SOLAR ACTIVITY WATCH: The Sun has been mostly quiet for weeks, but...

Space Weather News for July 13, 2004
http://spaceweather.com

SOLAR ACTIVITY WATCH: The Sun has been mostly quiet for weeks, but this
could soon change. One or more big sunspots are turning toward Earth,
raising the possibility of solar flares, geomagnetic storms and auroras in
the days and weeks ahead.

MORNING STAR: It's not easy waking up at dawn, but this week it's worth
doing. Venus, the "morning star," is absolutely brilliant in the eastern
sky around sunrise. On July 14th, Venus and the crescent moon will appear
side by side--a lovely sight. On July 15th Venus reaches maximum
brightness. The planet is delightful to see through a telescope; it looks
like a tiny crescent Moon.

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and sky maps

In article ,
Sam Wormley wrote:

On July 15th Venus reaches maximum brightness.

No, on that date Venus reaches maximum "brilliancy", which
is somewhat different. The "brilliancy" is defined in purely
geometrical terms: "maximum brilliancy" occurs when the
sunlit part of Venus' disk reaches its largest apparent area.

The date of maximum brightness depends on the phase function
for that celestial body. If the phase function was equal to
the phase itself, then "maximum brilliancy" would be the same
as maximum brightness. Such a phase function would imply that
the brightness of a clestial body (when corrected for varying
heliocentric and geocentric distances) would be exactly half
at half phase, compared to full phase. This isn't valid even
for a perfectly diffusing sphere, where the brightness at
half phase is exactly pi times fainter than the brightness at
full phase. Venus comes pretty close to this. For more rough
surfaces, such as the Moon or Mercury, the brightness at half
phase is some 10% of the brightness at full phase.

So the maximum brightness of Venus occurs somewhat later than
15 July. I haven't computed the precise date, and it really
doesn't matter, because Venus' brightness remains nearly
constant for several weeks during July. Thus there is definitely
no noticeable "peak" in Venus' brightness in July -- the
maximum brightness is a very very shallow "peak".



--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://www.stjarnhimlen.se/
http://home.tiscali.se/pausch/

In article ,
Sam Wormley wrote:

On July 15th Venus reaches maximum brightness.

No, on that date Venus reaches maximum "brilliancy", which
is somewhat different. The "brilliancy" is defined in purely
geometrical terms: "maximum brilliancy" occurs when the
sunlit part of Venus' disk reaches its largest apparent area.

The date of maximum brightness depends on the phase function
for that celestial body. If the phase function was equal to
the phase itself, then "maximum brilliancy" would be the same
as maximum brightness. Such a phase function would imply that
the brightness of a clestial body (when corrected for varying
heliocentric and geocentric distances) would be exactly half
at half phase, compared to full phase. This isn't valid even
for a perfectly diffusing sphere, where the brightness at
half phase is exactly pi times fainter than the brightness at
full phase. Venus comes pretty close to this. For more rough
surfaces, such as the Moon or Mercury, the brightness at half
phase is some 10% of the brightness at full phase.

So the maximum brightness of Venus occurs somewhat later than
15 July. I haven't computed the precise date, and it really
doesn't matter, because Venus' brightness remains nearly
constant for several weeks during July. Thus there is definitely
no noticeable "peak" in Venus' brightness in July -- the
maximum brightness is a very very shallow "peak".



--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://www.stjarnhimlen.se/
http://home.tiscali.se/pausch/

Paul Schlyter wrote:

No, on that date Venus reaches maximum "brilliancy", which
is somewhat different. The "brilliancy" is defined in purely
geometrical terms: "maximum brilliancy" occurs when the
sunlit part of Venus' disk reaches its largest apparent area.


Wrong-oh. Here's the definition of "brilliancy," as stated on page 723
of the _Explanatory Supplement to the Astronomical Almanac_ (1992):

brilliancy: for Mercury and Venus the quantity
k s^2 / r^2, where k = 0.5 ( 1 + cos i ), i is
the phase angle, s is the apparent semidiameter,
and r is the heliocentric distance.

Notice the 1 / r^2 factor. If "maximum brilliancy" occurs when the
sunlit part of the disk reaches largest apparent area -- that is, when
k s^2 is maximized -- then why does a 1 / r^2 factor come into play?
In other words, what does the planet's heliocentric distance have to do
with apparent area after the phase and angular diameter are accounted
for?

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~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Mark Gingrich San Leandro, California

Paul Schlyter wrote:

No, on that date Venus reaches maximum "brilliancy", which
is somewhat different. The "brilliancy" is defined in purely
geometrical terms: "maximum brilliancy" occurs when the
sunlit part of Venus' disk reaches its largest apparent area.


Wrong-oh. Here's the definition of "brilliancy," as stated on page 723
of the _Explanatory Supplement to the Astronomical Almanac_ (1992):

brilliancy: for Mercury and Venus the quantity
k s^2 / r^2, where k = 0.5 ( 1 + cos i ), i is
the phase angle, s is the apparent semidiameter,
and r is the heliocentric distance.

Notice the 1 / r^2 factor. If "maximum brilliancy" occurs when the
sunlit part of the disk reaches largest apparent area -- that is, when
k s^2 is maximized -- then why does a 1 / r^2 factor come into play?
In other words, what does the planet's heliocentric distance have to do
with apparent area after the phase and angular diameter are accounted
for?

--
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Mark Gingrich San Leandro, California