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September 10

What is the over/under for the closest a planet has been to Earth in the Phanerozoic? What about any planet pair?

2. Is the probabilistically most likely value for "what was the biggest Phanerozoic perturbation?" enough to cause detectable climate change if it magically happened now?

Planet means the kind we have 8 of. Sagittarian Milky Way (talk) 03:41, 10 September 2020 (UTC)[reply]

It is generally thought that the Solar System as a whole is unstable (see the article on Stability of the Solar System) and that the system of equations is is chaotic in the technical sense of mathematical chaos theory. On a time scale of a few million years nothing dramatic is to be expected, and the effects are too small to have been observed since Homo sapiens gazed up to the skies. But even the most precise long-term models for the orbital motion of the Solar System are not valid over more than a few tens of millions of years, let lone over the 500+ million years the Phanerozoic has lasted. Numerical integration of the differential equations on supercomputers suggests the possibility of collisions of Mercury, Mars or Venus with the Earth some 3.34 billion years into the future, but not sooner than within one billion years. Since the equations are time-symmetric, the models can equally be used to postdict the past planetary motions. I don't know if anyone has actually done that. It seems that for a time scale below a billion years into the past the result is likewise not likely to be dramatically different from the current orbits. But the lack of major upheaval for a long future time span is no guarantee of the same for the past. Until someone runs that simulation backwards the best answer to the question in the heading is that we don't know. As to the second question, current climate models have no contingency for a direct collision of Mars with Earth, but I think it is a fair bet the climate change would be detectable.^[1] --Lambiam 08:05, 10 September 2020 (UTC)[reply]

The closest planet to earth, on average, is Mercury (no really: [2], [3]). The closest planet to earth at the closest point on either of their orbits is Venus. The gravitational effect of Venus at its closest point is easy enough to calculate; it is neither close enough nor large enough for General Relativity to matter, so use F = G (M1 * M2)/(d^2). You should also do the calculation for the gravitational effect of the Sun on the earth too; I'd imagine the effect of Venus is well out of the range of the significant figures of our measurements. You may also want to do Jupiter, given the difference in masses, Jupiter may have a larger overall gravitational effect on Earth than Venus, but again, these numbers are going to be several orders of magnitude into the uncertainty range for the effect of both the Sun and the Moon, and at that level, basically meaningless as they would get lost in the normal expected variations of those bodies (basically just part of the "noise"). --Jayron 32 10:50, 10 September 2020 (UTC)[reply]

I've heard the Mercury thing before, apparently the math makes it not tied with Venus. Sagittarian Milky Way (talk) 01:09, 11 September 2020 (UTC)[reply]

One can estimate an upper bound on any perturbations of Earth's orbit by considering the hypothesis that the largest perturbations in the Earth's climate with unknown cause, was caused by a perturbations of the Earth's orbit. Now, going a bit beyond the Phanerozoic period, we can consider the snowball Earth period, and for that you actually need quite small perturbation of earth's orbit, way smaller than what can happen due to the effects mentioned by Lambian above. Count Iblis (talk) 15:03, 10 September 2020 (UTC)[reply]