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I came across this short: https://www.youtube.com/shorts/LjBaPxutpQo where Brian Cox says the idea of black holes dates back to 1790. It stemmed according to it from escape velocity and that you could at some point have escape velocities larger than the speed of light.

My understanding is that Newton's laws were still the prevalent theory back then with nothing superseding them. So while they would have imagined such objects to be quite dark, I don't think they would have expected that it would be impossible to escape them once inside the event horizon. Since Newtons laws say you can get to any speed you want if you accelerate long enough, I imagine they might have thought a powerful enough rocket could still get them out of such an object.

Is there anything that supports people believing that faster than light travel should be possible around the 1790s?

Note: my question is specifically around whether there is any evidence that people thought faster than light travel was possible in 1790 since Newton's laws allow it.

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Would they have known you can't go faster than light in 1790?

No, they did not know.

In 1783, John Michell considered what would happen to light if an object were too massive. He considered that light would not be able to escape the massive object due to its gravitational pull, foreshadowing the existence of black holes.

His calculation was classical, and he was not considering the speed of light as a limit, just a mass limit for a star, at which light could not escape.

Laplace came up with the same idea in 1796.

Before 1905 Einstein's special relativity, some scientists considered superluminal phenomena. Scientist believed for some time that forces like Coulomb law and Newton's universal gravitation were instantaneous. Laplace in "Description of the System of the Universe" considers that, when studying the Moon, that gravitation should exceed the speed of light (by a factor of $10^6$).

Also due Galilean relativity, it was considered that if light was emitted from a moving object, then light would go faster or slower that light emitted from a body at rest. Fresnel makes this argument in 1818.

In Two Planets by Kurd Lasswitz (1897)

the Martians mention their propulsion drive, expecting to soon reach propellant speeds beyond the speed of light.

(Courtesy of Scifi SE)

Source: Malykin, G. B., and E. A. Romanets. "Superluminal motion (review)" (2012) https://link.springer.com/article/10.1134/S0030400X12040145

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