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Validity of ephemeris time

Validity of ephemeris time


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In the wikipedia article for ephemeris time as first adopted in 1952, it does not explain clearly how or why it was superseded. For example, it reads:

In 1976 the IAU resolved that the theoretical basis for its current (1952) standard of Ephemeris Time was non-relativistic, and that therefore, beginning in 1984, Ephemeris Time would be replaced by two relativistic timescales intended to constitute dynamical timescales: Terrestrial Dynamical Time (TDT) and Barycentric Dynamical Time (TDB).[28] Difficulties were recognized, which led to these being in turn superseded in the 1990s by time scales Terrestrial Time (TT), Geocentric Coordinate Time GCT(TCG) and Barycentric Coordinate Time BCT(TCB). [16]

So, from this it appears that ephemeris time was never superseded and it continues to be evolved with a different theoretical basis?

From reading Robert Newton's books such as "Ancient planetary observations and the validity of ephemeris time", it would seem that ephemeris time is invalid because of non-secular accelerations in the motion of Mercury and Venus.

So, I guess my question is: does current astronomical theory consider ephemeris time to be invalid or valid, and if it considers it to be valid, then what is current evaluation of Newton's calculations and their implications for the validity of ephemeris time?


It depends on what one means by "Ephemeris Time." Officially, the Newtonian-based Ephemeris Time has been superseded by the relativistically-correct Barycentric Dynamic Time (TDB) and Barycentric Coordinate Time (TCB). However, the concept of what was meant by Ephemeris Time carries on to this day. The intent of Ephemeris Time was to use the solar system as a timekeeping device. This is what TDB and TCB do, but in a relativistic rather than Newtonian setting.

TCB is a theoretical time scale whose clocks are infinitely removed from the solar system, are co-moving with the solar system barycenter, and that tick at the rate of one tick per 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom (at a temperature of 0 K). (Note well: This is the same definition currently used for an SI second.) That TCB clocks are well removed from the solar system means that a second measured by an atomic clock on the surface of the Earth ticks a tiny bit slower than does a TCB clock.

These slightly different tick rates was perceived as a problem by some. The solution was eventually to redefine TDB as a scaled version of TCB such that, on average, TCB ticks at the same rate as atomic clocks on the surface of the Earth. Atomic clocks on the surface of the Earth tick faster / slower than would TCB clocks based on whether the Earth is further from / closer to the Sun than average. But averaged over the course of years, TCB and TAI remain more or less in sync.

Regarding the more or less: TDB is updated every year. As technology improves, these subtle updates change the timing of past events. TAI does not do this. As technology improves, older atomic clocks are replaced with newer ones. Atomic clocks have a shelf life of a decade or so. This can result in discontinuities in atomic time. This is not a problem with TDB as it is re-issued annually. This also means that TDB is independent of atomic time.


Ephemeris Time (ET)

The first time scales were based on the rotation of the Earth. However, as clocks became more precise, it became clear that the rotation of the Earth was not constant, as Flaamsted thought he had shown (Kant thought it wasn't). By 1950 , improvements in clocks made possible a precision greater than the variations in the rotation of the earth. A second found by subdividing the day was no longer adequate, as such a measurement would vary depending on when it was made.

To get away from the variations in the earth's rotation, a conference on Fundamental Constants in Astronomy (Paris, 1950) recommended that the time standard be based on the revolution of the Earth around the sun, instead of its rotation on its axis. The second would be defined as a fraction of one particular year, rather than a fraction of the mean solar day. The length of the year was based on Simon Newcomb's classic study Tables of the Sun ( 1895 ).


Ephemeris Time

ephemeris time
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ephemeris time (ET), astronomical time defined by the orbital motions of the earth, moon, and planets. The earth does not rotate with uniform speed, so the solar day is an imprecise unit of time.

Ephemeris Time
A uniform time measure now kept by atomic clocks. Ephemeris Time (ET) was used in the Astronomical Almanac from 1960-1983, but was replaced by barycentric dynamical time when the IAU 1976 System of Astronomical Constants was implemented in the Astronomical Almanac in 1984.

ephemeris time (abbr E.T.) The uniform measure of time defined by the laws of dynamics and determined in principle from the orbital motions of the planets, specifically the orbital motion of the earth as represented by Newcomb's Tables of the Sun. Compare universal time.

(ET). Determined in principle from the sun's apparent annual motion, ET is the numerical measure of uniform time, which is the independent variable in the gravitational theory of the earth's orbital motion, coming from Simon Newcomb's Tables of the Sun.

Dynamical Time Terrestrial Time. Once the worldwide system of time zones was in place, with UT proudly heading up the list, all should have been well forever after. But such was not to be. Astronomers working with solar-system dynamics noticed something very disturbing.

Since the Earth's rotation is irregular, any time scale derived from it such as Greenwich Mean Time led to recurring problems in predicting the Ephemerides for the positions of the Moon, Sun, planets and their natural satellites.

[LLM96]
Eta Aquilae
A pulsating star in the constellation Aquila. It was the first Cepheid variable star discovered, in 1784. [C95]
Etalon .

is in itself apt to refer to time in connection with any Astronomical Ephemeris. It has been used more specifically to refer:-.
(ET). This led to the internationally agreed definition of the latest SI second
Second .

(ET): the time scale used prior to 1984 as the independent variable in gravitational theories of the solar system. In 1984, ET was replaced by dynamical time.

(ET) Timescale used by astronomers from 1960 until 1984 in computing the predicted positions, or ephemerides, of the Sun, Moon and planets.

Dynamical Time, on the other hand, is a uniform time system based on atomic clocks it is a successor to "

", an earlier system based on planetary motions that served the same function (though not as precisely).

(ET) was used in publications of the ICQ/CBAT/MPC since then, TT has been used. The difference between TDT and UTC in 1994 was 60 seconds (i.e., UT + 60 seconds = TDT).
TERRESTRIAL PLANET: A name given to a planet composed mainly of rock and iron, similar to that of Earth.

Markowitz, W. et al. 1958, Frequency of cesium in terms of

, Physical Review Letters 1, 105-107
National Research Council 1991, Working Papers: Astronomy and Astrophysics Panel Reports, Washington, DC: The National Academies Press .


Acknowledgement

All calculations are by Fred Espenak, and he assumes full responsibility for their accuracy. Some of the algorithms used in predicting the Planetary Ephemeris Data are based on Astronomical Algorithms by Jean Meeus (Willmann-Bell, Inc., Richmond, 1998).

Return to: Planetary Ephemeris Data

All photographs, text and web pages are © Copyright 1970 - 2021 by Fred Espenak, unless otherwise noted. All rights reserved. They may not be reproduced, published, copied or transmitted in any form, including electronically on the Internet, without written permission of the author. Note that all images are digitally watermarked.


GLONASS Time and Ephemeris

There are many efforts underway to improve the GLONASS accuracy. The stability of the satellites’ onboard clocks has improved from 5 x 10 –13 to 1 x 10 –13 over 24 hours with precision thermal stabilization. The GLONASS Navigation Message will include the difference between GPS time and GLONASS time, which is significant. There are no leap seconds introduced to GPS Time. The same may be said of Galileo and BeiDou. However, things are different in GLONASS. Leap seconds are incorporated into the time standard of the system. Therefore, there is no integer-second difference between GLONASS Time and UTC as there is with GPS. The effect is that there's a difference between the time standards in terms of integer seconds, whole seconds, and that difference changes from time to time.

Still, that is not the whole story. The version of UTC used by GLONASS is the Coordinated Universal Time of Russia. The epoch and rate of Russian time, relative to UTC (BIH), is monitored and corrected periodically by the Main Metrological Center of Russian Time and Fre­quency Service (VNIIFTRI) at Mendeleevo (Moscow Region).

They establish the regional version of UTC known as UTC(SU). There is a constant offset of 3 hours between GLONASS Time and UTC (SU). GLONASS Central Synchronizer,CS, time is the foundation of GLONASS time, GLONASST. The GLONASS-M satellites are equipped with cesium clocks which are kept within 8 nanoseconds of GLONASST.

GLONASS Ephemeris

The phase center of the satellite’s transmitting antennas is provided in the PZ-90.11 Earth-Centered Earth-Fixed reference frame in the same right-handed three dimensional Cartesian coordinate system described in earlier lessons. A ll GLONASS satellites broadcast in accordance with PZ-90.11 (close to ITRF2000). They started to do so at 3:00 pm on December 31, 2013.

The GLONASS constellation currently has 30 operational satellites on orbit.


Definitions for ephemeris time ephemeris time

A former standard astronomical time scale intended to overcome the drawbacks of irregularly fluctuating mean solar time, superseded in the 1970s.

A modern relativistic-coordinate time scale.

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The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to: ⁕a former standard astronomical time scale adopted in 1952 by the IAU, and superseded in the 1970s. This time scale was proposed in 1948, to overcome the drawbacks of irregularly fluctuating mean solar time. The intent was to define a uniform time based on Newtonian theory. Ephemeris time was a first application of the concept of a dynamical time scale, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion. ⁕a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument Teph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by Teph is closely related to, but distinct from, the TCB time scale currently adopted as a standard by the IAU.


An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

The uniform time-scale used as the independent variable to calculate the orbits in the solar system prior to 1984. Ephemeris Time was adopted in 1960 to deal with irregularities in the → Earth's rotation that had been found to affect the course of mean solar time. The definition of Ephemeris Time is based on Newcomb's analytical theory of the Earth's motion around the Sun (Newcomb 1898), according to which the geometric mean longitude of the Sun with respect to the Earth-Moon barycenter is expressed by:
L = 279° 41' 48".04 + 129 602 768".13 T + 1''.089 T 2 ,
where L refers to the → mean equinox of date while T measures time from noon 1900 January 0 GMT in Julian centuries of 36525 days. Ephemeris Time is therefore defined as the instant near the beginning of the calendar year A.D. 1900 when the mean longitude of the Sun was 279° 41' 48''.04, at which instant the measure of ET was 1900 January 0, 12h precisely. In this system the fundamental unit was the → ephemeris second, which was defined so that the → tropical year at the epoch 1900.0 should be exactly 31 556 925,9747 seconds of ephemerides. Ephemeris Time was inconvenient in many ways and was supeseded with the → Terrestrial Dynamical Time (TDT), whose fundamental unit is the SI second.

The passage of a celestial body or point across the → ephemeris meridian.

Prefix meaning "upon, at, close upon (in space or time), on the occasion of, in addition."

Gk. epi- "upon, at, close upon (in space or time), on the occasion of, in addition," cognate with O.Pers./Av. apiy-, aipi- "upon, toward, along also however" Skt. api "also, besides."

Prefix api-, from O.Pers./Av. apiy-, aipi-, as above.

1) In → Ptolemaic system, a circular → orbit of a body around a point that itself orbits circularly another point. Such a system was formulated to explain some → planetary orbits in terms of → circular motions in a → geocentric cosmology.
2a) Math.: A circle that rolls, externally or internally on another circle, generating an → epicycloid or → hypocycloid.
2b) In → galactic dynamics models describing the → spiral arms, a → perturbation of simple circular orbits. → epicyclic theory.

1) Falak-e tadvir, from Ar. falak al-tadwir, from falak "sphere" + tadwir "causing to turn in a circle."
2) → epi-cycle.

Of or pertaining to an → epicycle.

In the → epicyclic theory of Galactic rotation, the frequency at which a star in the → Galactic disk describes an ellipse around its mean circular orbit. The epicyclic frequency relates to the → Oort's constants. In the solar neighborhood the epicyclic frequency is about 32 km s -1 kpc -1 .

In a → disk galaxy, the motion of a star about the orbital → guiding center when it is displaced radially. See also → epicyclic frequency, → epicyclic theory.

The theory that describes the Galactic dynamics, that is the orbits of stars and gas clouds in the → Galactic disk, as well as the spiral → density wave. Formulated by Bertil Lindblad (1895-1965), the epicyclic theory assumes that orbits are circular with small deviations. Star orbits are described by the superposition of two motions: i) a rotation of the star (epicenter) around the Galactic center at the circular angular velocity, Ω, and ii) a retrograde elliptical motion at → epicyclic frequency, κ. The epicyclic motion in the Galactic plane occurs in a retrograde sense to conserve → angular momentum. In general Ω and κ are different and, therefore, orbits do not close. However, seen by an observer who rotates with the epicenter, orbits are closed ellipses.

A curve traced by a point of a circle that rolls on the outside of a fixed circle. This curve was described by the Gk. mathematicians and astronomer Hipparchus, who made use of it to account for the apparent movement of many of the heavenly bodies.

The fifth of → Saturn's known satellites. It has a mean radius of 55 x 69 km and orbits its planet at a mean distance of 151,422 km. It shares the same → horseshoe orbit with → Janus. Epimetheus was discovered by Richard L. Walker in 1966. Also known as Saturn XI.

In Gk. mythology, brother of → Prometheus and → Atlas, and husband of → Pandora. His task was to populate the Earth with animals.

A → morphism f : Y → X if, for any two morphisms u,v : X → Z, u f = v f implies u = v.

1) An incident in the course of a series of events.
2) An incident, scene, etc., within a narrative, usually fully developed and either integrated within the main story or digressing from it (Dictionary.com).

From Fr. épisode from Gk. epeisodion "addition," noun use of neuter of epeisodios "coming in besides," from → epi- "in addition" + eisodos "a coming in, entrance" (from eis"into" + hodos "way," → period).

Apyâ, literally "coming in besides," from api-, → epi-, + â- present stem of âmadan "to come," → rise.

1) Pertaining to or of the nature of an episode.
2) Divided into separate or tenuously related parts or sections.
3) Occurring sporadically or incidentally (Dictionary.com).

A branch of philosophy that investigates the possibility, origins, nature, methods, and limits of human knowledge.

From Gk. episteme "knowledge," from Ionic Gk. epistasthai "to understand," literally "overstand," from → epi- "over, near" + histasthai "to stand" cognate with Pers. istâdan "to stand," → standard PIE base *sta- "to stand."

From šenaxt, → knowledge, + -šenâsi, → -logy.

1) The date for which → orbital elements or the positions of celestial objects are calculated. Specifying the epoch is important because the apparent positions of objects in the sky change gradually due to → precession and → nutation, while orbital elements change due to the gravitational effects of the → planets. The → standard epoch used in ephemerides (→ ephemeris) and stellar catalogues at present is January 1, 2000, 12h (written also as 2000.0). See also: → Julian epoch.
2) Same as → cosmological epoch, such as → current cosmological epoch, → electroweak epoch, → epoch of thermalization, → recombination epoch, → reionization epoch.
3) A period of time usually marked by some distinctive development or series of events. See also: → polarity epoch, → epoch angle.

From M.L. epocha, from Gk. epokhe "pause, cessation, fixed point," from epekhein "to pause, take up a position," from epi- "on" + ekhein "to hold, to have" cf. Av. hazah- "power, violence, superiority" Skt. sahate "he masters," sáhas- "power, violence, might" Goth. sigis O.H.G. sigu O.E. sige "victory" PIE base *segh- "to hold."

Zime, from Mid.Pers. zim "time, year, winter," from Av. zyam-, zayan- "winter," probably related to zaman "time" + nuance suffix .

The period during the → early Universe before the → recombination era when the photons were hot enough to ionize hydrogen. The density was so high that the interactions between → matter and → radiation were very numerous. Therefore, matter and photons were in constant contact and their → temperatures were the same. As a result, the radiation became → thermalized, i.e. the → electromagnetic spectrum of the radiation became that of a → blackbody, a process called → thermalization. Since the time of recombination the photons of → cosmic background radiation have been free to travel uninhibited by interactions with matter. Thus, their distribution of energy is a perfect → blackbody curve, as predicted by the → Big Bang theory and shown by several observations, such as → Cosmic Background Explorer (COBE), → Wilkinson Microwave Anisotropy Probe (WMAP), and → Planck Satellite.

A thought experiment developed in 1935 by A. Einstein (1879-1955), Boris Podolsky (1896-1966), and Nathan Rosen (1909-1995) to demonstrate that there is a fundamental inconsistency in → quantum mechanics. They imagined two physical systems that are allowed to interact initially so that they will subsequently be defined by a single quantum mechanical state. For example, a neutral → pion at rest which decays into a pair of → photons. The pair of photons is described by a single two-particle → wave function. Once separated, the two photons are still described by the same wave function, and a measurement of one → observable of the first system will determine the measurement of the corresponding observable of the second system. For example, if photon 1 is found to have → spin up along the x-axis, then photon 2 must have spin down along the x-axis, since the final total → angular momentum of the two-photon system must be the same as the angular momentum of the initial state. This means that we know the spin of photon 2 even without measuring it. Likewise, the measurement of another observable of the first system will determine the measurement of the corresponding observable of the second system, even though the systems are no longer physically linked in the traditional sense of local coupling (→ quantum entanglement). So, EPR argued that quantum mechanics was not a complete theory, but it could be corrected by postulating the existence of → hidden variables that furthermore would be "local". According to EPR, the specification of these local hidden parameters would predetermine the result of measuring any observable of the physical system. However, in 1964 John S. Bell developed a theorem, → Bell's inequality, to test for the existence of these hidden variables. He showed that if the inequality was satisfied, then no local hidden variable theory can reproduce the predictions of quantum mechanics. → Aspect experiment.

A. Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 41, 777 (15 May 1935) → paradox.

As great as like or alike in quantity, degree, value.

From L. æqualis "uniform, identical, equal," from æquus "level, even, just," of unknown origin, + -alis, → -al.


Validity of ephemeris time - Astronomy

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1. Distances of Venus

1.1. Indications

Figure 1 compares the heliocentric geometrical distance of Venus as calculated using the iauPlan94 function from the SOFA library of the IAU and using the VSOP87A model. Along the horizontal axis is displayed the heliocentric geometrical distance of Venus according to the VSOP model, measured in AU. Along the vertical axis is displayed the difference between the distance according to the IAU model and the distance according to the VSOP model, also measured in AU.

To show the variation in time somewhat, the period of nearly 6000 years has been divided into three parts of about 2000 years each. The data points for the first period (the years −2900 through about −1000) are shown in blue, the points for the second period (roughly −1000 to 1000) in black, and the points for the third period (roughly 1000 to 2900) in red. The points are drawn in that order, so a black point may hide a blue point, and a red point may hide a black and/or blue point.

The distribution of points along the horizontal axis shows that the distance from Venus to the Sun varies between about 0.717 and 0.730 AU, but that that variation decreases with time: the horizontal range declines from blue via black to red.

In the vertical direction we see that the difference (in the heliocentric geometric distance of Venus) between IAU and VSOP during the "red" period is not greater than about 5 × 10 &minus6 AU = 750 km, and is about the same for all distances for which there are red points. In the "blue" period the difference is often greater, up to about 8 × 10 &minus5 AU = 12000 km, and depends on the distance: for smaller distances the difference is often negative, and for larger distances it is often positive. This indicates that the IAU model has a slightly greater distance variation in the blue period than the VSOP model has.

If that were the only difference, then we would not find any blue points clearly to the upper left or lower right of the midpoint of all points, but we do find such points. That indicates that there is a phase difference in the blue period between the IAU model and the VSOP model, so that the perihelia of Venus are on average not at the same instants according to the IAU model as according to the VSOP model.

To see if these conclusions are warranted, we take a look at some appropriate other graphs.

Figure 2 shows the heliocentric distance of Venus for two periods of 50 days in the year −2899, according to the VSOP model and the IAU model. The upper graph shows an aphelion, and the lower graph a perihelion. In both graphs, the curved lines show the distances according to the scale along the left-hand side. The tenfold difference between the IAU distances and the VSOP distances is also indicated by the difference between the far less curved sloping line and the horizontal line in the graphs. For example, in the upper graph the sloping IAU line is near 0.7286 on the left-hand side, and the horizontal VSOP line is at 0.728 there, so the difference between the IAU distance and the VSOP distance is one tenth the difference between those two values, i.e. 0.00006 AU.

The upper graph shows that the aphelion distance according to the IAU model is greater than according to the VSOP model, and the lower graph shows that the perihelion distance according to the IAU model is less than according to the VSOP model. The difference between the aphelion distance and the perihelion distance is therefore greater according to the IAU model than according to the VSOP model, which fits with what we concluded earlier from Figure 1. Apparently the IAU model assumes a slightly greater eccentricity for the orbit of Venus for that period than the VSOP model does.

Moreover, we see that the aphelion and perihelion occur slightly earlier according to the IAU model than according to the VSOP model, so there is a phase difference between them, as we deduced already from Figure 1.

The temporal variation of the phase difference (IAU versus VSOP) during the nearly 6000 year period is shown in Figure 3. We see that the phase difference is about 8 hours around the year −2900 and then gradually declines.

Our deductions from Figure 1 were accurate, so such figures are useful.

Figure 4 shows diagrams like Figure 1 for all non-trivial combinations of the five investigated sources. The columns and rows have the same order: JPL, SWE, VSOP, IAU, SOLEX. The difference shown along the vertical axis is that between the source of the row and the source of the column. Figure 1 is included (reduced in size) in column 3, row 4. In the lower left half of the figure, all vertical axes have the same range, from −10 &minus4 to +10 &minus4 AU. In the upper right half, the vertical axis of each graph has a range that fits that graph ― usually that range is a lot less than in the lower left half. Those ranges (in AU) are listed in the following table.


Pulsar Astronomy .net The Pulsar Astronomy Network

The most simple pulsar data format is the ephemeris. This is the parameters used in the timing model. Ephemerdies come as text files with a .eph or .par extension.

There appears to be no formal specification of what parameters are used in these files, although a loose standard has developed, with the following common parameters.

ParameterUnitsDescriptionAliases
PSRJStringPulsar JName
RAJsex-hrRight Asscention (J2000)
DECJsex-degDeclination (J2000)
PEPOCHMJDPeriod Epoch
F0HzFundemental frequency of the PSRF (sometimes P/P0, the period)
F1Hz/sFirst derivitive of rotational freq
F2Hz/s/sSecond derivitive of rotational freq
POSEPOCHMJDPosition Epoch
DMpc/cm3Dispersion Measure
STARTMJDTime the eph is valid from
FINISHMJDTime the eph is valid till
BINARYStringThe binary model used (if any)
EPHVERIntegerThe eph version

The parameters for the binary motion are dependent on the binary model used.

For the BT model:

ParameterUnitsDescriptionAliases
A1ltsecprojected semimajor axis
ECC Eccentricity of the orbitE
T0MJDEpoch of periastron
PBdaysOrbital Period
OMdegLongitude of Periastron

The files are tab or whitespace seperated with a single line for each keyword. Note that exponentials can be writen with a standard &lsquoe&rsquo notation, or the rather more strange &lsquoD&rsquo notation. e.g.

The files produced by tempo and psrtime should be compatable. tempo2 can read tempo files, with the -tempo1 switch. tempo2 files are not backwards compatible to psrtime.


Dante's Astronomy

Dante's great masterpiece The Divine Comedy embodies a transcendental form of astronomy. Each of the three books of this epic medieval work begins with the upward look to the heavens in Greek tradition of the astronomer/philosopher. Just as significantly, each of the three books ends with the word Stelle, or stars. The last thought that this great poet leaves the reader with, is that his mind revolves with the love that moves "the sun, the moon, and other stars." There is no question that The Divine Comedy was conceived by a genius aflame with the passions that inspire amateur astronomers to this day aperture fever is something Dante Aligehiere would have understood completely.

To fully appreciate Dante's use of astronomy, we need to remember that 700 years ago astronomy and philosophy remained tightly integrated within the liberal arts of the first universities Oxford and Paris. This was the astronomy of Ptolemy, preserved by the works of Arab astronomers, a legacy that lives today in names such as Deneb, Aldebaran, and Alfraganus. Dante's pre-Copernican astronomy, was essentially a Greek system in which the stars and planets rode across the heavens on crystalline spheres set in motion by the hand of God. It was a pure form of naked eye astronomy, philosophically born of the primal human urge to explore, an impulse we still feel today as we look up at the stars and question the meaning of our existence.

Dante's astronomy brings to life the ancient philosophical tradition that looking to the stars in contemplation transforms and elevates the mind. Perhaps the finest example of this occurs in the beginning of Dante's second book, The Purgatory. Here after emerging from the subterranean confines of Hell (where one cannot look at the stars) Dante and his mentor Virgil pause from their climb up the mountain of Purgatory. They rest on an East-facing ledge in the early hours after dawn. Dante reveals his observational skills by noticing something unusual about the path of the sun through the sky. He turns to Virgil in amazement, perplexed that the sun is moving to the left of the meridian. Dante who started his journey in the northern hemisphere expects to see the sun moving to his right, to the south of the meridian. Within the works that Dante studied was a reverence for the fact (considered highly philosophical in a world without satellites) that the heavens appear to behave differently from different vantage points on a spherical earth. What Dante is coming to terms with is that his subterranean journey across hell took him straight through the earth, past its center, and up into the southern hemisphere.

Virgil asks Dante to remember all that he studied, then work out the significance of what he is seeing. In a sudden flash of understanding any amateur astronomer knows well, Dante "gets it:" he is seeing the motion of the sun from the other side of the world! As soon as Dante turns his mental worldview upside-down, it all makes sense. Dante brings to life the power of astronomy to transform our worldview (the very foundation of our experience of life on planet Earth) through poetry.

A second remarkable example can be found in The Paradiso as Dante reaches the crystalline sphere that carries the sun. Here, he pauses to gaze lovingly on the geometric points of the equinox before him. Describing with mathematical skill the intersection of the ecliptic with the other great circles of the Ptolemaic astronomy. Dante fills his poetry with the appreciation that the skewed relationship of the circles is the cause of the Earth's seasons.

The Divine Comedy reminds us not only of the tremendous power of visual astronomy to inspire us it also reminds us that the wonder and inspiration that we find in astronomy links us to some of the deepest philosophical questions of the western tradition. The Divine Comedy further entices us with the prospect of entering into this tradition through our own education. The light of Dante's intellect has the power to transform our own upward gaze to the stars into a celebration of our shared humanity. Amateur astronomers are heirs to an epic legacy of personal exploration, hidden in one of the foremost works of western literature, waiting to be noticed like the stars above.

[Editor's Note: Peter Lord is a long time member of SJAA, PAS, and other Bay Area astronomy clubs, a spacecraft engineer for Loral, and recent recipient of a Masters of Liberal Arts from Stanford. His thesis explored the astronomy in Dante's Divine Comedy.]