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Just looking into the dialogue by Plutarch "De facie quae in orbe Lunae apparet" and my impression is, they knew the law of universal gravitation quite well.

For instance, it is argued that

  • A body thrown to the center of Earth will oscillate around that center due to its momentum. That masses of a thousand talents weight, borne through the depth of the earth, stop when they reach the middle point, though nothing meets or resists them; or, if mere momentum carries them down beyond the middle point, they wheel round and turn back of themselves (...) That water rushing violently downwards, if it should reach this middle point— an incorporeal point as they say — would stand balanced around it for a pivot, swinging with an oscillation which never stops and never can be stopped.
  • All things on Earth attract to each other. And yet if every weighty body converges to the same point with all its parts, the earth will claim the heavy objects, not so much because she is middle of the whole, as because they are parts of herself.
  • The same should happen on other bodies, including the Moon and fiery bodies like Sun and the stars. If there is any body neither assigned originally to the earth, nor torn away from it, but having somewhere a substance and nature of its own, such as they would describe the moon to be, what is there to prevent its existing separately, self-centred, pressed together and compacted by its own parts? (...) For it is not proved that earth is the middle of the Universe, and, further, the way in which bodies here are collected and drawn together towards the earth suggests the manner in which bodies which have fallen together on to the moon may reasonably be supposed to keep their place with reference to her.
  • The distance to the stars is beyond measurement capabilities greater than the distance to the Moon, and the distance to the Sun is at least 80 times greater. She is lower than the stars by a distance which we cannot state in words, since numbers fail you mathematicians when you try to reckon it, but she touches the earth in a sense and revolves close to it
  • The distance to the Moon is (by highest estimate), 56 times the Earth's radius (which is quite precise).
  • The Moon is so much close to Earth that it nearly "touches" Earth and affects by its gravity even things on Earth: For she often fails to clear the earth's shadow, rising but little, because the illuminating body is so vast. But so nearly does she seem to graze the earth and to be almost in its embrace as she circles round, that she is shut off from the sun by it unless she rises enough to clear that shaded, terrestrial region, dark as night, which is the appanage of earth. Therefore I think we may say with confidence that the moon is within the precincts of earth when we see her blocked by earth's extremities. (...) Upon this basis, the distance of the sun from the moon works out to more than forty million three hundred thousand stades. So far has she been settled down from the sun because of her weight, and so nearly does she adjoin the earth, that, if we are to distribute estates according to localities, the 'portion and inheritance of the earth ' invites the moon to join her, and the moon has a next claim to chattels and persons on earth, in right of kinship and vicinity.
  • It is also claimed that life on the Moon is impossible due to thin atmosphere, no water and hot temperature: Then as to winds and clouds and showers, without which plants can neither receive nor maintain existence, it is out of the question to conceive of their being formed, because the surrounding atmosphere is too hot and too rare.

So, my question is: can we say that scientists at least hypothesized the law of universal gravity? Can we say that the possibility of atmosphere on the Moon was hypothesized, and it was considered too hot and thin to support life? Can it be said that this work more or less reflects the scientific consensus or mainstream views of the 1st and 2nd centuries?

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This is controversial. This passage from Plutarch (and some other evidence) has been thoroughly analyzed by Lucio Russo in several papers, and in his book:

  • Forgotten revolution: how science was born in 300 BC and why it had to be reborn, translated by S. Levy, Springer, 2004.

To my understanding, majority of historians do not accept his conclusions, particularly about the law of gravitation. Of course, the truth in science is not decided by majority. But the subject remains controversial.

The main problem is that most original scientific works from Hellenistic epoch are lost, and all we have is the mentioning in secondary sources like Pliny and Plutarch, the authors who did not really understand themselves what they were talking about.

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I agree with the answer from @Alexander Eremenko, as well as with @Mauro Allegranza's useful remark about ancient ideas related to (but not the same as) gravity. Also the following observations may be found useful.

The question really calls for understanding of what was meant both by the ideas mentioned in Plutarch's work referenced in the question, and also what was and is meant by the idea and theory of 'universal gravitation'.

Ancient understandings of the cosmos often made a distinction between terrestrial and celestial materials and laws. Effects now referred to gravity were often conceived as primarily local to the neighbourhood of the earth, while celestial motions were supposed governed by other principles, often principles of perfection, such as circular motion and geometry. A helpful sourcebook, even though mainly covering ideas later than those of Plutarch, is "A Source Book in Medieval Science" (ed. Edward Grant, 1974).

I'd agree that the passages quoted in the question do suggest that their author speculated on some extension of terrestrial effects. There are ideas of analogous effects for the moon, sun, and stars, perhaps including the possibility of local effects of weight for each, and also that the moon might be habitable. But nothing in the quoted passages appears to suggest any attempt to make out that these effects are more than local to the bodies concerned. Especially there appears to be no assimilation between terrestrial effects and celestial motions, no idea that both are governed by the same laws.

On the other hand, the idea of universal gravitation has, in particular, two fundamental components which are sometimes overlooked. (1) is the idea of gravity as centripetal accelerative force. (2) is the idea that such centripetal accelerative force occurs between all pairs of material objects, whether terrestrial or celestial, so that (for example) the physical cause of the heaviness of terrestrial objects, and the physical cause of the moon remaining in its orbit around the earth and of the planets remaining in their orbits around the sun, are of one and the same kind.

No suggestion of any of these centripetal accelerative gravitational ideas appears in Plutarch, and neither does their equal application to terrestrial effects and celestial motions. Steffen Ducheyne's "The main Business of natural Philosophy" (2012) is a useful source about these ideas and also about their understanding (and sometimes misunderstanding) over the last few centuries.

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  • $\begingroup$ I think, this passage suggests that the Moon affects terrestrial objects: "...so nearly does she adjoin the earth, that, if we are to distribute estates according to localities, the 'portion and inheritance of the earth ' invites the moon to join her, and the moon has a next claim to chattels and persons on earth, in right of kinship and vicinity." $\endgroup$
    – Anixx
    Sep 11, 2023 at 13:10
  • $\begingroup$ @Anixx : Yes to the extent that it suggests the moon is exceptionally close and can influence the earth. It seems not uncommon to have regarded the moon as in some way on a dividing line between the terrestrial and the celestial. But that's still an awful long way from what we know as gravitation, let alone a long way from having the universal qualifier. $\endgroup$
    – terry-s
    Sep 11, 2023 at 20:36

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