太阳和行星束缚暗物质对太阳系行星和卫星动力学的影响
Effect of Sun and Planet-Bound Dark Matter on Planet and Satellite Dynamics in the Solar System
摘要：
我们应用我们最近的研究结果，围绕质量变化的中心体的吸积现象的暗物质-假设不自我湮灭-太阳和太阳系的主要机构，由于其运动在整个银河系晕。我们检查其对行星及其卫星轨道的影响，时间尺度为太阳系的年龄。结果表明，太阳暗物质的吸积速率为\approx 10^-12 yr^-1（根据太阳暗物质含量的上限ΔM/M= 0.02-0.05来推断，假设在过去的4.5 Gyr中以某种方式积累了暗物质），那么在4.5 Gyr之前，行星将被移动到遥远的地方约10^-2-10^1 au。另一个结果是，地球轨道的半长轴（近似等于天文单位）将经历0.02-0.05 m yr^-1的长期增长，这与天文单位长期增长0.07 +/- 0.02 m yr^-1和0.05 m yr^-1的最新观测结果一致。假设太阳在未来数十亿年内将继续以过去的速率吸积暗物质，那么太阳系行星的轨道将缩小约10^-1- 10 ^1 au（地球的轨道将缩小\approx 0.2-0.5 au），这将对它们的命运产生影响，尤其是内行星。另一方面，月球和行星的星历表为太阳引力参数GM的长期变化设定了上限，该上限比10^-12 yr^-1小一个数量级。相反，行星上的暗物质吸积对它们的卫星产生的相关影响较小。事实上，4.5 Gyr以前，它们的轨道只比现在宽10^-2- 10 ^1 km。（节录）
英文摘要：
We apply our recent results on orbital dynamics around a mass-varying central body to the phenomenon of accretion of Dark Matter-assumed not self-annihilating-on the Sun and the major bodies of the solar system due to its motion throughout the Milky Way halo. We inspect its consequences on the orbits of the planets and their satellites over timescales of the order of the age of the solar system. It turns out that a solar Dark Matter accretion rate of \approx 10^-12 yr^-1, inferred from the upper limit ΔM/M= 0.02-0.05 on the Sun's Dark Matter content, assumed somehow accumulated during last 4.5 Gyr, would have displaced the planets faraway by about 10^-2-10^1 au 4.5 Gyr ago. Another consequence is that the semimajor axis of the Earth's orbit, approximately equal to the Astronomical Unit, would undergo a secular increase of 0.02-0.05 m yr^-1, in agreement with the latest observational determinations of the Astronomical Unit secular increase of 0.07 +/- 0.02 m yr^-1 and 0.05 m yr^-1. By assuming that the Sun will continue to accrete Dark Matter in the next billions year at the same rate as in the past, the orbits of its planets will shrink by about 10^-1-10^1 au (\approx 0.2-0.5 au for the Earth), with consequences for their fate, especially of the inner planets. On the other hand, lunar and planetary ephemerides set upper bounds on the secular variation of the Sun's gravitational parameter GM which are one one order of magnitude smaller than 10^-12 yr^-1. Dark Matter accretion on planets has, instead, less relevant consequences for their satellites. Indeed, 4.5 Gyr ago their orbits would have been just 10^-2-10^1 km wider than now. (Abridged)
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