Flamsteed's labours in astronomy and in the allied branches of science were now becoming generally known, and he gradually came to correspond with many distinguished men of learning. One of the first occasions which brought the talents of the young astronomer into fame was the publication of some calculations concerning certain astronomical phenomena which were to happen in the year 1670. In the monthly revolution of the moon its disc passes over those stars which lie along its track. The disappearance of a star by the interposition of the moon is called an "occultation." Owing to the fact that our satellite is comparatively near us, the position which the moon appears to occupy on the heavens varies from different parts of the earth, it consequently happens that a star which would be occulted to an observer in one locality, would often not be occulted to an observer who was situated elsewhere. Even when an occultation is visible from both places, the times at which the star disappears from view will, generally speaking, be different. Much calculation is therefore necessary to decide the circumstances under which the occultations of stars may be visible from any particular station.
Having a taste for such computations, Flamsteed calculated the occultations which were to happen in the year 1670, it being the case that several remarkable stars would be passed over by the moon during this year. Of course at the present time, we find such information duly set forth in the NAUTICAL ALMANAC, but a couple of centuries ago there was no such source of astronomical knowledge as is now to be found in that invaluable publication, which astronomers and navigators know so well. Flamsteed accordingly sent the results of his work to the President of the Royal Society. The paper which contained them was received very favourably, and at once brought Flamsteed into notice among the most eminent members of that illustrious body, one of whom, Mr. Collins, became through life his faithful friend and constant correspondent. Flamsteed's father was naturally gratified with the remarkable notice which his son was receiving from the great and learned; accordingly he desired him to go to London, that he might make the personal acquaintance of those scientific friends whom he had only known by correspondence previously. Flamsteed was indeed glad to avail himself of this opportunity. Thus he became acquainted with Dr. Barrow, and especially with Newton, who was then Lucasian Professor of Mathematics at Cambridge. It seems to have been in consequence of this visit to London that Flamsteed entered himself as a member of Jesus College, Cambridge. We have but little information as to his University career, but at all events he took his degree of M.A. on June 5th, 1674.
Up to this time it would seem that Flamsteed had been engaged, to a certain extent, in the business carried on by his father. It is true that he does not give any explicit details, yet there are frequent references to journeys which he had to take on business matters. But the time now approached when Flamsteed was to start on an independent career, and it appears that he took his degree in Cambridge with the object of entering into holy orders, so that he might settle in a small living near Derby, which was in the gift of a friend of his father, and would be at the disposal of the young astronomer. This scheme was, however, not carried out, but Flamsteed does not tell us why it failed, his only remark being, that "the good providence of God that had designed me for another station ordered it otherwise."Sir Jonas Moore, one of the influential friends whom Flamsteed's talents had attracted, seems to have procured for him the position of king's astronomer, with a salary of 100 pounds per annum. A larger salary appears to have been designed at first for this office, which was now being newly created, but as Flamsteed was resolved on taking holy orders, a lesser salary was in his case deemed sufficient. The building of the observatory, in which the first Astronomer Royal was to be installed, seems to have been brought about, or, at all events, its progress was accelerated, in a somewhat curious manner.