Newton's law of universal gravitation has been known since 1686 and it states that gravity is proportional to inverse square of the distance, but never fades to 0. This led to stories where various astronauts traveling e.g. to the Moon don't experience zero (or micro) gravity at all (e.g. The Unparalleled Adventure of One Hans Pfaall by E.A. Poe from 1835), or only at the L1 point where Moon's and Earth's gravity are equal (From the Earth to the Moon by J. Verne, 1865).
If I am not mistaken, even C.S. Lewis made this mistake in his Out of the Silent Planet as late as 1938.
What then was the first fiction (book, movie, short story) that described the zero-g during space travel according to currently known physical laws?
Answer
It's not much of a book admittedly, but despite its scienific foundations, "Breakfast in a Weightless Kitchen" (Завтрак в невесомой кухне), a 1914 short story by Yakov Isidorovich Perel'man (1882-1942), is anything but scientific in form.
Specifically, it is written as a "missing chapter" (today we would probably call that a fanfic) for Jules Verne's From the Earth to the Moon, where the main characters try (fairly badly) to make a breakfast in surprisingly well described microgravity.
It was originally published in 1914 as a stand-alone short story; since 1916 it had appeared in the second volume of Physics for Entertainment.
I actually was surprised to find out it was that early. Its depiction of zero-g is so good that it almost looks based on actual orbital flights, and the only reason I knew it wasn't that late is because, well, it can't have been any later than 1942 since the author died in that year.
Though yes, it's very possible that Tsiolkovsky managed to publish something on that topic earlier.
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