It is only a modern invention to make Conon a 'court astronomer'; no such rank existed in Ptolemaic Egypt...Conon is remembered particularly for Callimachus's poem Berenice's Lock about the constellation Coma Berenices. It may be as a result of this poem that Conon is well known to Virgil and Propertius.
The story of the constellation Coma Berenices is that Queen Berenice II, the wife of Ptolemy Euergetes, swore a vow that she would dedicate a lock of her hair to the temple if her husband returned victorious from the Third Syrian War. The war was fought by Ptolemy Euergetes to avenge the murder of his sister in Syria. When he returned victorious in 245 BC, Berenice cut off the lock of her hair and placed it in the temple. The following day the lock of hair had vanished and Conon declared that he could see it in the stars between Virgo, Leo and Bootes. From that time on the constellation has been known as Coma Berenices.
Conon was a lifelong friend of Archimedes and the two exchanged mathematical ideas. Heath writes :-
It was probably at Alexandria that [Archimedes] made the acquaintance of Conon of Samos (for whom he had the highest regard both as a mathematician and a friend).Pappus states that the curve now known as the spiral of Archimedes was discovered by Conon although it was much used by Archimedes. Heath writes in  that Conon was :-
... cited as the propounder of a theorem about the spiral in a plane which Archimedes proved: this would, however, seem to be a mistake, as Archimedes says at the beginning of his treatise that he sent certain theorems, without proofs, to Conon, who would certainly have proved them had he lived.Conon's work on conic sections became a basis for the fourth book of Conics of Apollonius of Perga despite the fact that Apollonius makes less than admiring remarks about Conon in the preface. Apollonius says that Conon sent a piece of work to Thrasydaeus which discussed the points of intersection of conics (including circles) but that Conon's results were incorrect and were seen to be so by Nicoteles of Cyrene. The work to which Apollonius refers is Conon's Pros Thrasydaion which is now lost so we cannot judge the accuracy of the comments.
Also lost is Conon's major work on astronomy, the seven books of De astrologia, which included solar eclipse observations. Ptolemy attributes seventeen "signs of the seasons" to Conon which he may have given in this work. As to Conon's skills as an observer, Seneca, writing in the first century AD, says :-
... that Conon was a careful observer and that he "recorded solar eclipses observed by the Egyptians".But Neugebauer  adds that this is:-
... a story difficult to take seriously in view of what we know of Egyptian astronomy.For discussion on Conon's work with Babylonian observations, see the article .
Another assessment of Conon came in poetic fashion from Catullus, the Roman poet (84 BC - 54 BC), who wrote that Conon (see for example ):-
... discerned all the lights of the vast universe, and disclosed the risings and settings of the stars, how the fiery brightness of the sun is darkened, and how the stars retreat at fixed times.
Article by: J J O'Connor and E F Robertson