The Western Roman Empire
What the well educated latin-speaking Romans knew of the Greek natural philosophy works came from popularizers and compilers such as Pliny the Elder (1st Cent. CE) who wrote a Natural History and Capella (early Vth Cent. CE). For those with a deeper interest in astronomy, natural philosophy works (such as those of Aristotle and Ptolemy) were available in Greek.  Most of the elite-class Romans that were interested in that subject were also fluent in Greek and were able to read the works in that language.
Decline of knowledge in the West 
Beginning in the third century CE, the Roman Empire fragments into the Latin speaking western empire and Greek speaking eastern empire. Over the centuries, contact between the two empires is gradually lost. Thus, even though the western world was aware of the great astronomical tradition of the Greeks via the popularizers, as literacy (especially Greek literacy) declined, the western world became gradually cut off from the original Greek works. By the time the western empire falls into barbarian hands (500 CE is a convenient date), the West had only one of Plato's dialogues (Timaeus), some fragments of Aristotle’s works on logic and what astronomical general information was available in the Roman compilations and popular works. 

In the West, few original contributions will be made for the next 500 years. During that time, it is the monasteries and the church (via such people as Isidore of Seville in the late VIth - early VIIth century, and Bede in the VIIIth Cent), that were the transmitters of what small popular amount of classical knowledge survived.

Continued transmission of knowledge in the East 

In contrast to the intellectually impoverished western worlds, the Eastern (Byzantine) Roman Empire continues to have vigorous intellectual centers. Bactria (Central Asia), Persia (modern Iran), and Alexandria in Egypt become major hellenistic cultural centers. In Persia, Christians (Nestorians) begin translating Greek works into Syriac as early as 450 CE and continue doing so for centuries. While there might be little new and original information added after the second century even in the eastern Mediterranean, there nevertheless is a continuous, unbroken, thousand year long transmission of hellenistic knowledge outward into other cultures.