(2007-10-10) The astronomical unit, fixed in 2012.
A unit of distance now defined as 149597870700 m.
The astronomical unit
(au) was first defined in 1672 by Jean-Dominique
Cassini (1625-1712)
as the mean distance from Earth to Sun. It was later redefined
more precisely as the semimajor radius of the orbit of a small mass which would take
one sidereal year to go around one solar mass.
The two definitions differ by about one part in a million.
So it was, at the beginning.
In 1672 the perihelion of Mars was simultaneously observed by Cassini from Paris and
by Jean Richer from
Cayenne
(French Guiana).
The parallax allowed them to derive a good approximation of the newly minted astronomical unit
of length. They underestimated the correct value
by less than 7%. (Previous guesses by
Tycho Brahe and Johannes
Kepler were more than 18 and 6 times too small, respectively.)
In 1938, the
International Astronomical Union modified the definition
of the astronomical unit
to eliminate any reference to the actual
sidereal year
which decays over time
(it was equal to 365.256363004 D at J2000.0).
Instead, they used a fixed duration equal to the
Gaussian year
of about 365.2568983 D that
Gauss worked out in 1809
(as his best estimate of the sidereal real which he thought
to be constant).
By definition (1938) the Gaussian year is the following exact duration:
2p / (0.01720209895) =
(365.25689832632816455955142419...) days
It is used to define the unit of length, not the unit of time.
More precisely, in 1976, an
astronomical
system of units was established by the IAU, with the
astronomical unit as the unit of length (A) and the
solar mass (S) as the unit of mass.
The basic unit of time is the day (D) of
86400 s (thus defined as an exact multiple of the "atomic"
SI second).
The secundary units of time are exact multiples of that astronomical or atomic
day (same thing). The year
is 365.25 D (31557600 s) and the
[Julian] century is 36525 D (exactly
3.15576 109 s).
Until 2012 (when the astronomical unit of length itself was redefined
as an exact number of meters) there were no exact
conversion factors
between SI units and astronomical units, except for units of time.
The value of the astronomical unit in meters
and the mass of the Sun expressed in kilograms were supposed to be derived
from measurements (both vary extremely slowly with time as the Sun
loses mass and gravitational pull).
Newton's gravitational constant (G)
had an exact value under the old definition of the
astronomical system of units outlined above. Namely:
k = 0.01720209895 rad/D is the
Gaussian gravitational constant
which was a defining constant, with that exact value, before the 2012 reform.
The product
G
. S
is the heliocentric gravitational constant which
is known with excellent precision in SI units, although neither of its factors is:
G . S =
1.32712440042 (8) 1020 m3/s2
The following relation used to link
the value A of the astronomical unit in meters
and that heliocentric gravitational constant G . S
(the relative uncertainty on the former is thus a third
of the uncertainty on the latter).
On August 31, 2012, the IAU decided that this was good enough
to make the metric value of the astronomical unit a defining constant
of the astronomical system of units (instead of the
Gaussian "constant" k which need not be mentioned anymore).
They argued that there was no longer any precision to be gained by evaluating ratios
of astronomical distances rather than expressing them directly in meters,
or in any convenient fixed multiple thereof, which is what the
astronomical unit of length thus becomes:
Astronomical unit (IAU, August 2012)
A = 1 au =
149597870700 m ( exactly )
In a vacuum, a photon travels one astronomical unit in 499.004783836... s.
Checksum : both 299792458 and 149597870700 are divisible by 73.
1 au = 149597870700 m =
22 . 3 . 52 . 73 . 877 . 7789 m
c = 299792458 m/s = 2 . 7 . 73 . 293339 m/s
Here's what I've gleaned from the bygone era when the heliocentric gravitational
constant (G.S) and the astronomical unit of length
(A) where firmly tied to each other
by a de jure value of the ratio G.S/A3.
Heralded values when
G.S / A3 was a defining constant (1938-2012).
Curiously enough, some lists quoted values of the two constants that
were grossly incompatible at the stated accuracy.
Also, the strict 3:1 ratio of the relative uncertainties
(excluding rounding)
translates into a clean 8:3 ratio when uncertainties are expressed
in units of the least significant digit...
(2012-11-06) The mean distance between the Earth and the Sun.
It's slightly more than one astronomical unit.
The
mean distance (d) between two bodies of masses M and m
orbiting each other with a period T is given by
Kepler's third law :
4 p 2 d 3
= G ( M + m ) T 2
If the period (T) of the Earth
around the Sun was exactly one Gaussian year,
the definition of the astronomical unit that was valid before 2012
would turn Kepler's law into the following equation for the Earth-Sun distance (d)
expressed in astronomical units :
d 3 = 1 + m / M
or, very nearly :
d = 1 + m / 3M
- m2 / 9M2
As the Earth-Moon system is
3.040432685(9) 10-6solar masses,
this gives the mean Earth-Sun distance as
1.000001013476535(4) astronomical units.
To be valid at the claimed precision of
4 10-15 (about 0.6 mm)
the so-called "mean distance" must be ultimately defined
in terms of orbital energies, not on raw distances
averaged over time (or else the averaging time would have to be
unrealistically long).
Indeed, in the ideal Keplerian motion of perfect spheres
(classically equivalent to two orbiting point-masses)
the time-average of the distance happens to be exactly equal
to the semimajor radius of the orbit, which depends only on the orbital energy.
If the value of T is not exactly equal to 1
(one Gaussian year)
then the above result has to be multiplied by
T2/3.
( 1 + x ) 2/3 =
1 + 2x/3 - x2/9 + ...
For example, when the sidereal year is given as 365.256363004 D then:
T = (365.256363004) (0.01720209895) / 2p
T2/3 = 0.99999902293
Multiplying this into the above, we obtain d =
1.00000003641 au
Using the metric equivalent of the au (149597870700 m)
we obtain the mean
Earth-Sun distance to a precision of 3 m :
149597876146 m.
(2012-11-06) The parsec (pc). The basic unit of interstellar distance.
Obtaining interstellar distances by triangulation.
By definition, a parsec is the radius of a circle
in which an angle of one arcsecond
subtends an arc of one astronomical unit
(A = 1 au).
Thus, the parsec (pc) is an exact multiple of the
astronomical unit, since a circle with a radius of
1 pc has a circumference of 1296000 au :
p pc = 648000 au
1 pc = ( 206264.80624709635515647335733...) au
As the astronomical unit has an exact metric equivalent
(149597870700 m) since 2012, so does the parsec:
1 pc =
3.0856775814913672789139... 1016 m
The parsec is a fairly large unit which is adapted to
the description of interstellar distances.
(The
closest star to the Sun
is 1.3 pc away).
Light-year :
The light-year is a commensurable unit with
an exact metric value. It is equal to the distance traveled
by light in a vacuum
over a period of one year (recall that the only year
recognized as a standard unit of time in astronomy is worth exactly 365.25 days, or 31557600 s).
(31557600 s) (999792458 m/s) = 9460730472580800 m
There are
3.261563777167433562138639707... light-years in a parsec.
(2006-11-28) The Interior of the Sun
Temperature and pressure are high enough to allow nuclear fusion.
(2006-11-28) The Chromosphere is the Surface of the Sun
After a long journey, core photons shine through the chromosphere.
(2004-11-11) The Corona
The Corona is a very hot region of rarefied gas which surrounds the Sun,
beyond its chromosphere.
It's normally visible only during a total solar eclipse.
At right is the eclipse of August 11, 1999
(which I witnessed from my late grandparents' backyard).
The light spectrum of the corona features a weak green emission line which was
first observed during the total solar eclipse of August 7, 1869.
This defied all explanations until 1939, when Grotrian and Edlen
attributed this to the presence in the Corona of highly ionised
iron: Fe XIV ("iron 14").
An atom of iron would lose 14 of its 26 electrons
only under incredibly high temperature: more than 1000 000 K,
as pointed out in 1942 by the Swedish astronomer
Bengt Edlén (1906-1993).
This scorching temperature is still not fully explained.
Mark Neumeyer (2004-11-18; email)
Solar Radiation and Solar Mass
Since the Sun gives off energy, wouldn't its mass decrease?
The Sun's mass does decrease, not only because it gives off energy, but also
because it gives off some matter particles
(Solar wind)
at an initial speed
that's sometimes sufficient to let them escape the Solar System.
As a result, the planets are slowly drifting outward.
Let's quantify this:
First, let's dispose of the Solar wind issue...
The escape velocity from the surface of the Sun is about 617 km/s.
The so-called fast solar wind emanates from the polar regions
of the Sun at a speed of about 800 km/s and is thus eventually lost
to interstellar space. On the other hand, what's called slow solar wind
emanates from the equatorial region at a speed (around 300 km/s) which doesn't
allow it to escape the Solar system.
Actually, at an outward velocity
v = 300 km/s = ½ vo ,
a particle would only travel a distance (d) of
15% of the solar radius (R) before falling back:
1 + d/R = 1 / (1 - v2/vo2 )½
All told, the mass that does escape via solar winds has been estimated
to be at most a few million tons per year.
The Sun loses this much through light and other electromagnetic radiation
in just a couple of seconds
(there are over 30 million seconds in a
year).
In other words the Sun loses about 10 million times less mass
through solar wind than it does via regular radiation, as discussed next...
The total bolometric power of the Sun is about
3.826 1026 W.
In terms of lost mass, this translates into about
4.257 109 kg/s.
(over 4 million metric ton(ne)s per second).
In one year (31557600 seconds),
that's about 1.3434 1017 kg,
which is still minuscule compared to the entire mass of the Sun itself
(1.989 1030 kg).
It takes about 15 million years for the Sun to lose
one millionth of its mass in the form of radiation.
Assuming that the power output of the Sun has been constant ever since its
formation 4550 000 000 years ago (which isn't quite so,
but close enough)
the Sun has thus lost to radiation about 0.03% of its original mass.
The fusion of hydrogen into helium
converts about 0.7% of mass into energy.
For a star like the Sun, an opaque layer exists
which slows down radiation emanating from the core.
The regime in which such a star settles imposes a "nuclear time scale"
allowing only 10% of its hydrogen to be consumed over the star's lifetime
(hydrogen makes up roughly 75% of the initial mass).
The above thus indicates that the Sun has already burned about half of
what its current regime allows.
This and other effects concerning the decays
of planetary orbits have been incorporated into our
long-term mathematical models of the Solar system.
There are other more dramatic evolutions of astronomical motions:
For example, we have biological evidence
that the lunar month was only 9 days long 420 million years ago
(instead of about 29.5 days today).
Each of these ancient days was itself about 12% shorter than a modern day.
(2004-11-04) The Titius-Bode Law
An empirical formula for the Solar distribution of planetary distances.
d(n) =
0.4 + 0.3´2n
for n = -¥, 0, 1, 2, (3), 4, 5, 6 ...
This formula happens to give a good approximation of distances to the Sun (expressed in
astronomical units) for the successive planets:
The Earth is, by definition, at a unit distance: d = 1 (n = 1).
The main asteroid belt is at the approximate location of a
"missing" planet (n = 3)
between Mars (n = 2) and Jupiter (n = 4)...
All told, the approximation
is surprisingly good as far as Uranus (n = 6) but it's about
29% too large for Neptune (n = 7) and fails by almost a factor of 2
for Pluto (n = 8)
[ formerly considered a planet ].
This empirical relationship is most commonly known as Bode's Law.
It was named after
Johann Elert Bode (1747-1826),
who published it in 1768.
Bode was to become director of the Observatory of Berlin, and he collaborated
with Johann Heinrich Lambert on the first ephemeris ever published in German.
The first calculations concerning the distribution of planetary distances are due to
Christian Freiherr von Wolf (1679-1754).
Wolf's calculations were first made popular in 1766 by Johann Daniel Dietz (1729-1796),
a professor of physics at the University of Wittenberg (Germany) who is best known
as Titius [of Wittenberg].
The thing is thus also known as the Titius-Bode law...
Of course, it's not a "law" at all, it's just an approximative relationship between the rank
of a planet in the Solar system and the size of its orbit.
Yet, the pattern is sufficiently simple and sufficiently precise that it does beg for
an explanation of some kind.
The Solar system's major planets came from the condensation of
a rotating cloud of dust and gas.
Most of this was hydrogen which aggregated at the center to form a ball (the Sun)
hot enough to ignite an ongoing nuclear reaction
as it was compressed by its own gravity...
The rest aggregated in a small number of planets around the Sun,
at distances which are fairly well described by the Titius-Bode law.
The details of the condensation of this primal cloud are not understood
well enough to allow any kind of "derivation" of the Titius-Bode relation,
at least for now.
(2005-08-30) The Inner Solar System
Four rocky planets: Mercury, Venus, Earth and Mars.
(2007-10-11)
Earth This is home :
(2005-08-30) The Asteroid Belt
Between Mars and Jupiter.
Ceres
is, by far, the moss massive body in the
asteroid belt
between the orbits of Mars and Jupiter.
It contains about 32% of the total mass in it.
The current classification makes
Ceres the only
dwarf planet in the asteroid belt.
Ceres was discovered on the first day of the 19th
century (January 1, 1801) by
Giuseppe Piazzi
(1746-1826).
In his History of Mathematics,
Florian Cajori
points out that the discovery of Ceres occurred just after the philosopher
G.W.F. Hegel had published a "proof" a priori
that such a thing was not possible!
For nearly half a century, Ceres was known as the eighth planet of the Solar system
(Uranus, the seventh planet, had been discovered in 1781 and Neptune would only be observed in
1846).
(2015-06-12) Chiron and the other centaurs Asteroids with decaying orbits, in the midst of the giant planets.
On October 18, 1977, using images taken two weeks earlier at
Palomar Observatory,
Charles T. Kowal (1940-2011)
discovered a minor planet near aphelion just outside the perihelion of Uranus.
At the time, no other minor planet besides Pluto had been observed this far out.
It was named Chiron in 1979 and the rule was proposed that
the names of other centaurs be reserved for other bodies with similar charasteristcs.
2060 Chiron
had previously been photographed as early as 1895 and those records helped
determine its eccentric orbit with great precision.
It was found that a close encounter with Saturn in AD 720
had brought Chiron's previous semimajor axis of 14.4 au
down to its current value of 13.7 au.
Chiron is at least 130 km un diameter. It originates from the
Kuiper belt and will become a
short-period comet in the next million years.
Likewise, other centaurs have relatively unstable decaying orbits.
(2008-09-01) The Discovery of Neptune (September 1846)
Urbain Le Verrier (1811-1877; X1831)
scooped John Couch Adams.
John Couch Adams
Urbain Le Verrier
In the Summer of 1846, Le Verrier was 35 and Adams was only 27.
Independently of each other, both had suspected that the observed anomalies in the orbit
of Uranus were due to an unknown planet, whose position they could derive mathematically.
Le Verrier presented his result to the
French Academy of Sciences
Monday 31 August 1846.
Two days later, Adams mailed his own work to the
Greenwich Observatory who ignored him.
On Friday 18 September, Le Verrier wrote a letter to
Johann Galle (1812-1910) at the
Berlin Observatory,
who received it five days later and duly found the predicted planet the same night
(23 September 1846).
(2005-08-27) Pluto,
Plutinos
and other planetoids in the Kuiper belt.
A Plutonian year is 1.5 times as long as a Neptunian year.
Pluto was discovered in 1930 by the American astronomer
Clyde William Tombaugh (1906-1997).
It is about 2360 km in diameter (roughly 2/3 the diameter of the Moon).
In proportion of its size, Pluto has the largest satellite of the Solar System
(unless 2003EL61 turns out to consist of two similar
bodies in a very tight orbit).
This moon is 1250 km in diameter and was discovered in 1978, by American
astronomer James Christy,
who named it Charon, after the mythical boatman of the Styx
(because the first syllable was the nickname of his wife Charlene).
Pluto and Charon are about 19000 km apart. They present the same face to each other
as they revolve around their center of gravity, in about 6.38 days.
In 1988, Pluto was found to have a very thin atmosphere of nitrogen, with
traces of methane and carbon monoxide. The atmospheric pressure at the surface
of Pluto is roughly 1 Pa (about 100 000 times less than on the
surface of the Earth).
Pluto revolves around the Sun in 247.7 years.
This is 50 % more than the giant planet Neptune,
because of a gravitational synchronization dominated by Neptune.
Planetoids which are in this same 3 to 2 resonance with Neptune are called
plutinos.
Pluto and such planetesimals are located in the Kuiper Belt.
After the recent discovery in the Kuiper Belt of several planetoids (i.e. nearly spherical
solar objects) whose sizes approach or exceed Pluto's,
the status of Pluto as the Solar System's ninth planet appeared mostly cultural
or historical, rather than astronomical or physical.
Pluto has just too much competition in its own
neighborhood to qualify, on merits alone, for the same status as the other 8 planets.
Although the status of Pluto as a planet
was reaffirmed by the International Astronomical Union in 1998,
Pluto fell from grace on 2006-08-24, when a new
definition of a planet was adopted which rules it out...
Such discoveries are often announced many months after being observed,
for healthy scientific reasons which occasionally yield to a combination of
peer pressure and media greed: For example,
2003UB313, 2005FY9 and 2003EL61 were all announced on July 27 and 28, 2005...
Eris
is the largest known dwarf planet; it's bigger than Pluto
(which ceased to be an official planet on 2006-08-24).
Prior to the official adoption of its name (on 2006-09-13), Eris had been known
as Xena
(or "the tenth planet")
to its discoverer, Mike Brown, and many others.
Dysnomia
(the satellite of Eris discovered on 2005-09-10) was previously dubbed
Gabrielle (after Xena's sidekick in the eponymous
TV series).
Eris is the name of the Greek goddess of strife,
whose Latin name is Discordia,
as opposed to Harmonia (Greek) and
Concordia (Latin).
Although a definite conclusion has yet to be reached,
an animated picture of 2003EL61
is consistent with the interpretation that it consists of two kernels in tight orbit
(4-hour period) with at least 2 distant moons around them.
Kuiper Belt Objects may be arbitrarily divided into 3 categories:
The inner belt, consisting mostly of Plutinos.
"Classical" Kuiper Belt Objects, with a period
of 400 years or less.
Scattered disk objects (SDO) beyond that point.
The Kuiper Belt was so
named
shortly after the discovery of 1992QB1, the first
object (besides Pluto and Charon) found in it,
by David C. Jewitt
(University of Hawaii) and
Jane X. Luu (Berkeley).
Gerard Peter Kuiper (1905-1973) was a Dutch-born American astronomer
who served as chief scientist of NASA's "Ranger" lunar probe program in the 1960's.
The existence of the Kuiper Belt was formally proposed in the 1980s
as the origin of short-period comets.
Centaurs being the transitional state.
On 2006-08-24, Resolution 5A
(amended by resolution 5B for the locution "classical planet")
introduced the distinction
between the 8 so-called classical planets :
(Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune) and a new concept
of dwarf planet which includes Pluto and Ceres
(the largest asteroid).
Both types of planets are bodies sufficiently large for gravitation to overcome rigid body forces,
so that a nearly spherical shape is obtained. Neither type can be a satellite
of a larger planet. However, a new condition was imposed that a [classical] planet
must dominate its orbital neighborhood and it should have cleared it from other bodies
(by collision or by capturing them as satellites).
That last requirement does not apply to dwarf planets.
By that new definition, Pluto is now a dwarf planet, which is merely taken as
the prototype of trans-Neptunian dwarf planets, for which the companion resolutions
6A and 6B introduce the denomination of plutonian objects.
An IAU process was instated to decide between the status of dwarf planet
or "Small Solar System Body" in borderline cases.
Eris (2800 km) is the largest dwarf planet. It's the fact that Eris
is larger than Pluto which prompted the new classification.
The largest Kuiper belt objects (KBO) tabulated above should also be
classified as dwarf planets.
1 Ceres (950 km) is by far the largest asteroid in the
main belt and
it's definitely considered a dwarf planet.
The asteroids 4 Vesta
(525 km) and
2 Pallas
(544 km) could eventually be assigned the same status.
(2010-04-24) In 7837, Neptune and Pluto come "close" to each other...
Can Neptune eventually capture Pluto?
I played around with a
nice clockwork model of the solar system,
until I found a "near miss" of Neptune and Pluto in the year 7837
(when their planar locations actually seem to coincide).
Other
people made the same remark.
Of course, this is mostly an optical illusion, since the two orbits do not really
intersect (their closest points are
2 billion kilometers apart).
Nevertheless, as each such close encounter can only reduce the distance between the
two orbits, we may wonder if the dynamics of the situation is such that Neptune
will eventually capture Pluto. The answer is no
because the close encounters
of Neptune and Pluto are not powerful enough to destroy at once the
stable 3 to 2 ratio in their orbital periods, which prevents a slow drift
to the 1 to 1 ratio that would be needed before Pluto could become a satellite of Neptune.
(2005-08-30) Heliosphere and Heliopause
The region aftected by solar wind, and its boundary.
(2005-08-27) The Oort Cloud
The outermost spherical shell at the fringe of the Solar System.
The Dutch astronomer Jan Hendrik Oort (1900-1992)
helped establish the rotation of our Milky Way galaxy
in the 1920's. In 1950, he proposed that the
outermost part of the Solar System was a spherical reservoir of comets...
As passerby stars come within a few light-years from the Sun, they could
disturb the orbits of some distant solar objects and turn them
into "long-period" comets bound for the inner Solar System.
This view is now universally accepted, although Oort's explanation for the
formation of the "cloud" is not...
Oort envisioned it as a remnant from the explosion
of a planet between Mars and Jupiter.
The fringe of the Solar System is now called the Oort Cloud.
It is bounded by a huge sphere centered on the Sun, whose radius is
estimated to be between 50 000 and 100 000 au
(with ludicrous precision, one light-year
is 63241.07708426628... au)
The diameter of that spherical cloud is thus often quoted as being
three light-years.
(2020-09-10) 'Oumuamua (1I/2017 U1) and Borisov (2I/2019 Q4).
1I/'Oumuamua and 2I/Borisov are the first interstellar objects ever observed passing through the
inner Solar system, on hyperbolic orbits.
1I/'Oumuamua is an elongated asteroid which was probably ejected from a distant
binary star whose identity is difficult to determine. It passed so close to the Sun
that its trajectory was sharply deflected before leaving the Solar system at the same speed it entered it.
2I/Borisov is a comet which was most probably ejected about one million years ago from the
Kruger 60 system, consisting of two
red dwarves 13.15 light-years away.
One is 27% the mass of the Sun. The other one only 18%.
