First of all, thank you Cassini for some concrete evidence highlighting Newman's error. There is quite a lot of information in this article - 'Galileo, Revelation and the Educated man' (see link that Cassini provides) so I intend to unpack this with some comments and questions:

Wrote Newman: "For that past controversy and its issue have taught me beyond all mistake, that men of the greatest theological knowledge may firmly believe that scientific conclusions are contrary to the Word of God, when they are not so, and pronounce that to be heresy which is truth.  It has taught me... that Scripture is not inspired to convey mere secular knowledge, whether about the heaven or the earth, or the race of man; and that I need not fear for Revelation whatever truths may be brought to light by means of observation and experience out of the world of phenomena which environ us.

Comment: Newman seemed to be a loyal son of the Church. For he believed as the Church believed at his time, that they had made a terrible mistake by judging Galileo so harshly for views, which, a century later, had been 
"proven" by science to be possible. In fact this entire essay is a defense of the Church for its sudden U-turn :

"Galileo on his knees abjured the heresy that the earth moved...And then at length, in our own day, the doctrine, which was the subject of it, was found to be so harmless in a religious point of view, that the books advocating it were taken off the Index, and the prohibition to print and publish the like was withdrawn."

"Such an alarm never can occur again, for the very reason that it has occurred once." 
Comment: Newman seems to be saying here that the Galileo case generated so much controversy, that the Church has learnt its lesson and is now more objective towards new physical "evidence".

"And I seem to myself here to be speaking under the protection and sanction of the Sacred Congregation of the Index itself, which has since the time of Galileo prescribed to itself a line of action, indication of its fearlessness of any results which may happen to religion from physical sciences."

Comment: 'Fearlessness' towards new theories, for Newman considers them non threatening to scripture which, he states, is written for salvation purposes and not for understanding natural science:

"Thus investigation, which Catholics would have suppressed as dangerous, when, in spite of them, it has had its course, results in conclusions favorable to their cause.  How little then need we fear the free exercise of reason!  How injurious is the suspicion entertained of it by religious men!  How true it is that nature and revelation are nothing but two separate communications from the same infinite Truth!

Newman then concludes that:
"If she [the Catholic Church] affirms, as I do not think she will affirm, that everything was made and finished in a moment though Scripture seems to say otherwise, and though science seems to prove otherwise, I affirm it too, and with an inward and sincere assent.  And, as her word is to be believed, so her command is to be obeyed.  I am as willing then to be silenced on doctrinal matters which are not of faith as to be taught in matters which are.  It would be nothing else than a great gain to be rid of the anxiety which haunts a person circuмstanced as I am, lest, by keeping silence on points as that on which I have begun to speak, I should perchance be hiding my talent in a napkin.  I should welcome the authority which by its decision allowed me to turn my mind to subjects more congenial to it."
Yes 

Question: Cassini, would you agree that Newman was a product of his times? That the Church itself held these views? And that he was merely defending/articulating the actions of the Church. I am not arguing that what he defended was true, only that what he was defending was also held to be true by even the reigning Pope - Pope Pius IX.

Question: Can this view constitute as heresy given it has not been defined clearly by the Church? There is no doubt that he is suggesting error and I concede to the evidence that he was teaching error. I also concede that he was a victim of Modernism as were the Popes who orchestrated the U-turn.

Question: What were Pope Pius X's view on the heliocentric theory?

Thanks to Cassini who approached the subject in a careful and charitable way, I have taken the time to further my research in the teachings of John Henry Newman. What I am discovering has left me stunned. To that I would have added confused if Cassini had not already prepared me on how Modernism had concretely entered the Catholic Church in 1820 and effected, one way or another, even the best of men such as Pope Pius X who spoke out against it.

In saying this, I owe the posters Pax and Ladislaus an apology. They were right and I was wrong; there is indeed something very suspect about the teachings of John Henry Newman. And as such, I now ask, how is it possible that Pope Leo XIII made him a cardinal - especially as the conservative English clergy of his day - almost to a man - treated him with suspicion?

For those that wonder at my change of position, I give you the following link to an E-book written by a Richard Sartino:
https://www.traditioninaction.org/bkreviews/A_028br_Newman.htm

 It's only 36 pages long, and some of it a little technical, however the information provided makes it clear that John Henry Newman did indeed have an agenda which he subtly and carefully planted into Catholics circles such as the Catholic periodical 'the Rambler'.

 Writes Sartino: "Unquestionably Newman was an exceptionally talented writer, capable of analyzing conceptions, terms, and fine shades of meaning that few have since been able to match; yet underneath and behind his writing there is an ambiguity, which many have noticed, that gives the impression that Newman was more clever than straightforward."

When I read those lines my mind flashed back to something Newman had written:"If she [the Catholic Church] affirms, as I do not think she will affirm, that everything was made and finished in a moment, though Scripture seems to say otherwise, and though science seems to prove otherwise, I affirm it too, and with an inward and sincere assent." Sincere assent? This does not read as 'sincere assent'. This reads as a clever way of stating 'the Church cannot affirm this because scripture and science prove otherwise' while appearing to 'submit to the judgement of authority'. Speaking from both sides of his mouth.

Once I realised his method, I began to see what Monsignor Talbot and Cardinal Mannings saw.