The simultaneity of the planets and the simultaneity of time

Eric Kraeghbod
The simultaneity of the planets
and the simultaneity of time
[ Simultaneity Theory - SIMT ]
April 2009
Copyright Eric Kraeghbod 2008-2009
The present English version is an approximative translation from the German original
Contents
The simultaneous existence of the planets during the last 500 years [1]
The simultaneous existence of the planets during one year and one day [16]
The simultaneous existence of the planets at a defined moment [21]
The construction of chronologies on the Earth [25]
Astronomical definitions of time moments (time points) [50]
Instruments for the measurement of time [64]
Development of planetary time systems [79]
Construction of a sidereal time system for the planet Mars [95]
Synchronization of the Earth sidereal time with the Mars sidereal time [124]
Method 1: Light-/radio signals with identical propagation time
to both planets [133]
Method 2: Radar signals [145]
Method 3: Transport of an atomic clock controlled by
millisecond pulsar signals [153]
Method 4: Observation of a determined event from both planets [163]
Synchronization of the Earth sidereal time or the Mars sidereal time with a third
and fourth planet [171]
The consequences of the synchronization between three planets [177]
2
The simultaneity of the planets
and the simultaneity of time
Descriptors: Planets, Time, Measurement, Simultaneity, Simultaneity Theory, SIMT
Prefatory note
The SIMT will be described in 183 statements. To each statement is added a current number to be
used for references within the text and for future extensions and additions like footnotes, bibliographic
references and links to internet sources.
The simultaneous existence of the planets during the last 500 years [1]
We consider only the Sun and the four nearest planets: Mercury, Venus, Earth, Mars. [2]
The Sun is the reference system for all movement data if there is no other celestial body indicated as
reference. [3]
Kopernikus (1473-1543) knew about the existence of the planets. [4]
Today (2008) we observe the same planets. [5]
During the approximately 500 years since Kopernikus all planets have existed continously. [6]
It has not been reported that one planet would not have existed for a shorter or longer period. [7]
We know of no physical procedure that would have made possible the short-term removal of a planet
and its subsequent restoration to its usual place. [8]
All planets are bodies moving against each other and against the Sun. [9]
The trajectory (orbit) of each planet depends on the reciprocal gravitational forces of all masses
existing simultaneously in the Sun’s system. [10]
The gravitational forces of all masses work simultaneously; the propagation velocity of gravitation is
unknown. [11]
The trajectories of the planets can be calculated from astronomical observations and physical laws.
[12]
The observations of the planets by terrestrial observers have no influence on the material constitution
or the states of motion of the planets. [13]
The calculations of the earlier and the future positions of the planets are controlled and confirmed by
astronomical observations. [14]
The simultaneous existence of the planets and their identity during the last 500 years have never
been doubted. [15]
3
The simultaneous existence of the planets during one year and one day [16]
From the simultaneous and uninterrupted existence of the planets during 500 years follows their
simultaneous existence during any deliberately chosen year, for instance during the year 1905. [17]
For the same reason there follows the simultaneous existence of the planets during any deliberately
chosen day of this year, for instance during the 30th of June 1905. [18]
In the following the 30th of June 1905 will be called the “first term”. [19]
In the following the 30th of June 2005 will be called the “second term”, [20]
The simultaneous existence of the planets at a defined moment [21]
From the simultaneous existence of the planets during one special day there follows their
simultaneous existence at any deliberately chosen moment of the day, for instance at 12 ‘o clock at
noon. [22]
The simultaneous existence of the planets in the Sun’s system at any moment during the last 500
years of their existence is an indubitable fact. [23]
The simultaneous existence of the planets allows the construction of simultaneous chronologies on
the planets. [24]
The construction of chronologies on the Earth [25]
The planet Earth offers two characteristic periodic movements as foundation of a chronology: the
rotation about its own axis (rotation) and the orbit around the Sun (orbit). [26]
For the purposes of the following exposition all different chronologies will be treated only in principle,
and all problems of their practical realisation will be considered as irrelevant and excluded, as for
instance
(a) irregularities caused by disturbances of the rotations or the orbits,
(b) the relations between rotation and orbit not beeing integer numbers,
(c) the construction of fictitious “mean times” to expand their coverage. [27]
The rotation of the Earth during the day causes the picture of an apparent movement of the Sun at
the sky and during the night the picture of an apparent rotation of the fixed stars (our Galaxis). [28]
Both apparent movements are used to define the duration of the day: this leads to two different
conceptions of the length of the day, the solar day and the sidereal day. [29]
The solar day and the sidereal day have different durations. [30]
The traditional division of one day into 24 hours, of one hour into 60 minutes and of one minute into
60 seconds leads to (3600x24=) 86400 seconds for one day. [31]
The two different conceptions for the duration of the day lead to two different conceptions for hours,
minutes and seconds. [32]
The sidereal day for a defined position (locality) on the Earth is the time between two passages of the
same star through the meridian of the locality, that means one complete rotation of the Earth against
the fixed stars. [33]
The solar day for a defined position on the Earth ist the time between two passages of the Sun
through the meridian of the locality, that means one complete rotation of the Earth against the Sun. [34]
During one day the Earth moves forward a certain portion on its orbit around the Sun. [35]
This movement of the Earth on its orbit in 24 hours does not change the position of the Earth against
the fixed stars. [36]
The same movement of the Earth on its orbit in 24 hours, however, changes the position of the Earth
in relation to the Sun: the Earth has moved forwards, the Sun (seen from the Earth) has remained
behind a small amount. [37]
4
For a complete rotation of the Earth in relation to the Sun the Earth must rotate each day some 4
minutes more than for a complete rotation against the fixed stars. [38]
The solar day therefore ist about 4 minutes longer than the sidereal day. [39]
The solar day by definition lasts:
24 hours 0 minutes 0 seconds [40]
The sidereal day is shorter than the solar day:
23 hours 56 minutes 4,0905 seconds [41]
This time difference of approximately 4 minutes between solar day and sidereal day in the course of
one year sums up to approximately one day:
365 x 4 = 1460 minutes = 24 hours 20 minutes [42]
A calculation with the more precise time difference (see #41) of approximately 3 minutes 56 seconds
(=236 seconds) gives something less than one day:
365 x 236 Sek. = 86140 Sek. = 1435 Min. 40 Sek. = 23 Std. 55 Min. 40 Sek. [43]
Observed from the Sun, the daily 4 additional minutes of rotation after the completion of one Earth
orbit are seen as one supplemental rotation of the Earth which therefore needs approximately one day
more. [44]
If there are two possible alternatives for the construction of a time system there arises the question:
which one is the more suitable to the purpose? [45]
The practical life of the human beeings is orientated towards the Sun and uses the solar time in a
construction of solar mean time which incorporates all irregularities. [46]
The astronomical science is orientated towards the fixed stars and uses the sidereal time because
this is independent from the movement of the Earth on its orbit around the Sun. [47]
Since the sidereal time is the more suitable time system for all events in the universe and therefore
has become authoritative, the solar time of our calendar has been made dependend from the sidereal
time and is permanently adapted to the “real” conditions of the sidereal time through corrections by leap
seconds. [48]
For all following considerations about the solar system and its planets the sidereal time of the Earth is
authoritative and will be used; if in a special case the solar time of the Earth should be intended this
has to be declared expressively. [49]
Astronomical definitions of time moments (time points) [50]
After the definition of unambiguous unities for the measurements of time duration in the sidereal time
system of the Earth [EAR-T] (second, minute, hour, year) one has to define time moments (points)
which can be identified through astronomical constellations for the purpose of synchronizing the time
system of the Earth with the development and the events of the universe. [51]
For a time system on the Earth one can use for instance periodically repeated constellations:
(a) the precession of the perihel of the Earth’s orbit: the yearly precession is a very small amount and
difficult to be observed; a complete rotation of the perihel takes about 25800 years and therefore is not
useful for the purpose of synchronizations; [52]
(b) the points of intersection of the Earth’s orbit (ecliptic) with the plane of the fictitious celestial
equator: there are two such points which are equally fictitious and cannot be observed directly. [53]
One of the two intersections of #53 is called the vernal equinox. [54]
The position of the vernal equinox as fictitious point at the sky is constructed from the coordinates of
the well known stars. [55]
The passage of the meridian by the vernal equinox (instead of the passage of a star, see #54)
defines the begin of the star day, at 0 hour sidereal time (EAR-T) for the locality of the observation.
[56]
The time between two passages of the meridian by the vernal equinox is the sideral day (EAR-T).
[57]
Since as a consequence of the precession of the perihel the vernal equinox (as a point on the
ecliptic) moves very slowly continuously in relation to the fixed stars, the sidereal day (of #57) is
approximately 9 milliseconds shorter than the sidereal day of #41. [58]
For the following the small difference between the two star day lengths has no importance. [59]
The beginning of the star day derived from the vernal equinox is valid for the locality of the
observation. [60]
5
The star time for the meridian of Greenwich serves as universal time for the Earth and is called
“Greenwich Mean Sidereal Time” (GMST). [61]
The mean solar time for the meridian of Greenwich (Greenwich Mean Time - GMT) which is the
basis of the “World Time”, today called “Universal Time” (UT), today is no longer derived from
astronomical observations of the Sun but for reasons of greater precision defined by numerical
derivation from GMST: thus the sidereal time has become the basis of the solar time. [62]
A derivation from the UT, called “Coordinated Universal Time” (UTC), is now the basis of all time
systems for the practical life on Earth and is spread through special time radio stations and other
media. [63]
Instruments for the measurement of time [64]
Instruments for the measurement of time are called clocks and on principle consist of 3 elements: a
source of regular time signals, a regulating device and a time display. Instruments without one of
theses elements are no clocks. [65]
The choice of the signal source defines the construction and the function of a clock. [66]
Irregularities in the functioning of a clock can be detected through comparison of a variety of clocks of
the same and of different types and can be reduced to a minimum through constructive measures. [67]
A clock without any irregularities cannot be constructed. [68]
Irregularities in the functioning of clocks and the resulting limits to the precision of the measurement
of time have no bearing on the purpose of the following exposition. [69]
Actually the clocks with the greatest precision in time keeping are atomic clocks. [70]
Especially suitable are the atoms of hydrogen and cesium. [71]
Preferred sources for time signals are the atoms of cesium-133 and its oscillations. [72]
The high stability of the time signal of cesium-133 has led to an international agreement about the
duration of the time unity second (SI-second): it has been defined as the duration of 9.192.631.770
oscillations. [73]
With this agreement the same fundamental unit has been defined for sidereal time and solar time.
[74]
The oscillation frequency of the hyperfine strucure of cesium-133 is considered to be constant but is
influenced by several physical conditions. Therefore the international time on Earth must be calculated
by a mean value of many atomic clocks (about 250) at different localities. [75]
The possible precision of atomic clocks depends on the constructive principles and the intended use.
The highest precision is achieved by stationary atomic clocks on Earth under laboratory conditions.
These clocks move
- together with the Earth’s rotation with the specific velocity of their latitude parallel
(equator: 40.000 km per 24 hours = 1667 km/hour),
- together with the Earth on its orbit around the Sun
(with a velocity of approximately 30 km/second = 108.000 km/hour),
- together with the Sun’s system in the Galaxy towards the constellation Leo
(with 370 km/sec = 1.330.000 km/hour),
- together with the whole Galaxis in relation to the 3-K cosmic background radiation
(with a velocity of about 600 km/sec = 2.200.000 km/hour). [76]
Smaller transportable atomic clocks achieve less precision and are used for instance in the statellites
of the GPS System for the precise measurement of the time the radio signals take to arrive at the
locality of the receiver. [77]
The physical science supposes that the atomic properties of the time signal sources in atomic clocks
all over the universe will deliver the same time rate which is influenced only very slightly by the
conditions of the surrounding of the clock (for instance gravitational fields). [78]
6
Development of planetary time systems [79]
The other 3 planets (Mercury, Venus, Mars) too rotate around their axes and move on orbits around
the Sun. [80]
Thus they offer the same conditions as the Earth for the development of their own peculiar time
systems which will be designated with the following abbreviations: MER-T ; VEN-T ; EAR-T ; MAR-T.
[81]
On principle there could be constructed a solar time and a sidereal time for each of the planets. [82]
Since there is no “practical life” of any living beings on the other planets for whom a solar time system
could make sense all further discussions about time systems on these planets will be limited to sidereal
time systems. Therefore in the following used abbreviations mean:
MER-T: Mercury sidereal time
VEN-T: Venus sidereal time
EAR-T: Earth sidereal time
MAR-T: Mars sidereal time. [83]
The periods of rotation of all planets have been defined by astronomical observations from the Earth
and are given in multiples of the Earth rotation or in EAR-T. [84]
The rotation periods given in EAR-T have the following values (taken from: Bernd Lang: Das Sonnensystem. 2007):
Merkur: 58 days 16 hours
Venus: 243 days 0 hours 14 minutes
Erde: 23 hours 56 minutes 4 seconds Mars: 24 hours 37 minutes 32 seconds [85]
All planets of our solar system do rotate against the same fixed stars sky. [86]
The axes of three of the four planets have the following angles of inclination in relation to the planes
of their orbits:
[Mercury: 0 degrees]
Venus: 177,3 degrees
Earth: 23 degrees 27'
Mars: 25 degrees 11' [87]
Consequently for these three planets (Venus, Earth, Mars) the intersections of their fictitious celestial
equators with their orbit planes can be constructed; see the vernal equinox for the Earth, #54. [88]
For Mercury without inclination of his axis to his orbit’s plane there is no intersection point between
his fictitious celestial equator and its orbit’s plane. For this planet one can choose other points on his
orbit, for instance his perihel whose precession is known. [89]
As the data for all rotation periods in EAR-T show (see #85) time systems for all planets can be
constructed. [90]
Furthermore by way of example the data of #85 show that the construction of a time system for one
of the planets (for instance the Earth) is sufficient to be able to convert data of the different time
systems of all 4 planets from one system to the other unequivocally. [91]
The practicability of the development of time systems for Mercury, Venus and Mars does not depend
either from the physical conditions on the planets (structure of the surface, atmosphere, climate etc.) or
from the possibility to install observation and measurement instruments. [92]
The astronomical sciences are capable to construct time systems for the planets through earthbound
and satellite based observations as is demonstrated since many decades by the calculation of the
rotation periods. [93]
On principle, the development of time systems for the planets does not depend on the possible
precision because all time systems are affected by irregularities of the clocks and the measurements; it
is only essential to determine the dimension of the measurement errors. [94]
Construction of a sidereal time system for the planet Mars [95]
As foundation for a Mars sidereal time system (MAR-T) there may be used astronomical
observations and measurements
- on the Earth; [96]
- on board of space vehicles (space probes, satellites); [97]
- on the Mars after the planned landing of space probes or manned space vehicles from the Earth. [98]
7
The realization of the MAR-T can follow the structure of the Earth sidereal time system (EAR-T):
- the Mars orbit around the Sun takes 687 EAR-T days; [99]
- the Mars rotation takes in EAR-T: 24 hours 37 minutes 32 seconds ; [100]
- from both values can be calculated the number of Mars rotations (Mars sidereal days) during one
Mars orbit (Mars days during the Mars year). [101]
Mars orbit time divided through Mars rotation time gives the number of Mars days for one Mars orbit
(the Mars year). [102]
The very precisely known Mars rotation in EAR-T (see #85: 24 hours 37 minutes 32 seconds) can
directly be broken down into 24 MAR-T hours, with 60 MAR-T minutes per hour and 60 MAR-T
seconds per minute. [103]
For the MAR-T second the specific number of oscillations of cesium-133 has to be defined. [104]
The subdivisions into hours, minutes etc. could be done decimally as well. [105]
Herewith a Mars sidereal time system (MAR-T) would have been constructed within a certain error
limit. [106]
For methodological reasons of easier comparability and representation in astronomical discussions
one prefers to do without the construction of a Mars sidereal time system (MAR-T) and gives the
duration of Mars movements and of all other events in the solar system in Earth sidereal time (EAR-T)
measurements. [107]
The foundation and justification of the procedure of #107 is given with two facts:
(1) The fixed stars sky whose apparent rotation (different for all planets) is the basis for the
construction of the sidereal time systems for each planet, is the same for all rotating planets of the
solar system. [108]
(2) The motions and orbit data of each planet could be recognized and calculated from observations
on the other planets. [109]
List of all elementary data of the planet Mars according to actual publications (see #85), given in
EAR-T:
1 Mars year:
1 Mars day:
1 Mars hour:
1 Mars minute:
1 Mars second:
24 Earth hours 37 min 12 sec=
88632:24=3693 Earth sec :60=
3693 Earth sec:60=
61,55 Earth sec.:60=
Distance Mars - Sun:
Corresponding figures of the Earth:
at the perihel: 206,645 million km [115]
at the aphel:
249,229 million km [117]
mean distance: 227,9 million km [119]
147,1 million km [116]
152,1 million km [118]
149,6 million km [120]
The propagation time of light (298000 km/sec)
from the Sun to Mars:
at mean distance: 12,74 Earth minutes [121]
Shortest distance Earth-Mars at Mars perihel:
686,96 Earth days [110]
88632 Earth seconds [111]
61,55 Earth minutes [112]
61,55 Earth seconds [113]
1,0258 Earth seconds[114]
8,37 minutes [122]
55 million km [123]
Synchronization of the Earth sidereal time with the Mars sidereal time [124]
The construction of a Mars sidereal time has been done; see #95-114. [125]
On principle the construction of a time system for a planet does not include the definition of a
beginning or another defined moment. [126]
Because of the orientation at the same fixed stars (see #86) one can calculate the data of time
durations between the time systems but not the definition of the same moment. [127]
The capability of two time systems to measure for one and the same event the same time first needs
the synchronization of the two time systems. [128]
8
The synchronization consists in a definition or establishment of an event, organized once but possibly
to be repeated for verification, which simultaneously can be perceived and identified from both
planetary time systems. [129]
The synchronization therefore is no natural condition but a planned technical procedure to fix a
certain moment for the entire observation space of both time systems. [130]
For the synchronization of two planetary time systems there exist several methods. [131]
The precision of the synchronization can be achieved only with a certain margin of error, but can be
improved systematically through the use of all methods at hand. [132]
Method 1: Light-/radio signals with identical propagation time to both planets [133]
For the propagation of the light-/radio signal an approximative isotropy (equal propagation velocity in
all space regions and space directions) in the cosmic space is assumed. [134]
Through astronomical observations and calculations a position in the solar system has to be defined
which at a known time is equidistant from both planets. [135]
Positioning of a light or radio source (space probe) at this position. [136]
Simultaneous emission of two signals, one in direction Mars and one in direction Earth. [137]
At the condition of equal propagation velocity for both signals the signals arrive simultaneously at the
positions of their target planets at the time of the signals’ emission. [138]
During the propagation of the signals both planets move slightly forward on their orbits around the
Sun. [139]
New calculation of the propagation times of the signals to the new planetary positions und their additional propagation times. [140]
Registration of the arrival times of the signals on both planets. [141]
Calculation of both corrected propagation times to the planets’ positions at the time of the signals’
arrival. [142]
Calculation of the time of emission of the signals in each of the two planetary time systems. [143]
The time systems on both planets now have marked the same moment (emission of signals) and
therewith are synchronized. [144]
Method 2: Radar signals [145]
Emission of radar signals from one planet directly to the other planet, reflection of the signals and
their reception on the emitting planet. [146]
Experiences with radar signals from the Earth to the Moon and to Venus have been reported in the
literature. [147]
Radar signal from the Earth to Mars, preferably at the time of the smallest distance between both
planets. [148]
On Mars the time of the arrival of the radar signal will be measured in MAR-T. [149]
On Earth the times for emission and arrival of the radar signals will be measured in EAR-T. [150]
On Earth the whole time for transmission of the signal to Mars and returning to the Earth will be
analysed for the respective times for going and returning: thus the time of the arrival of the signal on
Mars can be calculated in EAR-T. [151]
Therewith the same time (arrival and reflection of the radar signal on Mars) has been determined
according to MAR-T and according to EAR-T (see #95 and #33; 57) and a synchronization between the
two planetary time systems has been established. [152]
9
Method 3 : Transport of an atomic clock controlled by millisecond pulsar signals [153]
A space probe carries an atomic clock from the Earth to Mars. [154]
During the space flight the construction of the clock is subjected to influences of different kind which
may cause irregularities in the timekeeping: accelerations on curved trajectory, gravitational and
magnetic fields etc. [155]
During the whole flight and the landing on Mars a telescope on board of the probe is directed to a well
known millisecond pulsar whose signal frequency stability has been controlled precisly for a longer
period. [156]
Millisecond pulsars demonstrate a stability of signal frequency in the magnitude of atomic clocks but
are not subjected to the influences indicated for atomic clocks. [157]
The great distances of the pulsars in our galaxy from the solar system guarantee that the pulsar
signals arrive at every point of the solar system with the same signal frequency. [158]
If the course of the space probe is rectangular to the direction of the arriving signals from the
millisecond pulsar there will be no doppler effect in the registration of the signals. [159]
If the course of the space probe makes any other angle with the arriving signals then the resulting
doppler effect in the registration of the signals can be calculated and the signal can be corrected
through the pulsar signal. [160]
During the whole flight the atomic clock will be controlled and if necessary corrected by the pulsar
signal. [161]
The atomic clock controlled by the very stable signal frequency of the millisecond pulsar transports
the EAR-T to Mars and there serves to synchronize the MAR-T with the EAR-T. [162]
Method 4: Observation of a determined event from both planets [163]
This method is a variant of method 1 (signals with identical propagation time). [164]
The conditions of a technically produced signal at a known position and of the identical propagation
time to both planets are abandoned. Instead there are two other conditions: a well determined
observable event in the solar system and the precise knowledge of the distances of both planets from
the event. [165]
Example for such a determined event: the Earth on its orbit around te Sun passes the vernal equinox
(see #54). [166]
The event is observed on both planets and the time of the event is measured in each proprietary time
system. [167]
From the known distance of each planet from the event at the time of the observation the propagation
time of the light can be calculated. [168]
In each of the two planetary time systems through the knowledge of the propagation time the time of
the event can be calculated: observation time minus propagation time. [169]
Thus the same event has been determined in both time systems and the synchronization of the two
planetary time systems has been established. [170]
Synchronization of the Earth sidereal time or the Mars sidereal time
with a third and fourth planet [171]
After the sychronization between EAR-T and MAR-T there are for every moment in their common
observation space one measured EAR-T and one measured MAR-T which can be converted by a
certain conversion factor. [172]
Because the measurements of the same event in both time systems determine the same time of the
event, the time system of one planet (the time unit second) could be transferred onto the other: this
happens already since manny years by giving the Mars data in EAR-T. [173]
10
Both time systems could be controlled and corrected permanently on their planets by the signals from
millisecond pulsars, taking into consideration the moving directions of the planets in relation to the
pulsar signals and eventually Doppler effects. [174]
After the synchronisation of the time systems of two planets further time systems for the other planets
can be constructed and synchronized. [175]
The use and authority of the Earth sidereal time (EAR-T) for all events on Mars can be extended to
all objects in the universe, and thus a construction and synchronization of other time systems for more
objects in space is not necessary. [176]
The consequences of the synchronization between three planets [177]
After the synchronization of a third planetary time system with the first two systems it is possible to
determine unequivocally the time of any event that can be observed from one or more planets in all
three time systems through calculation of the distances and the propagation times from the event to the
different observers. [178]
Thus it is guaranteed that one and the same event in space will be determined for the same time by
observers on different planets. [179]
Thus in the whole observation space of the three planets (= the visible part of the cosmos) the
simultaneity of different simultaneous events can be determined reliably. [180]
If there are several events one after the other, on all planets for each event will be measured the
same time and for the sequence of the events the same temporal order. [181]
The assumption that from different observation points (for instance planets) for the same sequence
of events the temporal order of the events could be determined differently is excluded absolutely
through the succesful synchronization of their time systems. [182]
The time between the two determined days (according to #19; 20) which on the Earth in EAR-T is 1
year will be determined in the time systems of the other planets and after conversion to EAR-T as the
same duration. [183]
11