Short answers, pulled from the story.
Muhammad ibn Ibrahīm al-Fazārī and Ya'qūb ibn Tāriq translated the Zij al-Sindhind into Arabic in 770. This work marked the first major translation of astronomical knowledge into Arabic, bridging centuries of Indian and Persian scientific tradition with the emerging Islamic world.
Caliph al-Ma'mun ordered the construction of the first observatory in Baghdad during the early 9th century. This facility established a precedent for state-sponsored astronomical research within the House of Wisdom institution.
Nasir al-Din al-Tusi invented the Tusi couple, a mathematical device where a small circle rotates inside a larger circle twice its diameter. This concept caused linear oscillation along a diameter and replaced the problematic equant in planetary models.
The Persian Solar Calendar known as the jalali calendar remains in official use today in Iran and Afghanistan. Prince Malik Shah I established this calendar in Isfahan where Omar Khayyám and many collaborators constructed a zij.
Al-Battani plotted coordinates for 1,022 stars in Iraq during the 10th century. This work transformed the traditional use of celestial globes from observational tools into data recording devices.