THE RIGHT ANGLE REMAINDER RULE – FORMAT ONE.
To see how these examples are calculated, click on this link:-
Example 1. The Solar System contains Four Giant Planets. The SUM of their Rotation Periods = 2.247130 Earth days. During this time period, Earth rotates 2 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 1.18 degrees.)
Example 2. Jupiter has just Four LARGE (“Galilean”) Satellites. The SUM of their Orbital Periods = 29.16389019 Earth days. During this time period, Earth rotates 29 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 2.255 degrees.)
Example 3. The Solar System contains just (exactly) Twenty LARGE Satellites. The SUM of their Orbital Periods = 227.0038274 Earth days. During TWICE this time period, Earth rotates 455 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 0.23 degrees.)
Example 4. The SUM of The Rotation Periods of The Sun and The Moon = 51.983911 Earth days. During TWICE this time period, Earth rotates 104 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 0.89 degrees.)
Example 5. The SUM of The Rotation Periods of The Seven Inner Solar System Revolving Bodies (Mercury, Venus, Earth, Mars, The Moon, and – Mars satellites – Phobos and Deimos) = 332.59114 Earth days. During this time period, Earth rotates 333 complete rotations plus A REMAINDER of TWO RIGHT ANGLES. (Error 0.616 degrees.)
Example 6. The SUM of The Rotation Periods of The Sun and The Four Inner Solar System Planets = 328.3503767 Earth days. During this time period, Earth rotates 329 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 0.238 degrees.)
Example 7. The Two Gas Giants are (neighbour planets) Jupiter and Saturn. The SUM of The Rotation Periods of The Two Gas Giants and their LARGE Satellites = 136.7518987 Earth days. During TWICE this time period, Earth rotates 274 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 0.936 degrees.)
Example 8. The Three OUTERMOST Planets are:- Uranus, Neptune, and Pluto. These planets have just Seven LARGE Satellites. The SUM of The Orbital Periods of these seven satellites = 42.51122652 Earth days. During TWICE this time period, Earth rotates 85 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 1.88 degrees.)
Example 9. The SUM of The Orbital and Rotation Periods of (Earth’s neighbour planet) Venus = 467.71937 Earth days. During this time period, Earth rotates 468 complete rotations plus A REMAINDER of FOUR RIGHT ANGLES. (Error 0.037 degrees.)
Example 10. The SUM of The Rotation Periods of Venus and its Satellite Neith (which is not currently observed, due to absence, or poor visibility, or for whatever reason) = 252.3107 Earth days. During this time period, Earth rotates 252 complete rotations plus A REMAINDER of FOUR RIGHT ANGLES. (Error 0.53 degrees.)
INNERMOST SATELLITES.
Every planet that has satellites must have one INNERMOST Satellite. For example, Mars’ INNERMOST Satellite is Phobos; and Jupiter’s INNERMOST Satellite is Metis etc.
Example 11. The Solar System contains seven planets that have satellites, and thus there are Seven INNERMOST Satellites in The Solar System. The SUM of the Orbital Periods of these Seven INNERMOST Satellites = 35.5270603 Earth days. During TWICE this time period, Earth rotates 71 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 0.48 degrees.)
Example 12. The SUM of The Orbital Periods of The INNERMOST Satellites of (each of) The Four Giant Planets = 1.499250 Earth days. During this time period, Earth rotates 1 complete rotation plus A REMAINDER of TWO RIGHT ANGLES. (Error 1.2 degrees.)
Example 13. In this example, we look at The INNERMOST Satellites of The Inner Solar System. The Sun’s INNERMOST “Satellite” (planet) is Mercury. Venus’ INNERMOST Satellite is Neith (which has not been seen recently – due to its current (inexplicable!) absence, or due to poor visibility, or for whatever reason). Earth’s INNERMOST Satellite is the Moon; and Mars’ INNERMOST Satellite is Phobos. The SUM of The Orbital Periods of these four INNERMOST Satellites = 124.90177 Earth days. During this time period, Earth rotates 125 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 2.258 degrees.)
Example 14. The Two Gas Giants are Jupiter and Saturn. The INNERMOST Satellites of these two planets are – respectively – Metis and Pan. The SUM of The Orbital Periods of Metis and Pan = 0.86983 Earth days. During TWICE this time period, Earth rotates 1 complete rotation plus A REMAINDER of THREE RIGHT ANGLES. (Error 2.008 degrees.)
PRIMARY SATELLITES.
A PRIMARY SATELLITE is the LARGEST Satellite for a particular planet. For example, Jupiter has just Four Large Satellites (although many small ones), of which Ganymede is The Largest. In that case, Jupiter’s Primary Satellite is Ganymede. Every planet that has satellites must have a PRIMARY SATELLITE
Example 15. The SUM of The Rotation Periods of Earth and Mars and their PRIMARY Satellites = 29.6638 Earth days. During this time period, Earth rotates 29 complete rotations plus A REMAINDER of THREE RIGHT ANGLES. (Error 1.796 degrees.)
Example 16. The Two Ice Giants are Uranus and Neptune. The PRIMARY Satellites of these two planets are:- Uranus satellite Titania, and Neptune Satellite Triton. The SUM of The Orbital Periods of these two satellites = 14.5827144 Earth days. During TWICE this time period, Earth rotates 29 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 1.7 degrees.)
Example 17. The SUM of the Sidereal and Synodic Rotation Periods of The Sun = 51.11028 Earth days. During this time period, Earth rotates 51 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 0.076 degrees.)
Example 18. The SUM of the Sidereal and Synodic Revolution Periods of The Moon = 56.8522492 Earth days. During this time period, Earth rotates 56 complete rotations plus A REMAINDER of FOUR RIGHT ANGLES. (Error 2.84 degrees.)
Example 19. The SUM of The Synodic Revolution Period plus the Synodic Rotation Period of Mercury = 185.741 Earth days. During this time period, Earth rotates 186 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 0.17 degrees.)
SATELLITE “DAYS”.
The “Day” of a satellite is the length of time between successive appearances of that satellite on a fixed horizon of the parent planet. For example – The Moon’s Orbital Period = 27.321661 Earth days, but The Lunar Day = 1.0350501 Earth days. The following examples will all involve satellite “days”.
Example 20. There are Three Inner Solar System Satellites (excluding Venus Satellite – Neith, which is no longer to be seen, for whatever reason). These are:- The Moon, and The Two Mars Satellites Phobos and Deimos. The SUM of The “Days” of these three satellites = 6.9747531 Earth days. During this time period, Earth rotates 6 complete rotations plus A REMAINDER of FOUR RIGHT ANGLES. (Error 2.21 degrees.)
Example 21. Jupiter has just Four LARGE Satellites – Io, Europa, Ganymede, and Callisto. The “Days” of each of these four satellites are as follows:- Io 0.539692 Earth days; and Europa 0.468042; and Ganymede 0.438907 Earth days.; and Callisto 0.424046 Earth days. The SUM of these four time periods = 1.870687 Earth days. During TWICE this time period, Earth rotates 3 complete rotations plus A REMAINDER of THREE RIGHT ANGLES. (Error 0.58 degrees.)
Example 22 The Three Inferior Bodies (ie:- more “central” in the Solar System than Earth is) are:- The Sun, Mercury, and Venus. The SUM of The Orbital and Rotation Periods of these three bodies = 638.99702 Earth days. During this time period, Earth ROTATES 640 complete rotations plus A REMAINDER of THREE RIGHT ANGLES. (Error 1.27 degrees.)
and also:-
During this time period of 638.99702 Earth days, Earth REVOLVES 1 complete revolution plus A REMAINDER of THREE RIGHT ANGLES. (Error 0.199 degrees.)
Example 23. The SUM of The Synodic Revolution Periods of The Seven Inner Solar Revolving Bodies = 1876.1074 Earth days. During this time period, Earth rotates 1881 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error 2.22 degrees).
Example 24. The Naked-Eye Visible Planets are Mercury, Venus, Earth, Mars, Jupiter, and Saturn. (Actually, Uranus can also be seen by the naked eye, but nobody ever noticed it until 1781. Effectively, we can consider it as NOT Naked-Eye Visible.)
The Naked-Eye Visible Planets have just THIRTEEN LARGE Satellites. The SUM of The Orbital Periods of these Thirteen LARGE Satellites = 184.497569 Earth days. During this time period, Earth rotates 184 complete rotations plus A REMAINDER of FOUR RIGHT ANGLES (Error 0.97 degrees).
and also:-
During this time period of 184.497569 Earth days, Earth revolves altogether a total of 181.84 degrees, which is TWO RIGHT ANGLES (error 1.84 degrees).
Example 25. The Solar System contains just (exactly) Twenty LARGE Satellites. The SUM of their Orbital Periods = 227.0038274 Earth days. During TWICE this time period, Earth revolves 1 complete revolution plus A REMAINDER of ONE RIGHT ANGLE. (Error 2.526 degrees.)
Example 26. Venus is our closest neighbour planet. The SUM of Venus’ Synodic REVOLUTION Period plus Venus’ Synodic ROTATION Period = 729.8481 Earth days. During this time period, Earth REVOLVES 1 complete revolution plus A REMAINDER of FOUR RIGHT ANGLES (Error 0.655 degrees).