Jovian orbit has an indispensable eccentricity (c. 0.05). It is by half of astronomical unit (75 million kilometers) nearer to the Sun in perihelion than in aphelion. Jupiter seems to compress and release all the bodies in space towards the Sun.
Distant satellites of Jupiter synchronize their periods with the Sun. Their orbital periods are whole number fractions of Jovian period (J/6, J/17, ...), i.e. (722 days, 255 days,...).
Period observed in Solar wind (c. 1.3 years) seems to be also such a fraction (J/9, i.e. 1.317 years).
Ratios of Jovian period to synodical periods of inner planets:
J/(M,R)= 11.861983/0.2762169= 42.944451
J/(M,E)= 11.861983/0.3172552= 37.389405
J/(M,V)= 11.861983/0.3958007= 29.969586
J/(V,R)= 11.861983/0.9142273= 12.974873
J/(V,E)= 11.861983/1.5986896= 7.419816
J/(E,R)= 11.861983/2.1353487= 5.555057
Cases J/(M,R), J/(M,V) and J/(V,R) give nearly whole number ratio.
Beats:
((E,R),J/6) = (2.13535, 1.97700) = 26.660 y
((V,E),J/7) = (1.59869, 1.69457) = 28.255 y
((M,E),J/37) = (0.31726, 0.32059) = 30.462 y
((M,R),J/43) = (0.27622, 0.27586) = 213.563 y
((M,V),J/30) = (0.39580, 0.39540) = 389.986 y
((V,R),J/13) = (0.91423, 0.91246) = 472.085 y
Beats of conjunction M-V-R are higher then the other beats.
Beats ((M,R),J/43) makes nearly exactly half of the Babylonian period (B/2 = 18*J = 213.516 y).
From all combinations of synodical periods the highest value of beats is:
(((M,V),(V,R)), J/17)= (0.69798, 0.69776) = 2242.4806 y.
During 1900-2000 conjunctions M-V-R appear after passing of Jupiter through the perihelion:
J in perihelion M-V M-R V-R
---------------------------------------
1904.42 1904.53 1904.52 1904.48
1916.31 1916.39 1916.37 1916.32
1928.19 1928.31 1928.27 1928.20
1940.02 1940.16 1940.15 1940.13
1951.90 1952.01 1952.00 1951.98
1963.78 1963.93 1963.90 1963.85
1975.61 1975.79 1975.79 1975.79
1987.49 1987.64 1987.64 1987.65
1999.38 1999.54 1999.52 1999.50
Let us assume, it holds:
J/(E,R)= 50/9. (11.861983/2.1353487= 5.555057).
During 50 conjunctions E-R, i.e. during c. 106.76 years (quarter of Babylonian period) Jupiter travels 9 cycles.
Let J = 11.861983 y, E = 1.0000174 y.
From (E,R') = J*9/50 = 2.1351570 y is R' = 1.8809970 y (687.0342 d).
Let also:
(M',R')= J/43= 11.861983/43= 0.2758601
(M',V')= J/30= 11.861983/30= 0.3953994
(V',R')= J/13= 11.861983/13= 0.9124602
Hence:
M'= 0.2405778 y ( 87.8710 d), (M'/M) = 1/1.00112
V'= 0.6144125 y (224.4142 d), (V'/V) = 1/1.00128
E = 1.0000174 y (365.2564 d),
R'= 1.8809970 y (687.0342 d), (R'/R) = 1/1.00008
J = 11.861983 y
Let B = 36*J (c. 427.03 y, Babylonian period).
In the mentioned model it holds:
1/M'-5/V'+4/E = 8/B
3/V'-7/E+4/R' = 4/B
Conjunctions of inner planets at opposition with Jupiter (precision 30°):
1243.53, 1288.23, 1332.99;
1529.71, 1574.39, 1619.14;
1815.86, 1860.60, 1905.30.
(Distance of these triads is c. 286.15 years; 24*J= 284.7 years).
Similar configurations (precision 35°):
1905.3, 1950.1, 2005.9, 2050.6.
In years 1905-1906 and about y.1950 seismicity increased;
Gutenberg, Richter, ∑E, interval 1904-1952:
|
Year |
1905 |
1906 |
1911 |
1917 |
1918 |
1920 |
1923 |
1933 |
1934 |
1938 |
1941 |
1946 |
1950 |
|
∑E>15 |
23.1 |
59.7 |
27.7 |
15.1 |
20.8 |
26.8 |
18.6 |
21.1 |
17.6 |
20.0 |
15.5 |
17.2 |
39.6 |
Will intensity of earthquakes increase
also in years 2005-2006 and 2050-2051?
One of the greatest solar spots was observed (Newcomb S.) 2.3.1905 (maximum, c. 1/3 of solar hemisphere).
Opposition (precision 20°) happened 22.4.1905:
Date Difference Jul.date Math.date
137 Mar 17 AD( 0.00000) #1771172.5 ( 137.21032)
282 Jul 14 AD( 145.32512) #1824252.5 ( 282.53855)
468 Feb 18 AD( 185.59890) #1892042.5 ( 468.14141)
754 Apr 12 AD( 286.14648) #1996557.5 ( 754.29400)
1288 Mar 19 AD( 533.93566) #2191577.5 (1288.24106)
1574 May 17 AD( 286.16016) #2296097.5 (1574.40734)
1619 Feb 20 AD( 44.73648) #2312437.5 (1619.14478)
1860 Aug 10 AD( 241.46475) #2400632.5 (1860.61468)
1905 Apr 22 AD( 44.69541) #2416957.5 (1905.31105)
2191 Jun 26 AD( 286.17385) #2521482.5 (2191.49102)
Let phenomenon P means that given planets align into straight line. Let us consider the following algorithm:
For configuration Mercury-Venus-Mars-Jupiter, k=3 days, K=3600 days and accuracy 15° (of triads M-R-J and V-R-J) we get on interval 1600-2000 this sequence of data:
Date (Difference) Julian date (Math. date) Solar extreme
1600 Mar 1 AD ( -) #2305508 (1600.17249) -
1611 Apr 12 AD ( 11.11294) #2309567 (1611.28566) 1610.8
1622 May 17 AD ( 11.09651) #2313620 (1622.38241) 1619.0
1633 Jun 21 AD ( 11.09651) #2317673 (1633.47915) 1634.0
1644 Sep 15 AD ( 11.23614) #2321777 (1644.71553) 1645.0
1655 Dec 29 AD ( 11.28542) #2325899 (1656.00120) 1655.0
1667 Feb 8 AD ( 11.11294) #2329958 (1667.11437) 1666.0
1678 Mar 21 AD ( 11.11294) #2334017 (1678.22754) 1679.5
1689 Jun 12 AD ( 11.22793) #2338118 (1689.45571) 1689.5
1700 Oct 1 AD ( 11.30185) #2342246 (1700.75780) 1698.0
1711 Nov 15 AD ( 11.12115) #2346308 (1711.87919) 1712.0
1722 Dec 23 AD ( 11.10472) #2350364 (1722.98415) 1723.5
1734 Mar 16 AD ( 11.22793) #2354465 (1734.21231) 1734.0
1745 Jul 1 AD ( 11.29363) #2358590 (1745.50619) 1745.0
1756 Aug 14 AD ( 11.12115) #2362652 (1756.62757) 1755.2
1767 Sep 19 AD ( 11.09651) #2366705 (1767.72432) 1766.5
1778 Dec 5 AD ( 11.21150) #2370800 (1778.93606) -
1790 Jan 9 AD ( 11.09651) #2374853 (1790.03281) -
1801 Apr 30 AD ( 11.30185) #2378981 (1801.33490) 1798.3
1812 Jun 7 AD ( 11.10472) #2383037 (1812.43985) 1810.6
1823 Jul 13 AD ( 11.09651) #2387090 (1823.53660) 1823.3
1834 Sep 22 AD ( 11.19507) #2391179 (1834.73191) 1833.9
1845 Nov 2 AD ( 11.11294) #2395238 (1845.84509) 1843.5
1857 Mar 1 AD ( 11.32649) #2399375 (1857.17182) 1856.0
1868 Apr 11 AD ( 11.11294) #2403434 (1868.28499) 1867.2
1879 Jun 22 AD ( 11.19507) #2407523 (1879.48030) 1878.9
1890 Aug 2 AD ( 11.11294) #2411582 (1890.59347) 1889.6
1901 Dec 3 AD ( 11.33470) #2415722 (1901.92842) 1901.7
1913 Jan 13 AD ( 11.11294) #2419781 (1913.04159) 1913.6
1924 Mar 25 AD ( 11.19507) #2423870 (1924.23690) 1923.6
1935 May 3 AD ( 11.10472) #2427926 (1935.34186) -
--------------------------------------------------------------
1946 Sep 2 AD ( 11.33470) #2432066 (1946.67681) 1947.5
1957 Oct 13 AD ( 11.11294) #2436125 (1957.78998) 1957.9
1968 Dec 11 AD ( 11.16222) #2440202 (1968.95244) 1968.9
1980 Jan 22 AD ( 11.11294) #2444261 (1980.06561) 1979.9
1991 Feb 26 AD ( 11.09651) #2448314 (1991.16236) 1989.6
In years 1600-1925 (exception 1770-1790) data coincide with solar minima.
(Then phase shift occurs and data - in years 1950-2000 - follow solar maxima.)
See also symmetry and solar activity.
Selected data of straight configurations V-E-J or E-V-J
(see also outline of configurations M-R-J and V-R-J above).
Date (Difference) Julian date (Math. date)
1600 Mar 4 AD ( -) #2305511 (1600.18070)
1611 Aug 17 AD ( 11.45243) #2309694 (1611.63338)
1622 Aug 8 AD ( 10.97604) #2313703 (1622.60965)
1633 Dec 27 AD ( 11.38672) #2317862 (1633.99662)
1644 Dec 12 AD ( 10.95962) #2321865 (1644.95647)
1656 May 23 AD ( 11.44422) #2326045 (1656.40093)
1667 May 12 AD ( 10.96783) #2330051 (1667.36900)
1678 Oct 3 AD ( 11.39493) #2334213 (1678.76417)
1689 Sep 18 AD ( 10.95962) #2338216 (1689.72402)
1701 Feb 25 AD ( 11.43600) #2342393 (1701.16027)
1712 Feb 14 AD ( 10.96783) #2346399 (1712.12834)
1723 Jul 8 AD ( 11.39493) #2350561 (1723.52351)
1734 Jun 23 AD ( 10.95962) #2354564 (1734.48336)
1745 Dec 5 AD ( 11.45243) #2358747 (1745.93604)
1756 Nov 29 AD ( 10.98426) #2362759 (1756.92053)
1767 Nov 15 AD ( 10.95962) #2366762 (1767.88038)
1779 Apr 8 AD ( 11.39493) #2370924 (1779.27556)
1790 Sep 20 AD ( 11.45243) #2375107 (1790.72823)
1801 Sep 15 AD ( 10.98426) #2379119 (1801.71273)
1812 Aug 31 AD ( 10.95962) #2383122 (1812.67258)
1824 Jan 20 AD ( 11.38672) #2387281 (1824.05954)
1835 Jul 1 AD ( 11.44422) #2391461 (1835.50400)
1846 Jun 22 AD ( 10.97604) #2395470 (1846.48028)
1857 Jun 7 AD ( 10.95962) #2399473 (1857.44013)
1868 Oct 26 AD ( 11.38672) #2403632 (1868.82710)
1880 Apr 3 AD ( 11.43600) #2407809 (1880.26334)
1891 Mar 23 AD ( 10.96783) #2411815 (1891.23141)
1902 Mar 9 AD ( 10.95962) #2415818 (1902.19126)
1913 Jul 31 AD ( 11.39493) #2419980 (1913.58644)
1925 Jan 6 AD ( 11.43600) #2424157 (1925.02268)
1936 Jan 1 AD ( 10.98426) #2428169 (1936.00718)
1946 Dec 17 AD ( 10.95962) #2432172 (1946.96703)
1958 May 13 AD ( 11.40315) #2436337 (1958.37042)
1969 Apr 28 AD ( 10.95962) #2440340 (1969.33027)
1980 Oct 16 AD ( 11.46886) #2444529 (1980.79937)
1991 Oct 2 AD ( 10.95962) #2448532 (1991.75922)
Let q=A/J, r= (A,J)/J, where A is orbital period of an asteroid. Ratios q are often evaluated, ratios r are simpler.
E.g. ratios q= 1/3, 2/5, 3/7, 4/9, 5/11 correspond to r= 1/2, 2/3, 3/4, 4/5, 5/6,..., i.e. n/(n+1).
Asteroids q=2/3 (Hilda), 3/4 (Thule),.. have r=2/1,3/1,..., i.e. n.