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Do you need 1000 years? 50 years? 1-hour accuracy? 1-second accuracy? A simple linear interpolation for the perihelia from the year 2000 to 2050 gives a maximum error of about 1.3 days for the year 2009 and a mean absolute error of about 19.3 hours: et = 31558511.31638778 * year - 63116806104.00429 et is the so called ephemeris time (used by NAIF team in the ...

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Most moons orbit in the equatorial planes of the planets they orbit. Earth's moon is a big exception. Because of the varying tilt angles of planets, some satellite systems are too far out out the planes between their planets and their stars, and so never pass into the shadows of their planets and never get eclipsed by their planets. Other planets have ...

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Is our solar system inherently stable or unstable? Yes. This is not an either / or question. There are multiple conjectures regarding instabilities in both the early and late solar system: A fifth giant planet may have been ejected from the solar system early in the solar system’s evolution. Neptune and Uranus may have switched places early in the solar ...

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There is no easy formula for what you want. Astronomical Algorithms provides an algorithm for the times of perihelion and aphelion passages of the Earth-Moon barycenter. The times at which the Earth itself is closest to / furthest from the Sun is made much more complex by the fact that the Earth and Moon orbit one another as well as the Sun. Because ...

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The solar system is chaotic, but it is also stable! The fixed and linkages between the bars of a double pendulum allow for very rapid energy transfer between the arms. This makes the chaotic motion develop rapidly. The interactions between planets are gravitational and much much weaker, moreover, the planets are heavier and it takes a lot more energy to ...

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This is basically a repeat of Aristarchus’ experiment of trying to figure out the distance between the Earth and the Moon from a lunar eclipse. See for example https://pwg.gsfc.nasa.gov/stargaze/Shipprc2.htm So, we know that Iapetus orbits Saturn in 79.3215 days, at an average distance of 3,560,820 km. Saturn’s diameter is 116,464 km, and it orbits the Sun ...

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To describe the position of an orbiting body you need 6 numbers. There are different ways to do this: You can give the position $(x,y,z)$ and velocity $(\dot x, \dot y, \dot z)$. At a given time $t_0$, and then use Newtons laws to work out the position of the planet at any time in the future. You can give the orbital parameters: Eccentricity (the shape of ...

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