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> nothing special about special relativity What's special about special relativity is that the spacetime is flat, i.e., there is no gravitation at all. This w

> nothing special about special relativity What's special about special relativity is that the spacetime is flat, i.e., there is no gravitation at all. This work is about the sun's gravity, i.e. the (weakly) curved spacetime sourced by the central mass of our solar system, and so is about general relativity and not special relativity. > change any of the underlying rules, it's going to become stable The relevant thing here is chaos. [italicizations below are mine] §3.1 in the authors' preprint at <https://arxiv.org/abs/2303.05567 https://arxiv.org/abs/2303.05567> makes the point: "because the systems are chaotic and we use slightly different general relativistic corrections in each simulation, the simulations diverge quickly. This is effectively the same as varying the initial conditions of one planet by a tiny amount". Quoting Wikipedia's Chaos Theory article: "Chaos theory is [...] focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions". (The initial conditions in question are the orbital parameters--or more broadly the momentum--of Mercury. The equivalence is fairly obvious, but I think I prefer to look it at similar to your wording, "... change any of the underlying rules ...", although not just any rule, they change a specific rule (or closely related family of rules, more on that below).) In the paper's §3.2 they identify the most prominent post-Newtonian contribution ("... the precession from GR (the gravito electric effect) .. follows closest behind Newtonian planet-planet interactions and is more than three orders of magnitude more influential than any additional effects"), and the paper in general focuses on the question of whether simulated planet-planet interactions' tendencies to eject Mercury from the solar system are dampened by GR's influence on the perihelion precession of Mercury. (Their answer: yes - Mercury sticks around for many billions of years even if the gravito-electric effect is small, but if it's zero, simulated Mercury is typically yeeted right out of simulated solar system in relatively few billions of years). More specifically they look at the evolution of Mercury's orbital eccentricity and use it as a proxy for Mercury's ejection <https://www.urbandictionary.com/define.php?term=Yeet https://www.urbandictionary.com/define.php?term=Yeet>. Mercury's orbit becomes more elliptical if over long periods of time its perihelion coincides with the perihelion of Jupiter. With practically any perihelion or ascending node precession of Mercury or Jupiter, Mercury's orbit remains roughly circular. Even more specifically in their eqn. (2) they parameterize the general relativity corrections to the planets' perihelion precessions, and vary the parameter (eqn (3)). Eqns. (1) & (2), with the parameter \alpha set to unity, are straightforwardly extracted from an approximate solution to the Einstein Field Equations (of General Relativity; the EFEs), but going the other way from a modification of the parameter \alpha to a solution of the EFEs is something reviewers or a paper in reply may question, since it's not as straightforward. (One might compare how (Milgrom's) MOND can be seen as a parametrization in the same spirit eqns (1) & (2), "simples", but nobody has completely reverse-engineered the parametrized equation back into a set of relativistic field equations. The authors touch on this at the bottom of the first page's second column.)

defrost 4y ago
I understand the point made about effectively the same as varying the initial conditions thanks to spending some student time on Smale and non linear dynamics, and I appreciate this paper is exploring the sensitivity of gravitational N-body systems with respect to GR perturbations, however this caught my eye: > and is more than three orders of magnitude more influential than any additional effects Mercury is just so damn close to the sun, how much force does the solar wind pressure exert on the planet (directly | via magnetic field interactions)? I imagine it must be non trivial and subject to variation.
- zyrxvo 4y ago
  Hey, I'm the first author on this paper. We don't expect solar wind to have a strong effect. I focus on dynamics and not electromagnetic effects, but we took our values for the effects contributing to the perihelion precession of Mercury from NASA by Park et al. (2017) Precession of Mercury's Perihelion from Ranging to the MESSENGER Spacecraft <https://iopscience.iop.org/article/10.3847/1538-3881/aa5be2 https://iopscience.iop.org/article/10.3847/1538-3881/aa5be2>. However, I don't have an order of magnitude estimate for the effect and like you said, the effect is certainly subject to variation, especially due to the Sun's solar cycle <https://en.wikipedia.org/wiki/Solar_cycle https://en.wikipedia.org/wiki/Solar_cycle>. My guess is that since the effect of solar wind isn't included in the calculations and measurements by Park et al. (2017), then it's likely around a thousandth of an arcsecond per century or less.
  - defrost 4y ago
    Thanks for the reply, I was in the ground based geophysics game for a decade or two and I'm fine with the envelope guess work and principle focus on gravity + GR dynamics .. but I am now piqued by this, I'm grabbing Park (thanks for the link) and will poke about further.
    - raattgift 4y ago
      There's an orbiting-body size and shape (and ultimately mass) dependence on solar radiation pressure's effects on the evolutions of orbits in the solar system that dominates other factors for bigger solar system bodies (planets, dwarf planets, round moons). For planetary orbits, perturbations from radiation pressure while the sun is on the main sequence will be so small as to be negligible. Small perturbations may matter over billions of years, but perhaps more billions than the sun has life. Small bodies which are not in hydrostatic equilibrium (i.e., not massive enough to be round through gravitational collapse) can experience many orders of magnitude larger perturbations. However, for lumpy asteroids, radiation pressure gives net accelerations orders of magnitude below 10^-10 m/s^2. A literature search on the Yarkovksy effect might take you to radiation-pressure work on larger, rounder bodies (or more likely their outermost layers' chemistry and density), possibly even planets. Effects like these are generally proportional to ellipticy of the body itself and its rotation, and inversely proportional the body's size, with insolation and albedo as surprisingly minor factors. The Yarkovsky effect might cause a small, lumpy, quickly-spinning asteroid-belt body to dive into the inner solar system. https://arxiv.org/abs/1708.05513 https://arxiv.org/abs/1708.05513 has an interesting overview. At a more pop-sci level, https://skyandtelescope.org/astronomy-news/the-asteroid-and-the-pea/ https://skyandtelescope.org/astronomy-news/the-asteroid-and-... The MESSENGER programme did some science on Mercury's exosphere <https://en.wikipedia.org/wiki/Atmosphere_of_Mercury https://en.wikipedia.org/wiki/Atmosphere_of_Mercury> (and effects like ion sputtering photon-stimulated desorption, each of which kicks mainly sodium atoms off Mercury's surface into its long cometary tail) that is likely to be interesting, but is likely to undermine the idea that electromagnetic forces are significant with respect to the planet's orbital evolution. There is a substantial body of literature on radiation pressure's effects on artificial Earth satellites, but such devices are certainly not in hydrostatic equilibrium and rarely anything close to spherical (extended solar panels, etc.) Putting "solar radiation pressure satellites" into your favourite Internet search engine will be fruitful. There is also a body of literature where the radial solar radiation force is important in calculating the trajectories of space probes sent to various parts of our solar system. Again, these are low-mass objects on many-year flights. The Mariner programme generated papers relevant to Mercury e.g. the 160 pages of <https://ntrs.nasa.gov/citations/19750009204 https://ntrs.nasa.gov/citations/19750009204>.

defrost 4y ago

I understand the point made about effectively the same as varying the initial conditions thanks to spending some student time on Smale and non linear dynamics, and I appreciate this paper is exploring the sensitivity of gravitational N-body systems with respect to GR perturbations, however this caught my eye: > and is more than three orders of magnitude more influential than any additional effects Mercury is just so damn close to the sun, how much force does the solar wind pressure exert on the planet (directly | via magnetic field interactions)? I imagine it must be non trivial and subject to variation.

zyrxvo 4y ago
Hey, I'm the first author on this paper. We don't expect solar wind to have a strong effect. I focus on dynamics and not electromagnetic effects, but we took our values for the effects contributing to the perihelion precession of Mercury from NASA by Park et al. (2017) Precession of Mercury's Perihelion from Ranging to the MESSENGER Spacecraft <https://iopscience.iop.org/article/10.3847/1538-3881/aa5be2 https://iopscience.iop.org/article/10.3847/1538-3881/aa5be2>. However, I don't have an order of magnitude estimate for the effect and like you said, the effect is certainly subject to variation, especially due to the Sun's solar cycle <https://en.wikipedia.org/wiki/Solar_cycle https://en.wikipedia.org/wiki/Solar_cycle>. My guess is that since the effect of solar wind isn't included in the calculations and measurements by Park et al. (2017), then it's likely around a thousandth of an arcsecond per century or less.
- defrost 4y ago
  Thanks for the reply, I was in the ground based geophysics game for a decade or two and I'm fine with the envelope guess work and principle focus on gravity + GR dynamics .. but I am now piqued by this, I'm grabbing Park (thanks for the link) and will poke about further.
  - raattgift 4y ago
    There's an orbiting-body size and shape (and ultimately mass) dependence on solar radiation pressure's effects on the evolutions of orbits in the solar system that dominates other factors for bigger solar system bodies (planets, dwarf planets, round moons). For planetary orbits, perturbations from radiation pressure while the sun is on the main sequence will be so small as to be negligible. Small perturbations may matter over billions of years, but perhaps more billions than the sun has life. Small bodies which are not in hydrostatic equilibrium (i.e., not massive enough to be round through gravitational collapse) can experience many orders of magnitude larger perturbations. However, for lumpy asteroids, radiation pressure gives net accelerations orders of magnitude below 10^-10 m/s^2. A literature search on the Yarkovksy effect might take you to radiation-pressure work on larger, rounder bodies (or more likely their outermost layers' chemistry and density), possibly even planets. Effects like these are generally proportional to ellipticy of the body itself and its rotation, and inversely proportional the body's size, with insolation and albedo as surprisingly minor factors. The Yarkovsky effect might cause a small, lumpy, quickly-spinning asteroid-belt body to dive into the inner solar system. https://arxiv.org/abs/1708.05513 https://arxiv.org/abs/1708.05513 has an interesting overview. At a more pop-sci level, https://skyandtelescope.org/astronomy-news/the-asteroid-and-the-pea/ https://skyandtelescope.org/astronomy-news/the-asteroid-and-... The MESSENGER programme did some science on Mercury's exosphere <https://en.wikipedia.org/wiki/Atmosphere_of_Mercury https://en.wikipedia.org/wiki/Atmosphere_of_Mercury> (and effects like ion sputtering photon-stimulated desorption, each of which kicks mainly sodium atoms off Mercury's surface into its long cometary tail) that is likely to be interesting, but is likely to undermine the idea that electromagnetic forces are significant with respect to the planet's orbital evolution. There is a substantial body of literature on radiation pressure's effects on artificial Earth satellites, but such devices are certainly not in hydrostatic equilibrium and rarely anything close to spherical (extended solar panels, etc.) Putting "solar radiation pressure satellites" into your favourite Internet search engine will be fruitful. There is also a body of literature where the radial solar radiation force is important in calculating the trajectories of space probes sent to various parts of our solar system. Again, these are low-mass objects on many-year flights. The Mariner programme generated papers relevant to Mercury e.g. the 160 pages of <https://ntrs.nasa.gov/citations/19750009204 https://ntrs.nasa.gov/citations/19750009204>.