Synchronization of conjunctions

• Galilean moons
• Natural month
• Lunar eccentricity and inclination
• Asteroids and comets

Galilean moons

Are Galilean moons synchronized with conjunctions of pair Venus-Earth?

conjunct. V-E|  conjunctions of all Galilean sattelites
-----------------------------------------------------
   1970.87   |   1970.89  1971.29  1971.69  1972.09
   1972.47   |   1972.49  1972.89  1973.29  1973.69
   1974.07   |   1974.09  1974.49  1974.89  1975.29
   1975.66   |   1975.69  1976.09  1976.49  1976.89
   1977.27   |   1977.28  1977.68  1978.08  1978.48
   1978.86   |   1978.88  1979.28  1979.68  1980.08
   1980.46   |   1980.48  1980.88  1981.28  1981.68
   1982.06   |   1982.08  1982.48 ...

Conjunctions of all Galilean satellites of Jupiter appear with period 437.64 d (Meeus), i.e. 1.1982 years.
During this time Venus pass from the furthermost west to the furthermost east elongation (439-443 d).

Period 437.64 days corresponds approximately to:

• 3/4 synodic period Venus-Earth
  (3/4*(V,E)=3/4*583.92=437.94 days)
• period of Chandler spiral motion of earth magnetic pole
  (according to various authors it has value 1.17-1.21 y;
  e.g. Jeffreys: 1.202 y; Rudnik: 1.193 y, Fairbridge 1.1855 y,...)
• period of nutation of earth axis
  (438 d)
• J/10; tenth of orbital period of Jupiter
  (J/10=433.26 d)
• 16 sidereal lunations
  (16*27.3217=437.15 d)

Natural month

Sometimes it appears to be preferable to divide year to 13 months (see synodical periods we have:
((E,L),-(V,E)) = (29.53, 583.92) = 28.11 days.

Lunar eccentricity and inclination

Let it holds for period P,Q:
(V,E) = (M,P) and (E,R) = (Q,V),
i.e.
[P,V] = [M,E] and [Q,R] = [V,E],
where M,V,E,R are orbital periods of Mercury, Venus, Earth and Mars.
Then
1/P = 1/M-1/V+1/E; P= 103.55 days = 207.10 days/2 and
1/Q = 1/V+1/E-1/R; Q= 174.50 days = 349.00 days/2.

Eccentricity of lunar orbit changes with period c. 205.9 days (Meeus), inclination of lunar orbit with period c. 173.3 days (346.6 days).
(Do they have any connection with cycles P and Q?)

Beats:
(205.9, 207.1) = 35540 days ( 97.3 years),
(346.6, 349.0) = 50400 days (138.0 years).

See Eclipse year.

Asteroids and comets

The more eccentric orbit is, the more probable seems to be synchronization of body with certain orbital period (rather than with synodic period).

Halley comet crosses solar system at least a few millenia. So, it possibly has been synchronized with motion of other, greater bodies. Some theorist assume relation to period 13J/2 = 77.1 years.
From axial period J-S we get:
9*[J,S]/2 = 9*16.913/2 = 76.11 years.

Orbital period of asteroid Chiron is 50.42 years.
From axial period J-S we get:
3*[J,S] = 3*16.913 = 50.74 years.