I know exactly the kind of headline you mean.
There's a difference between surprising science and technical truth presented as if everyone has been wrong for centuries. A lot of modern science clickbait has migrated into that second category.
"Jupiter does not orbit the Sun" is technically true in the same sense that:
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The Earth doesn't orbit the Sun exactly.
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The Sun doesn't sit still.
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The Solar System doesn't orbit the center of the Milky Way in a neat ellipse.
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Nothing is ever really stationary.
In celestial mechanics, every two bodies orbit their common barycenter (center of mass). For the Sun–Jupiter pair, that barycenter is sometimes actually outside the Sun's surface because Jupiter is so massive. Astronomers have known this for generations.
The headline is counting on readers interpreting "does not orbit the Sun" as "everything you learned in school was wrong," when the article usually ends up explaining a nuance that undergraduate physics students learn in the first week of orbital mechanics.
It's similar to headlines like:
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"Scientists say there are not four seasons."
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"The Earth isn't round."
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"There is no such thing as sunrise."
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"Humans are not descended from apes."
Each contains a kernel of technical truth wrapped in wording designed to trigger the "Wait, what?" reflex.
The unfortunate part is that it trains readers to distrust perfectly useful approximations. For everyday purposes, saying "Jupiter orbits the Sun" is every bit as reasonable as saying "the Sun rises in the east." Both statements communicate reality accurately enough for normal human conversation.
The old clickbait formula was "You won't believe what happened next." The newer version is "Everything you know is wrong," even when what follows is merely a footnote.
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