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The above passage is the one they have all used to OK the 1820 U-turn. It never mentions Galileo, or sunrise or sunset, but was put in to cover the 1820 U-turn by his predecessor Pope Pius VII. But having confirmed earlier in his encyclical that the Church teaching did not allow the moving-sun of all the Fathers to be changed, the letter cannot be used as a licence to change the 1616 decree. But they did use it and still do.

I think we agree on these facts: There was a 1616 docuмent which condemned heliocentrism and books promoting it were put on the Index.  There was an 1820 docuмent which allowed heliocentrism and books promoting it were taken off the Index. 

It is hard to understand how this could happen, although neither docuмent was infallible.  Many people explain it by saying that Pope Paul V made a mistake that Pope Pius VII corrected.

I see that you explain this as Pope Pius VII making a scandalous mistake, while Pope Paul V was the one who was right.  I prefer an explanation in which both popes were correct and the difference was a response to changes in scientific knowledge, as St. Robert Bellarmine suggested was possible. 

As you have kindly pointed out, there are many sources that agree with how I understand Providentissimus Deus as supporting my explanation.  Obviously, I disagree with how you have understood it.  It does not explicitly state that Church teaching does not allow a moving sun and I don't think it implies it as you claim. While I do think that geocentrism is a reasonable position, I think that currently Catholics are free to disagree with it.

So heliocentrism was contrary to the Sacred Scriptures in 1616, but then was no longer contrary to the Sacred Scriptures in 1820?  Either it is or it isn't, and that has nothing to do with the "state of science". 

St. Robert said that the interpretation of Scripture could change if there were a "true demonstration":

. I say that if there were a true demonstration that the sun is at the center of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary; and say rather that we do not understand them than that what is demonstrated is false.

The Church did change her position on heliocentrism in 1820 and this seems to me like a reasonable way to explain it.  Or perhaps we should just date sedevacantism back to 1800.

The Church did change her position on heliocentrism in 1820 and this seems to me like a reasonable way to explain it.  Or perhaps we should just date sedevacantism back to 1800.

Nonsense.  You yourself admitted that neither ruling was infallible and therefore irreformable.  This doesn't mean that one of them wasn't wrong, nor does it lead to sedevacantism.  Certainly the 1616 decision was closer to meeting the notes of infallibility, whereas the 1800 one clearly did not, as it did not teach anything that must be held by the faithful (the main note of infallibility).