Final answer:
The Babylonians were the ancient culture most renowned for their ability to predict eclipses, thanks to their sophisticated astronomy and mathematical skills.
Step-by-step explanation:
The ancient culture that had the greatest known success in predicting eclipses was the Babylonians. The Babylonians inherited the scientific traditions of ancient Mesopotamia, excelling as astronomers and mathematicians, which enabled them to predict eclipses with considerable accuracy.
Their detailed calendar systems and understanding of celestial mechanics were a testament to their advanced knowledge in these fields. Unlike other cultures at the time, the Babylonians meticulously recorded astronomical phenomena, laying the foundations of our current understanding of the motions of the heavenly bodies.
By counting the days between solstices and equinoxes, they were able to create an accurate calendar which helped in agricultural planning and was intertwined with their cultural and religious practices.