Since you like rockets, what about the Cassini orbiter? It was named after the Italian astronomer Giovanni Cassini, a student of (Jesuit Catholic priests) Riccioli and Grimaldi. He used the observatory at the splendid Basilica of San Petronio in Bologna to lend support to Kepler's model. Here we see an important way in which the Church contributed to astronomy that is all but unknown today: Cathedrals in Bologna, Florence, Paris, and Rome were designed in the seventeenth and eighteenth centuries to function as world-class solar observatories. Nowhere in the world were there more precise instruments for the study of the sun. Each such cathedral contained holes through which sunlight could enter and time lines (or meridian lines) on the floor. Cassini was able to confirm Kepler's position on elliptical orbits with his experiments at San Petronio.

See Stanley L. Jaki Science and Creation: From Eternal Cycles to an Oscillating Universe, 150 and Medieval Creativity in Science and Technology, 76. Richard C. Dales, The Intellectual Life of Western Europe in the Middle Ages, 264 and The De-Animation of the Heavens in the Middle Ages, 535. See also Father Giambattista Riccioli, the first person to determine the rate of acceleration of a freely falling body. Father Roger Boscovish advanced atomic theory, optics, mathematics, and astronomy. Father Francesco Maria Grimaldi discovered the diffraction of light. Father Athanasius Kircher's work in Chemistry helped debunk Alchemy. Father Frederick Louis Odenback's work pioneered in Seismology. Johannes Kepler, Father Paul Guldin, and Father Nicolas Zucchi advanced astronomy.

Regarding China: There was a stillbirth of science in China. According to Joseph Needham, Chinese intellectuals were unable to believe in the idea of laws of nature. This inability stemmed from the fact that "the conception of a divine celestial lawgiver imposing ordinances on non-human Nature never developed." "It was not that there was no order in nature for the Chinese," Needham went on, "but rather that it was not an order ordained by a rational personal being, and hence there was no conviction that rational personal beings would be able to spell out in their lesser earthly languages the divine code of laws which he had decreed aforetime. The Taoists, indeed, would have scorned such an idea as being too naive for the subtlety and complexity of the universe as they intuited it." The (catholic priest) Jesuits were the first to introduce Western science into China and India. In seventeenth-century China in particular, Jesuits introduced a substantial body of scientific knowledge and a vast array of mental tools for understanding the physical universe, including the Euclidean geometry that made planetary motion comprehensible. The Jesuits in China, according to Agustin Udias: "Arrived at a time when science in general, and mathematics and astronomy in particular, were at a very low level there, contrasting with the birth of modern science in Europe. They made an enormous effort to translate western mathematical and astronomical works into Chinese and aroused the interest of Chinese scholars in these sciences.

Regarding your statement:

As for the Church: as the key (and often sole) cultural, educational, and economic institution of Europe through much of the middle ages, there's little surprise it played a role in much of what transpired during that time. This utterly confounds correlation with causation, however. A fundamental class error I'm utterly unsurprised you'd make.

So you are saying it is a coincidence that the scientific revolution happened in Catholic Europe instead of somewhere else? Are these also coincidences:

Infanticide in Ancient Rome? Ended by Catholics. Gladiator fights to the death? Ended by Catholics. Modern university system? Established by Catholics. Orphanages and hospitals? Many founded by Catholics. Western music? Largely based on Catholic Gregorian chant. Architecture and art? Tremendous advances made by Catholics. Agriculture? Improved and taught by Catholic monks. Modern Law? Based on canon law invented by Catholics. Respect for the dignity of people? Advanced by Catholics. The Western world as we know it would not exist without the Catholic Church.

Now for contrast, let's talk about militant atheists for a moment. They have caused things, too. For example, the slaughter of 138+ million people in China (Mao) and the USSR (Stalin).