shkrobius (shkrobius) wrote,
shkrobius
shkrobius

On apples and Newtons. 2

part 1 on http://shkrobius.livejournal.com/153606.html

Newton was fortunate that the protean task before him, that is discovering the celestial mechanics, was greatly assisted by the solar system itself. In a story by Asimov (Nightfall) set on a fictional planet orbiting a six star system, computers were invented long before the laws of gravity had been elucidated. In our system, orbital motions are approximated by two-body problems with perturbations, so one can fairly easily guess the laws of motion. We are generously provided for. We are given the example of Jovian moons orbiting Jupiter, to get the idea of satellites. We are given a nearby planet, Mars, whose trajectory in the sky can be traced in the sky with high accuracy without complex instuments. Save for the complication of living on a rotating planet orbiting the Sun, we were set for the discovery.

Even in a single star system, one can easily imagine obstacles that do not occur here. Imagine living on the only planet in the system. It would be impossible to make observations of other planets. The "ideal" situation for discovering the theory of gravity (no perturbations) is also the most forbidding. However, I argue that such a situation is extremely unlikely to arise: Newtons cannot be found on lonely planets:

...if the process of formation planetary from planetesimals is correct, it becomes possible that the planetary systems will always be in a state of marginal stability, like our own Solar system. At the end of the phase of formation of the system it can remain a great number of bodies, but in this case the system is strongly unstable, and is led to a collision or an ejection. After this event, the system becomes more stable, with constantly, a time of stability comparable with its age. In particular, a system with only one planet, or even with two planets like Jupiter and Saturn, will not be able to exist, because this system would be too stable so that gravitational instabilities could not evacuate the totality of the other bodies initially present. More precisely, if such a System exists, it will have to also remain there a multitude of small bodies, which will not have been evacuated by these gravitational instabilities.
Laskar (http://www.scholarpedia.org/article/Stability_of_the_solar_system)

Planets are formed by accretion of planetosimals. Without several planets, a system cannot provide sufficient gravitational instability to eject planetosimals that did not make it into planets, so the lonely planet will be embedded into a cloud of dust and planetosimals that will be bombarding its surface. Life as we know it would be impossible on such a planet, and even a visitor would not observe much in the sky (because of the dust in the disk); what will be observed will appear completely chaotic. Newtons are possible only in solar systems of many planets that arrived at marginal long-term stability after a period of instability. So gravitational physics itself destines Newtons to inhabit the places where the dsicovery of this physics is easy.

A greater challenge is atmospheric transparency: these other planets should be observed from the surface. One can argue that such opacity excludes Newtons: photosynthesis would be impossible; poor Newtons would be reduced to chemolithotrophy. I am not sure this is the case: the presence of organics and N2 in reduced atmosphere guarantees UV synthesis of hydrocrabon/tolin haze in the upper atmosphere. These chemicals will rain down and can serve as the basis for organic life; photosynthesis does not have to be either biogenic or occur at the surface level. If a geologically active planet has water and CO2, some methane will be produced by serpintization of rocks
http://www.agu.org/pubs/crossref/2005/2005GL022691.shtml
http://geology.gsapubs.org/content/38/10/959.full
I suppose it is not impossible that Newtons can live on such planets. However, it is hard to imagine that they will develop interest in celestial mechanics given that the existence of other worlds like theirs would be purely conjectural. They can discover such worlds only by flying into space, but I cannot imagine what would incentivize them to do that. We do not drill to the center of the Earth hoping to discover new worlds there, although it is possible that such worlds may exist there; flying upwards a thousand miles would sound equally esoteric to them. On such a planet, the laws of mechanics and gravity would need be discovered completely without astronomical support.

In principle that is possible. Their notion of gravity would be that of the constant gravitational field. That would be sufficient to get interested in the motion of projectiles and the pendulum. They would discover that their world is round and that it rotates without observing the sky. If they have a moon, there will be tides; however, a genius beyond that of Newton would be required to explain them. I do not expect that they will. The greatest discovery in their history will be made accidentally. They will be flying for travel and warfare, trying to get higher and higher in order to reduce atmospheric drag. One day they may inadvertantly penetrate their cocoon and see the sun, the stars, the planets, and their moon, if they have one. Their Newtons (as in Asimov's world, but for a different reason) will appear only at the end of lengthy technological evolution rather than its beginning.

But can this evolution even begin without a Newton? Our mechanical thinking was fully informed by observing the skies. It might've been possible to discover mechanics without this assistance, but thousands of years did not produce a genius capable of such a feat. We take the starry skies above us as a given, but (to parphrase Kant) these starry skies are no more of a given that the moral law within us.

That is to say that our greatest scientist was assisted by the heavens themselves.

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