Tom Van Flandern <tomvf@metaresearch.org>
2004/06/11
Abstract. Articles about the
black drop effect during the 2004 June 8 transit of Venus reveal that the
explanation for this previously well-understood phenomenon has been largely
forgotten. The Appendix contains a table of the best transits visible from each
major solar system planet.
Introduction
Innermost planet Mercury passes in front of the
Sun's disk as seen from Earth (a "transit") once or twice every
decade. We also observe the Galilean moons of Jupiter occasionally transiting
in front of Jupiter's disk, although no outer planet can ever transit the Sun
as seen from Earth. Other types of transits are rarer. One of those rarities
occurred on 2004 June 8, when the planet Venus transited in front of the Sun's
disk for the first time since 1882. We have to wait only eight years for the
next transit of Venus, which will be at least partially visible from most of
North America on 2012 June 6. However, there will then be an interval of over a
century before another Venus transit occurs.[1]
Transits
of Venus are more interesting to watch than transits of Mercury, and not just
because they are rarer. Venus is larger and closer to Earth during transits
than Mercury, so its disk is roughly six times the size of Mercury's during
transit. See Figure 1.[2]
But because of irradiation (see below), Venus may appear a full order of
magnitude larger than Mercury. Moreover, Mercury has no significant atmosphere,
whereas Venus has a very thick atmosphere. An atmosphere can concentrate
background light by refraction. The result is that Venus occasionally shows an
"airglow" halo of illumination around its disk. This is most easily
seen near the Sun's limb, when only part of the disk of Venus is in front of
the Sun's photosphere.
Historically, transits provided valuable data
about the distances to these bodies and the scale of the solar system. However,
modern observation techniques have made that type of usage obsolete. So
transits are watched mainly because of public interest and the sense of our
place in the solar system that they provide. We are privileged to be able to
watch another planet pass in front of our own Sun, and to be among the first
dozen generations in human history to know what these bodies are and how far
they are away, and to be able to predict the local circumstances of these
events to within seconds even decades in advance.
Although this transit of Venus lasted about six
hours in total (for those in Europe, Africa, and Asia), only the end of the
event could be seen from the Eastern U.S. The beginning and end of a transit
produce an unusual phenomenon called the "black drop". In this
article we will answer questions about what that means and what causes it. As
with much human knowledge that hasn’t been used for a long while, many of
today's astronomers, science writers, and historians seem to have forgotten
about or to have never been taught the correct explanation for the black drop.
What is the black
drop?
The disk of Venus is large enough that it may
take 20 minutes or so to completely cross the Sun's limb so that the whole
planet appears in silhouette. As Venus (or Mercury) is just moving onto the
Sun's disk, some number of seconds before the circular disk of the planet
separates from the limb, it begins to "drag" a black extension behind
it, much like leaving a wake. This elongates and persists well after the moment
when sunlight apparently should surround the entire planet disk. Then rather
rapidly, this black wake disappears, and the disk looks circular.
At
the end of the transit, a symmetric event occurs. The round planet disk
approaches the Sun's limb. But distinctly before it gets there, a black
extension rapidly appears between the disk and the limb. For both ingress and
egress, the appearance of this extension is called the "black drop".
See Figure 2.[3]
We can be certain that the effect is not caused
by the atmosphere of Venus because Mercury shows it too, and Mercury has no
sensible atmosphere. And it is not an optical illusion in the eye because
photographic plates see it also. Many modern scholars refer to the effect as a
mystery, and some mention that 19th century observers found it
confounding because it prevented them from making accurate timings of the
moment of contact. However, as recently as a generation ago, astronomers were
fully aware of the cause of the black drop, and had applied that knowledge to
other types of astronomical observations as well.
What causes the
black drop?
When I first browsed through the photographic
Palomar Sky Survey 40 years ago, I noted that bright stars were enlarged in
size according to how bright they were. So I turned to the plate containing the
image of Sirius, the brightest star, and noted that its photographic image was
huge – so much so that it hid other stars, galaxies, quasars, and whatever
background objects might lie close to the same look direction. And yet the
source of this huge smudge was a point source of light. Why did the image
spread so much?
Later, I learned about
"seeing", an important factor to every Earthbound observer of the
skies through a telescope. "Seeing" represents the apparent size of
most point sources of light as their light is slightly scattered by passing
through constantly moving air cells in Earth's atmosphere. These cells absorb
and re-emit passing light, and refract (bend) its direction of travel. The
result is that point sources on the sky have "seeing disks", enlarged
by the atmosphere to a degree that depends on how calm or rough the atmospheric
turbulence is at any given time. Winds at any altitude have the potential to
make seeing disks larger. Moreover, the amount of the enlargement depends on
the contrast between the brightness of the object and the darkness of the
background, and also on the length of time that the light detector accumulates
photons. The greater the brightness differential, the greater the difference
between the real image size and its apparent size, always in the sense that
light spreads and overlaps dark.
In the astronomers' handbooks of
more than a generation ago, it was widely recognized that the apparent
diameters of bright bodies were enlarged by just such a light-spreading effect
known formally as "irradiation". If corrections were not applied, one
would get an exaggerated estimate for the diameters of bright bodies. This
apparent enlargement was especially a factor for predicting solar eclipses
accurately, the times of which depend on the true diameters of the Sun and Moon
rather than their apparent diameters. The corrections applied to compensate for
irradiation were described in the ephemeris and almanac publications of that
era.[4]
Of
course, just as the bright Sun's apparent diameter was enlarged by spreading of
light onto the dark background sky, the same bright photosphere also spread its
light (while passing through Earth's atmosphere) onto the black disks of
planets transiting the Sun. So in the case of transits, irradiation of sunlight
made the apparent planet diameters smaller because the planets were the darker
image. See Figure 3.3
This difference between apparent and true planet
disk diameters is of little practical importance except in critical cases such
as eclipses. A simple but important consequence is that, because the amount of
shrinking of the apparent diameter during transits is independent of the size
of the diameter, objects one-third the apparent diameter of Mercury (a few arc
seconds) would be completely overlapped by spreading solar light and display no
visible disk whatever! That is undoubtedly why no asteroid or artificial
satellite has ever been observed to transit the Sun, and why historic searches
for inter-Mercurial planets transiting the Sun would have probably been
unsuccessful even if such planets had existed.
Armed with this knowledge about irradiation, we
can easily understand the black drop phenomenon. In the left half of Figure 3,
the Sun's limb appears at a greater angular distance from the planet than it
really is, both because the planet's disk appears smaller than it is, and
because the Sun's disk appears larger than it is. Then the apparent planet disk
approaching the limb remains circular until the instant when the invisible true
limbs of planet and Sun make contact. At that moment, light can no longer
originate from that point, so it can no longer spread and make the Sun's limb
appear enlarged or the planet's limb appear shrunk. So we have the black drop,
when the true planet disk and the true solar limb reveal themselves.
If the Sun's photosphere was of
uniform brightness all the way to its limb and the planet had no atmosphere,
the black drop would be a near-instantaneous effect. However, the real
photosphere has limb darkening because of light having to be directed toward
Earth at ever greater angles from the normal, and because the optical path of
light from the limb has more opacity. (For the same reason, the Sun appears
dimmer as it approaches Earth's horizon.) Moreover, the photosphere does not
just end, but fades gradually into the much dimmer, ruby red chromosphere that
normally can be seen only during total solar eclipses. [When using a
hydrogen-alpha filter, the chromosphere is relatively bright, producing a
"limb brightening" effect that drastically changes the appearance
near this internal ("second" or "third") contact of the Sun
and Venus limbs.]
So
the gradual dimming of the Sun's photosphere near its limb makes the black drop
effect of short-but-finite duration (a handful of seconds). And the airglow halo
of refracted sunlight passing through the atmosphere of Venus creates
additional ambiguity about when the exact contact has occurred. Nevertheless,
contrary to the impression stated by astronomers in past transits of Venus
before this effect was anticipated or understood, the black drop is the most
readily timed event during the entire transit, and corresponds more precisely
to the true instant of contact with the same solar limb used to compute eclipses
so accurately. So now that we understand what causes the black drop, we can
appreciate that it provides a timing advantage rather than a disadvantage.
Irradiation is
also seen with lunar occultations
Other astronomical phenomena also show this
irradiation effect – the apparent spreading of light from bright areas onto any
adjacent dark areas. One of the most common, visible to amateur astronomers far
more frequently than transits, is lunar occultations. When a star is bright
enough to remain visible near the Moon's bright (daylight) limb, or even for
fainter stars near the Moon's darker (night side) limb when that side of the
crescent Moon is illuminated by Earthshine, irradiation makes the Moon's limb
appear larger than it really is. As a direct result, the star appears to
penetrate the Moon's limb by a short distance, as if burrowing into the
surface, before the true limb cuts off its light almost instantaneously. See
Figure 4.[5]
The fact that the
occultation occurs with the same rapidity whether the Moon’s limb is visible or
invisible to the observer confirms that the light in space is not being
altered, and the illusion of irradiation must arise in Earth’s atmosphere.
Photoelectric photometers can detect the actual speed at which the star
disappears, which is not instantaneous because of diffraction. (Diffraction is
the bending of lightwaves passing any sharp edge.) If one brings two fingers
together without quite touching, a black-drop-like apparent touch can still be
seen because of diffraction. But lunar image spread from diffraction is roughly
three orders of magnitude smaller than that from variable refraction through
moving terrestrial air cells. A typical seeing-enlarged star image would take
several seconds for the Moon to cover. However, except for the rare star that
has a sensible diameter or a close companion, the actual disappearance of a
star at the Moon’s limb takes only a handful of milliseconds.
My thanks to Greg
Hennessy <greg.hennessy@tantalus.cox.net> for drawing my attention to an
observation of the black drop effect during a 1999 November 15 Mercury transit
observed from the TRACE satellite in near-Earth space. These authors point out that
all ground-based observers are subject to a much larger and time-variable
black-drop effect because of “seeing” effects in Earth’s atmosphere. But when
that is no longer present in space, a smaller, predictable effect from
diffraction remains visible from orbit.[6]
Another correspondent, Peter Abrahams <telscope@europa.com>, mentioned
two relatively recent articles by Bradley Schaefer. The first attributes the
ground-based black drop simply to “terrestrial atmospheric smearing, which
blurs the image.”[7]
The second states: "the ideal image … will suffer smearing … that will
produce a somewhat fuzzy image with contour lines (i.e., what is perceived as
the edge) that are shaped like the Black Drop. The primary causes of smearing
are the usual astronomical seeing (associated with small angle scattering in
our Earth's atmosphere) and the usual diffraction in the telescope (the Airy
pattern). Other contributing smearing mechanisms that generally do not
dominate are imperfections in the telescope's optics, imperfections in the
observer's eyes, the finite angular resolution of the detector, and even the
physical size of the telescope's aperture."[8]
Conclusion
The black drop phenomenon seen
during transits is a well-understood manifestation of irradiation, the
spreading of photons by rapidly moving air cells. It provides an advantage for
the accurate timing of internal (second and third) contacts for transits, not a
disadvantage. Figure 5 shows one of the best photos of the actual black drop
effect, taken by Uwe Schürkamp in Germany during the 2004 June 8 Venus transit.[9]
Those
who missed the 2004 June 8 transit of Venus still have the 2012 June 6 event to
look forward to, which will be visible from most of North America, especially the
western parts. But if you miss that opportunity, you will need to book a ticket
on a spacecraft to see such a transit in your lifetime, because the following
transit of Venus from Earth after 2012 will be in the year 2117.
For many observers, the seconds
when the black drop occurs may be the most interesting of this rare, multi-hour
astronomical manifestation of Earth's place in the solar system, a transit of
Venus.
Appendix
As people think about our place in the solar
system, they are now starting to ask questions that would have had no
foreseeable relevance to Earth residents the last time a Venus transit
occurred, such as "What would an Earth transit look like if viewed from
Mars?" It is interesting to contemplate that by the time of the 2117 Venus
transit, people may be making plans to actually observe just such "science
fiction" events.
Table I shows a few of the
possibilities. (Angles are in arc seconds. Transiting planet angular diameters
are also expressed as a percentage of the Sun's angular diameter.) It is
interesting to note that no transits of solar system planets observed from
other major planets present a larger angular diameter than transits of Venus
present to Earth observers. But Earth and its Moon present the only
opportunities for a 2-body transit if viewed from Mars. And transits of Jupiter
observed from Saturn block the largest fraction of the arriving sunlight,
roughly 5%. These events would last a day or two. During that period, sunlight
reflected from Saturn and its rings would be dimmer than normal by an amount
easily detected from Earth by a photometer. If views of transits of Jupiter
seen from Saturn's moons were also considered, the window of opportunity for
witnessing such an event would be even greater. (In fact, Jupiter's large
shadow might cause temporary physical changes for asteroids and comets that
enter it.) Transits of Jupiter and Saturn visible from Uranus or Neptune or
their major moons should likewise have a detectable effect on the shadowed
body's brightness. Our readers are challenged to be the first to predict the
date and time of any such event.
Table I. The best transits visible from each
major solar system planet
|
Observer's
Planet
|
Transiting
Planet
|
Sun angular
diameter
|
Planet ang. diam. (%Sun)
|
Comments
|
|
Venus
|
Mercury
|
2650"
|
16" (1%)
|
Mercury varies from
13-19"
|
|
Earth
|
Venus
|
1920"
|
60" (3%)
|
next: 2012/06/06
|
|
Mars
|
Earth
|
1260"
|
34" (3%)
|
our Moon's
diameter: 9"
|
|
Jupiter
|
Earth
|
370"
|
4" (1%)
|
irradiation à invisible?
|
|
Saturn
|
Jupiter
|
200"
|
45" (22%)
|
Ganymede: 1.6"
(invisible)
|
|
Uranus
|
Saturn
|
100"
|
17" (17%)
|
rings outer diameter:
39"
|
|
Neptune
|
Saturn
|
64"
|
8" (12%)
|
Jupiter: also
8"
|
|
Neptune
|
Uranus
|
64"
|
3" (5%)
|
irradiation à invisible?
|
