According to Vashistha Siddhanta which was 'supposedly' composed around 1200-1100 BCE, they definitely could predict the motion of sun and moon. Here is a 1980 paper on the topic.

https://www.jstor.org/stable/41133571

Here is the eclipse the author is talking about. I extracted the information from the NASA site he mentioned in the article.

https://eclipse.gsfc.nasa.gov/5MCSEmap/-0999--0900/-900-11-05.gif

https://eclipse.gsfc.nasa.gov/SEcat5/SE-0999--0900.html