FORMAT ONE DEMONSTRATIONS.
On this webpage, I will show the calculations pertaining to all the 26 examples of THE RIGHT ANGLE REMAINDER RULE – FORMAT ONE.
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.)
DEMONSTRATION:- Here are the names and Rotation Periods (expressed in Earth days) of The Four Giant Planets. Jupiter 0.41353831 and Saturn 0.44401 and Uranus 0.71833 and Neptune 0.671252
The SUM of these four periods = 2.247130 Earth days.
Earth’s Rotation Period = 0.997269663 Earth days.
2.247130 ÷ 0.997269663 = 2.25328 Earth rotations.
0.25328 x 360 = 91.18 degrees.
90 degrees = 1 right angle.
Error = 91.18 minus 90 = 1.18 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Jupiter’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/jup-rot
To verify the rotation periods of Saturn, Uranus, and Neptune, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Orbital Periods (expressed in Earth days) of The Four LARGE “Galilean” satellites of Jupiter:- Io 1.769137786 and Europa 3.551181041 and Ganymede 7.15455296 and Callisto 16.6890184
The SUM of these four periods = 29.16389019 Earth days.
29.16389019 ÷ 0.997269663 = 29.243735 Earth rotations.
0.243735 x 360 = 87.74 degrees.
90 degrees = 1 right angle.
Error = 90 minus 87.74 = 2.255 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Orbital Periods of The Four LARGE “Galilean” satellites of Jupiter, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Orbital Periods (expressed in Earth days) of The Twenty LARGE Satellites of The Solar System:- Earth satellite – The Moon 27.321661 and Jupiter Satellites – Io 1.769137786 and Europa 3.551181041 and Ganymede 7.15455296 and Callisto 16.6890184 and Saturn Satellites – Mimas 0.942421813 and Enceladus 1.370217855 and Tethys 1.887802160 and Dione 2.736914742 and Rhea 4.517500436 and Titan 15.94542068 and Hyperion 21.2766088 and Iapetus 79.3301825 and Uranus Satellites – Miranda 1.4134840 and Ariel 2.52037932 and Umbriel 4.1441765 and Titania 8.7058703 and Oberon 13.4632423 and Neptune Satellite – Triton 5.8768441 and Pluto satellite – Charon 6.387230
The SUM of these 20 orbital; periods = 227.0038274 Earth days.
TWICE this time period = 227.0038274 x 2 = 454.0076548 Earth days.
454.0076548 ÷ 0.997269663 = 455.2506425 Earth rotations.
0.2506425 x 360 = 90 23 degrees.
90 degrees = 1 right angle.
Error = 90.23 minus 90 = 0.23 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify the orbital periods of The Twenty LARGE Satellites of The Solar System, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Rotation Periods (expressed in Earth days) of The Sun and Moon:- The Sun 24.66225 and the Moon 27.321661
The SUM of these two periods = 51.983911 Earth days.
TWICE this time period = 51.983911 x 2 = 103.967822 Earth days.
103.967822 ÷ 0.997269663 = 104.252466 Earth rotations.
0.252466 x 360 = 90.89 degrees.
90 degrees = 1 right angle.
Error = 90.89 minus 90 = 0.89 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Sun’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify The Moon’s Rotation Period (which is equal to its orbital period, due to “tidal locking”), click on this link:-
www.solarsystemtimeperiods.com/large-sats
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and rotation periods (expressed in Earth days) of The Seven Inner Solar System Revolving Bodies:- Mercury 58.6462 and Venus 243.0187 and Earth 0.997269663 and Mars 1.025957 and The Moon 27.321661 and – Mars satellites – Phobos 0.31891023 and Deimos 1.2624407 The SUM of these seven periods = 332.59114 Earth days.
332.59114 ÷ 0.997269663 = 333.50171 Earth rotations.
0.50171 x 360 = 180.616 degrees.
180 degrees = 2 right angles.
Error = 180.616 minus 180 = 0.616 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Rotation Periods of Mercury, and Venus, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify The Rotation Period of Mars, click on this link:-
www.solarsystemtimeperiods.com/mars-rotation
To verify The Rotation Periods (which are equal to their orbital periods, due to “tidal locking”) of The Moon, Phobos, and Deimos, click on this link:-
www.solarsystemtimeperiods.com/large-sats
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and rotation periods (expressed in Earth days) of The Sun and The Four Inner Solar System Planets:- The Sun 24.66225 and Mercury 58.6462 and Venus 243.0187 and Earth 0.997269663 and Mars 1.025957
The SUM of these five periods = 328.3503767 Earth days.
328.3503767 ÷ 0.997269663 = 329.249338 Earth rotations.
0.249338 x 360 = 89.762 degrees.
90 degrees = 1 right angle.
Error = 90 minus 89.76 = 0.238
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Rotation Periods of The Sun, Mercury, and Venus, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify The Rotation Period of Mars, click on this link:-
www.solarsystemtimeperiods.com/mars-rotation
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Rotation Periods (expressed in Earth days) of The Two Gas Giants and their LARGE Satellites:- Jupiter 0.41353831 and Jupiter Satellites – Io 1.769137786 and Europa 3.551181041 and Ganymede 7.15455296 and Callisto 16.6890184 and Saturn 0.44401 and Saturn Satellites – Mimas 0.942421813 and Enceladus 1.370217855 and Tethys 1.887802160 and Dione 2.736914742 and Rhea 4.517500436 and Titan 15.94542068 and Hyperion “chaotic” rotation, and therefore excluded from the calculation – and Iapetus 79.3301825
The SUM of these thirteen periods = 136.7518987 Earth days.
TWICE this time period = 136.7518987 x 2 = 273.5037974 Earth days.
273.5037974 ÷ 0.997269663 = 274.2525994 Earth rotations.
0.2525994 x 360 = 90.936 degrees.
90 degrees = 1 right angle.
Error = 90.936 minus 90 = 0.936 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Jupiter’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/jup-rot
To verify the rotation period of Saturn, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify the orbital periods of The LARGE Satellites of Jupiter and Saturn, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify that Hyperion has “chaotic” rotation, click on this link (See the rotation period column in the table.):-
www.solarsystemtimeperiods.com/planet-orbital
To verify that satellite rotation periods are equal to their orbital periods (due to “tidal locking”), click on this link (See the letter S – standing for “same” in the rotation periods column):-
www.solarsystemtimeperiods.com/planet-orbital
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and orbital periods (expressed in Earth days) of The LARGE Satellites of The Three OUTERMOST Planets:- Uranus Satellites – Miranda 1.4134840 and Ariel 2.52037932 and Umbriel 4.1441765 and Titania 8.7058703 and Oberon 13.4632423 and Neptune Satellite – Triton 5.8768441 and Pluto satellite – Charon 6.387230
The SUM of The Orbital Periods of these seven satellites = 42.51122652 Earth days.
TWICE this time period = 85.02245304 Earth days.
85.02245304 ÷ 0.997269663 = 85.255229 Earth rotations.
0.255229 x 360 = 91.88 degrees.
90 degrees = 1 right angle.
Error = 91.88 minus 90 = 1.88 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify the orbital periods of the LARGE Satellites of Uranus and Neptune, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify Charon’s orbital period, click on this link:-
www.solarsystemtimeperiods.com/pluto-sats
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
To verify that Uranus, Neptune, and Pluto are The Three OUTERMOST Planets, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
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 0.0036 degrees.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Venus’ Orbital Period = 224.70067 Earth days.
Venus Rotation Period = 243.0187 Earth days.
The SUM of these two periods = 467.71937 Earth days.
467.71937 ÷ 0.997269663 = 468.99999 Earth rotations.
0.99999 x 360 = 359.9964 degrees.
360 degrees = 4 right angles.
Error = 360 minus 359.9964 = 0.0036 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Venus’ Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/orbital
To verify Venus’ Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Venus’ Rotation Period = 243.0187 Earth days.
Neith Rotation Period = 9.292 Earth days.
The SUM of these two periods = 252.3107 Earth days.
252.3107 ÷ 0.997269663 = 253.001479 Earth rotations.
253.001479 minus 252 = 1.001479 Earth rotations.
1.001479 x 360 = 360.53 degrees.
360 degrees = 4 right angles.
Error = 360.53 minus 360 = 0.53 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Venus’ Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify Neith’s Rotation Period (which is the same as its orbital period, due to “tidal locking”), click on this link:-
www.solarsystemtimeperiods.com/venus-sat
To verify that satellite Rotation Periods are equal to their orbital periods (See the letter S – standing for “same” in the rotation period column in the table), click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Orbital Periods (expressed in Earth days) of The Seven INNERMOST Satellites of The Solar System:- Mercury and Venus have no satellites. Earth’s INERMOST Satellite is The Moon (27.321661), and Mars’ INNERMOST Satellite is Phobos (0.31891023), and Jupiter’s INNERMOST Satellite is Metis (0.294780), and Saturn’s INNERMOST Satellite is Pan (0.57505), and Uranus’ INNERMOST Satellite is Cordelia (0.3350331), and Neptune’s INNERMOST Satellite is Naiad (0.294396), and Pluto’s INNERMOST Satellite is Charon (6.387230)
The SUM of these seven periods = 35.5270603 Earth days.
TWICE this time period = 71.05412066 Earth days.
71.05412066 ÷ 0.997269663 = 71.24865 Earth rotations.
0.24865 x 360 = 89.515 degrees.
90 degrees = 1 right angle.
Error = 90 minus 89.515 = 0.48 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Moon’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify Phobos’ Orbital Period (and that it is Mars’ INNERMOST satellite), click on these link:-
www.solarsystemtimeperiods.com/large-sats
and
www.solarsystemtimeperiods.com/planet-orbital
To verify Metis’ Orbital Period (and that it is Jupiter’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/jup-inner
To verify Pan’s Orbital Period (and that it is Saturn’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/saturn-sats
To verify Cordelia’s Orbital Period (and that it is Uranus’ INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/uranus-innermost
To verify Naiad’s Rotation Period (and that it is Neptune’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/neptune-sats
To verify Charon’s Orbital Period (and that it is Pluto’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/pluto-sats
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Orbital Periods (expressed in Earth days) of The INNERMOST Satellites of (each of) The Four Giant Planets:- Jupiter’s INNERMOST Satellite is Metis (0.294780), and Saturn’s INNERMOST Satellite is Pan (0.57505), and Uranus’ INNERMOST Satellite is Cordelia (0.3350331), and Neptune’s INNERMOST Satellite is Naiad (0.294396).
The SUM of these four periods = 1.499250 Earth days.
1.499250 ÷ 0.997269663 = 1.503355 Earth rotations.
0.503355 x 360 = 181.2 degrees.
180 degrees = 2 right angles.
Error = 181.2 minus 180 = 1.2 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify planet sizes (See the mass and radius columns in the table), and thus to verify The Four Giant Planets, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify Metis’ Orbital Period (and that it is Jupiter’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/jup-inner
To verify Pan’s Orbital Period (and that it is Saturn’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/saturn-sats
To verify Cordelia’s Orbital Period (and that it is Uranus’ INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/uranus-innermost
To verify Naiad’s Rotation Period (and that it is Neptune’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/neptune-sats
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Orbital Periods (expressed in Earth days) of The INNERMOST Satellites of The Inner Solar System:- The Sun’s INNERMOST “Satellite” (planet) is Mercury (87.9692), and Venus’ INNERMOST Satellite is Neith (9.292), and Earth’s INNERMOST Satellite is the Moon (27.321661), and Mars’ INNERMOST Satellite is Phobos (0.31891023).
The SUM of these four periods = 124.90177 Earth days.
124.90177 ÷ 0.997269663 = 125.243728 Earth rotations.
0.243728 x 360 = 87.742 degrees.
90 degrees = 1 right angle.
Error = 90 minus 87.742 = 2.258 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Mercury’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/orbital
To verify The Moon’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify Neith’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/venus-sat
To verify Phobos’ Orbital Period (and that it is Mars ’INNERMOST satellite), click on these links:-
www.solarsystemtimeperiods.com/large-sats
and
www.solarsystemtimeperiods.com/planet-orbital
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Orbital Periods (expressed in Earth days) of The INNERMOST Satellites of (each of) The Two Gas Giants – Jupiter and Saturn:-
Jupiter’s INNERMOST Satellite is Metis (0.294780), and Saturn’s INNERMOST Satellite is Pan (0.57505)
The SUM of these two periods = 0.86983 Earth days.
TWICE this time period = 1.73966 Earth days.
1.73966 ÷ 0.997269663 = 1.744423 Earth rotations.
0.744423 x 360 = 267.992 degrees.
270 degrees = 3 right angles.
Error = 270 minus 267.992 = 2.008 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Metis’ Orbital Period (and that it is Jupiter’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/jup-inner
To verify Pan’s Orbital Period (and that it is Saturn’s INNERMOST Satellite), click on this link:-
www.solarsystemtimeperiods.com/saturn-sats
To verify The Two Gas Giants, type into a Google search the term “The Two Gas Giants”, and see the Wikipedia entry entitled “Gas Giants”.
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Rotation Periods (expressed in Earth days) of Earth and Mars and their PRIMARY Satellites:- Earth 0.997269663 and Earth’s PRIMARY Satellite – The Moon 27.321661 and Mars 1.025957 and Mars’ PRIMARY Satellite – Phobos 0.31891023
The SUM of these four periods = 29.6638 Earth days.
29.6638 ÷ 0.997269663 = 29.74501 Earth rotations.
0.74501 x 360 = 268.204 degrees.
270 degrees = 3 right angles.
Error = 270 minus 268.204 = 1.796 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Mars’ Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/mars-rotation
To verify The Moon’s Rotation Period (which is equal to its orbital period, due to “tidal locking”), click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify Phobos’ Rotation Period (which is equal to its orbital period, due to “tidal locking”), click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Orbital Periods (expressed in Earth days) of The PRIMARY Satellites of Uranus and Neptune:- Uranus’ PRIMARY Satellite Titania 8.7058703 and Neptune’s PRIMARY Satellite Triton 5.8768441
The SUM of these two periods = 14.5827144 Earth days.
TWICE this time period = 29.1654288 Earth days.
29.1654288 ÷ 0.997269663 = 29.245278 Earth rotations.
0.245278 x 360 = 88.300 degrees.
90 degrees = 1 right angle.
Error = 90 minus 88.300 = 1.7 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
To verify The Orbital Periods of Titania and Triton, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify The Two Ice Giants, type into a Google search the term “The Two Ice Giants”, and see the Wikipedia entry entitled “Ice Giants”.
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
The Sun’s (Sidereal) Rotation Period = 24.66225 Earth days.
The Sun’s SYNODIC Rotation Period = 26.44803 Earth days.
The SUM of these two periods = 51.11028 Earth days.
51.11028 ÷ 0.997269663 = 51.25021 Earth rotations.
0.25021 x 360 = 90.076 degrees.
90 degrees = 1 right angle.
Error = 90.76 minus 90 = 0.076 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Sun’s (Sidereal) Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify The Sun’s SYNODIC Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/syn-rot
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
The Moon’s (Sidereal) Rotation Period = 27.321661 Earth days.
The Moon’s SYNODIC Rotation Period = 29.5305882 Earth days.
The SUM of these two periods = 56.8522492 Earth days.
56.8522492 ÷ 0.997269663 = 57.0079 Earth rotations.
57.0079 minus 56 = 1.0079 Earth rotations.
1.0079 x 360 = 362.84 degrees.
360 degrees = 4 right angles.
Error = 362.84 minus 360 = 2.84 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Moon’s (Sidereal) Revolution Period, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify The Moon’s Synodic Revolution Period, click on this link:-
www.solarsystemtimeperiods.com/planet-synodic
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Mercury’s Synodic Revolution Period = 115.8774 Earth days.
Mercury’s Synodic Rotation Period = 69.8636 Earth days.
The SUM of these two periods = 185.741 Earth days.
185.741 ÷ 0.997269663 = 186.249524 Earth rotations.
0.249524 x 360 = 89.83 degrees.
90 degrees = 1 right angle.
Error = 90 minus 89.83 = 0.17 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Mercury’s Synodic Revolution Period, click on this link:-
www.solarsystemtimeperiods.com/planet-synodic
To verify Mercury’s Synodic Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/syn-rot
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 two examples will 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 = 6.9747551 Earth days. During this time period, Earth rotates 6 complete rotations plus A REMAINDER of FOUR RIGHT ANGLES. (Error 2.21 degrees.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
The Lunar Day = 1.0350501 Earth days.
The Phobosic Day = 0.462753 Earth days.
The Deimosic Day = 5.476952 Earth days.
The SUM of these three periods = 6.9747551 Earth days.
6.9747551 ÷ 0.997269663 = 6.99385 Earth rotations.
0.99385 x 360 = 357.786 degrees.
360 degrees = 4 right angles.
Error = 360 minus 357.786 = 2.21 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Inner Solar System Satellites, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify the “days” of these three satellites, click on this link:-
www.solarsystemtimeperiods.com/days
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.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
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.
TWICE this time period = 3.741374 Earth days.
3.741374 ÷ 0.997269663 = 3.751617 Earth rotations.
0.751617 x 360 = 270.58 degrees.
270 degrees = 3 right angles.
Error = 270.582 minus 270 = 0.58 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
To verify The Four LARGE Jupiter Satellites, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify the “days” of these four satellites, click on this link:-
www.solarsystemtimeperiods.com/days
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 One complete revolution plus A REMAINDER of THREE RIGHT ANGLES. (Error 0.199 degrees.)
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
The Sun’s Rotation Period = 24.66225 Earth days.
Mercury’s Rotation Period = 58.6462 Earth days.
Venus’ Rotation Period = 243.0187 Earth days.
Mercury’s Orbital Period = 87.9692 Earth days.
Venus’ Orbital Period = 224.70067 Earth days.
The SUM of these five periods = 638.99702 Earth days.
638.99702 ÷ 0.997269663 = 640.746474 Earth rotations.
0.746474 x 360 = 268.73 degrees.
270 degrees = 3 right angles.
Error = 270 minus 268.73 = 1.27 degrees.
and also:-
Earth’s Orbital Period (ie:- the Earth Year) = 365.25636 Earth days.
638.99702 ÷ 365.25636 = 1.749448 Earth revolutions.
0.749448 x 360 = 269.801 degrees.
270 degrees = 3 right angles.
Error = 270 minus 269.801 = 0.199 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Rotation Periods of The Sun, Mercury, and Venus, click on this link:-
www.solarsystemtimeperiods.com/planet-orbital
To verify The Orbital Periods of Mercury and Venus, click on this link:-
www.solarsystemtimeperiods.com/orbital
To verify Earth’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
Example 23. The SUM of The Synodic Revolution Periods of The Seven Inner Solar Revolving Bodies = 1876.1069 Earth days. During this time period, Earth rotates 1881 complete rotations plus A REMAINDER of ONE RIGHT ANGLE. (Error = 2.41 degrees).
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Here are the names and Synodic Revolution Periods (expressed in Earth days) of The Seven Inner Solar Revolving Bodies:- Mercury 115.8774 and Venus 583.9205 and Earth 365.25636 and Mars 779.9382 and The Moon 29.5305882 and (Mars satellites) Phobos 0.319058343 and Deimos 1.264764923
The SUM of these seven periods = 1876.1069 Earth days.
1876.1069 ÷ 0.997269663 = 1881.2433 Earth rotations.
0.2433 x 360 = 87.59 degrees.
90 degrees = 1 right angle.
Error = 90 minus 87.59 = 2.41 degrees.
To verify Earth’s Rotation Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Synodic Revolution Periods of The Moon, Mercury, Venus, and Mars, click on this link:-
www.solarsystemtimeperiods.com/planet-synodic
To verify The Synodic Revolution Periods of Phobos and Deimos, click on this link:-
www.solarsystemtimeperiods.com/syn-rot
Earth’s “Synodic” Revolution Period is (effectively) the same as its Orbital Period. To verify Earth’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
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).
DEMONSTRATION:- Earth’s Rotation Period = 0.997269663 Earth days.
Earth’s Orbital Period (ie:- the Earth Year) = 365.25636 Earth days.
Here are the names and orbital periods (expressed in Earth days) of The THIRTEEN LARGE Satellites of The Naked-Eye Visible Planets:- Mercury has no satellites, and Venus has no LARGE satellites. Earth satellite – The Moon 27.321661 and Mars has no LARGE satellites; and Jupiter Satellites – Io 1.769137786 and Europa 3.551181041 and Ganymede 7.15455296 and Callisto 16.6890184 and Saturn Satellites – Mimas 0.942421813 and Enceladus 1.370217855 and Tethys 1.887802160 and Dione 2.736914742 and Rhea 4.517500436 and Titan 15.94542068 and Hyperion 21.2766088 and Iapetus 79.3301825
The SUM of The Orbital Periods of these Thirteen LARGE Satellites = 184.497569 Earth days.
184.497569 ÷ 0.997269663 = 185.0026887 Earth rotations.
185.0026887 minus 184 = 1.0026887 Earth rotations.
1.0026887 x 360 = 360.97 degrees.
360 degrees = 4 right angles.
Error = 360.97 minus 360 = 0.97 degrees,
and also:-
184.497569 ÷ 365.25636 = 0.505118 Earth revolutions.
0.505118 x 360 = 181.84 degrees.
180 degrees = 2 right angles.
Error = 181.84 minus 180 = 1.84 degrees.
To verify Earth’s Rotation Period, and Earth’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify The Naked-Eye Visible Planets, click on this link:-
www.solarsystemtimeperiods.com/naked-eye
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
To verify The Orbital Periods of The THIRTEEN LARGE Satellites of The Naked-Eye Visible Planets, click on this link:-
www.solarsystemtimeperiods.com/large-sats
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.)
DEMONSTRATION:- Earth’s Orbital Period (ie:- the Earth Year) = 365.25636 Earth days.
Here are the names and Orbital Periods (expressed in Earth days) of The Twenty LARGE Satellites of The Solar System:- Earth satellite – The Moon 27.321661 and Jupiter Satellites – Io 1.769137786 and Europa 3.551181041 and Ganymede 7.15455296 and Callisto 16.6890184 and Saturn Satellites – Mimas 0.942421813 and Enceladus 1.370217855 and Tethys 1.887802160 and Dione 2.736914742 and Rhea 4.517500436 and Titan 15.94542068 and Hyperion 21.2766088 and Iapetus 79.3301825 and Uranus Satellites – Miranda 1.4134840 and Ariel 2.52037932 and Umbriel 4.1441765 and Titania 8.7058703 and Oberon 13.4632423 and Neptune Satellite – Triton 5.8768441 and Pluto satellite – Charon 6.387230
The SUM of these 20 orbital; periods = 227.0038274 Earth days.
TWICE this time period = 227.0038274 x 2 = 454.0076548 Earth days.
454.0076548 ÷ 365.25636 = 1.24298 Earth revolutions.
0.24298 x 360 = 87.474 degrees.
90 degrees = 1 right angle.
Error = 90 minus 87.474 = 2.526 degrees.
To verify Earth’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify the orbital periods of The Twenty LARGE Satellites of The Solar System, click on this link:-
www.solarsystemtimeperiods.com/large-sats
To verify planet and satellite sizes, click on this link (See the radius and mass columns in the table):-
www.solarsystemtimeperiods.com/planet-orbital
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).
DEMONSTRATION:- Earth’s Orbital Period (ie:- the Earth Year) = 365.25636 Earth days.
Venus’ Synodic REVOLUTION Period = 583.9205 Earth days.
Venus’ Synodic ROTATION Period = 145.9276 Earth days.
The SUM of these two periods = 729.8481 Earth days.
729.8481 ÷ 365.25636 = 1.99818 Earth revolutions.
0.99818 x 360 = 359.345 degrees.
360 degrees = 4 right angles.
Error = 360 minus 359.345 = 0.655 degrees.
To verify Earth’s Orbital Period, click on this link:-
www.solarsystemtimeperiods.com/earth-periods
To verify Venus’ Synodic REVOLUTION Period, click on this link:-
www.solarsystemtimeperiods.com/planet-synodic
To verify Venus’ Synodic ROTATION Period, click on this link:-
www.solarsystemtimeperiods.com/syn-rot