Orbits of Planets

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19 years 5 months ago #11940 by Larry Burford
Althought under some circumstances a particular pair of planets or moons (1) can become gravitatinally resonant over some time interval, their orbits are in general randomly related to each orher. Chaos rules in multi-body gravitational dynamics and as a result no planet or moon follows the same path on successive orbits. There are always small deviations from the last orbit, and from the orbit before that, etc. The eccintricity of each particular orbit changes over time. And the direction of each of the orbital axes also changes with time. Sometimes the deviations accumulate, sometimes they cancel.

Regards,
LB

(1) Jupiter (or is it Saturn?) has a pair of moons that currently travel in almost exactly the same orbit. Every so many orbits one catches up with the other and they "swap" orbits. The one that was slightly inside (and faster than) the other is now slightly outside (and slower than) the other. The orbital ellipses of these two bodies are closely aligned.

BTW, these two moons are an excellant real world example of the impossibility-of-two-body-capture for gravity only interactions.

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19 years 5 months ago #13417 by tvanflandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Gregg</i>
<br />Each planet has an elliptical orbit. Are the apogees of these orbits more or less in a straight line or are they entirely random?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Random. Moreover, all the ellipses revolve at different rates (such as Mercury's famous excess advance of perihelion rate), so the directions of perihelion and aphelion are always changing. ["Apogee" means the point in the orbit farthest from Earth. "Aphelion" means the point farthest from the Sun. The generic terms are "apocenter" and "pericenter" ("peri" meaning closest).]

So is it possible that someday, by pure chance, all the aphelions might line up? No, because the orbits are not in the same plane either. They have relative inclinations (tilts) that are comparable in size to their eccentricities (ellipticity).

Just as linear alignments of multiple planets are impossible, so too are linear alignments of apogees. And nodes. The occasional fuss you see about such "alignments" refer to groupings such as several planets all on the same side of the Sun at the same time -- as if that was anything more than a geometric curiosity. Planetary gravitational forces are quite negligible here on Earth compared with forces from the Sun and Moon, and would be so even if all planets lined up. -|Tom|-

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19 years 5 months ago #13350 by Gregg
Replied by Gregg on topic Reply from Gregg Wilson
[Originally posted by Larry Burford]
Chaos rules in multi-body gravitational dynamics and as a result no planet or moon follows the same path on successive orbits. There are always small deviations from the last orbit, and from the orbit before that, etc. The eccintricity of each particular orbit changes over time. And the direction of each of the orbital axes also changes with time. Sometimes the deviations accumulate, sometimes they cancel.

Planetary gravitational forces are quite negligible here on Earth compared with forces from the Sun and Moon, and would be so even if all planets lined up. -|Tom|-

<hr noshade size="1">
Follow up question - speculation only: If a planet has a "solid" nuclear core such that its inertial mass greatly exceeds its gravitational mass, would its orbit be highly stable and resistant to changes in the gravitational flux? (According to conventional radiometric dating the planets are 4.5 billion years old or older. It appears that the orbits are extremely stable.)


Gregg Wilson

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19 years 5 months ago #12367 by tvanflandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Gregg</i>
<br />If a planet has a "solid" nuclear core such that its inertial mass greatly exceeds its gravitational mass, would its orbit be highly stable and resistant to changes in the gravitational flux?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Resistant to changes, yes. Stability would be mostly unaffected or made slightly worse because the planet could not fully imitate all the motion changes experienced by the central star. (Recall that the central star's motion is as easily changed by perturbations as that of any planet.)

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">(According to conventional radiometric dating the planets are 4.5 billion years old or older. It appears that the orbits are extremely stable.)<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Moreover, their gravitational and inertial masses are equal to the accuracy of observations. As outlined in <i>Pushing Gravity</i>, gravitational shielding effects are very small for solar system planets. -|Tom|-

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19 years 1 week ago #14398 by Joe Keller
Replied by Joe Keller on topic Reply from
Evidence of FitzGerald Contraction in the Solar System

Definition. "FitzGerald contraction" will mean here that matter contracts according to beta^2/2 but space does not.

The latitude of the solar apex motion in "ecliptic coordinates". The best available determination of the solar apex motion seems to be the Hipparcos satellite full data set, which gives (Abad et al, Astronomy & Astrophysics, Jan 2003) 24 km/s toward Declination +34, RA 276; error is 1 km/s and 2 degrees. For brevity, I will introduce about another degree of error, by using the perpendicular to Earth's orbit, to approximate the direction of orbital angular momentum of the entire solar system. So, the axis of the solar system differs (using RA = 270), 90 - (23.5 + 34) = 32.5 degrees, from the solar apex motion. Perhaps Jupiter's orbit, and the sun's pole, precess about the apex direction; the direction of the sun's pole is consistent with this.

Axial tilts of the rapidly rotating planets. A planet should rotate most easily when its axis is parallel to the solar apex motion, because then its FitzGerald contraction does not change direction relative to the planet's body. If the drag is as the sine of the angle, then the motion seems to gravitate, as if by a potential, toward the situation where the solar apex motion vector is on the precession circle, because the largest integral for r^(-k) * ds, occurs when the circle touches the origin. Indeed Earth, Mars, Saturn and Neptune have axial tilts ranging monotonically from 23 to 29 degrees; as the orbital speed becomes less important, the values approach 32.

Other planets outside a planet's orbital plane, work to change that planet's axial tilt. This effect is by far the weakest on Jupiter, so it may have yet to find the stablest (32 deg.) axial tilt.

Mechanism of the drag on rotation. The Miller, Morley/Miller and Michelson/Morley experiments all found an interferometer phase shift as if Earth, and everything near it, were FitzGerald contracted according to, mainly, the component of the solar apex motion along Earth's axis. The equatorial component of solar apex motion, and the orbital motion, displayed minified effects, on the net FitzGerald contraction.

Perhaps from gravitational energy considerations, only a solid inner planetary core inside a molten outer core, can respond to changing FitzGerald contraction during rotation. Uranus is less dense than Neptune. A molten core could provide Uranus' magnetic field. A lack of any solid inner core could explain why Uranus' rotational axis was perturbed all the way to 98 degrees, heedless of the 32 degree optimum. Perhaps without a molten outer core, Mars lacks a magnetic field; but, a molten outer core in an earlier epoch caused its former geologic activity, and set its axial tilt.

Internal heat production. When there are solid inner and liquid outer cores, heat production could be proportional to the mass of the solid inner core, and some power, perhaps the fourth, of the rotation frequency. My calculation shows that the FitzGerald compression of atoms in Earth's solid core (1.7% of Earth's mass) would, by increasing the atomic electric field energy, involve about 10^4 times the needed heat, if all of the energy became waste
heat.

The known internal heat productions of Earth (44 terawatts), and of Jupiter, Saturn and Neptune (all 1 to 3 times absorbed solar radiation), together with their rotational frequencies, imply plausible ratios of their inner core masses. Uranus' lack of internal heat could be additional evidence of its lack of a solid inner core.

A much different solar apex motion billions of years ago could have caused a different axial tilt of the planets then.

- Joseph C. Keller

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