The Solar System
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
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 near the surface of the Sun can be computed to be
about 600 km/s.
Well, the so-called "fast" Solar wind emanates from the polar regions of the Sun faster
than that (at 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
(the Sun's gravitation eventually pulls the
stuff back in, after a fairly long journey).
All told, the mass of the Solar wind that does escape 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
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 (about
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 is not quite so)
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 so-called decay
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.
The Titius-Bode Law
An empirical formula for the Solar distribution of planetary distances.
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
asronomical 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).
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.
The Inner Solar System
Four rocky planets: Mercury, Venus, Earth and Mars.
The Asteroid Belt
Between Mars and Jupiter.
The gaseous planets
Four gaseous planets: Jupiter, Saturn, Uranus and Neptune.
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 to the planet, Pluto has the largest satellite of the Solar System:
It 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
Pluto and such planetesimals are located in the Kuiper Belt.
Since 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 has been questioned.
It has been reaffirmed by the International Astronomical Union in 1998,
but such a status is already best viewed as cultural and/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.
Such discoveries are often announced many months after being first observed,
for healthy scientific reasons which occasionally yield to a combination of
peer pressure and media greed: For example, three of the above
(2003UB313, 2005FY9, 2003EL61) were announced on July 27 and 28, 2005...
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
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.
Bodies of the Solar System by Haluk Akcam
Planetoids with Distant Aphelions
Scattered disk objects (SDO) and wanderers, beyond the Kuiper Belt.
With a semimajor axis of 480 AU, Sedna is so distant that it has been
considered part of the
Heliosphere and Heliopause
The region aftected by solar wind, and its boundary.
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 about one light-year (1730 astronomical units) corresponding
to orbital periods of 70000 years or so.