievers. Those who said, 'Our rainfall was due to the Blessing and Mercy of Allah,' are believers in Me and disbelievers in the stars; and those who said, 'Our rainfall was due to this and that (star) disbelieved in Me and affirmed their belief in the stars.'”
Agreed upon by Al-Bukhary and Muslim on the authority of
Zayd ibn Khalid Al-Juhany (may Allah be pleased with him).
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.