Ryukyu Astronomy Club Newsletter http://www.nexstarsite.com/rac.htm 

Volume 2, Issue 2  June 2003 
Next Club Meeting 
June 28th
Conference Room B at the Camp Lester Naval Hospital
May General Meeting
The
May General Meeting of the Ryukyu Astronomy Club was held on the 31st in
Conference Room B at the Navy Hospital. Attendance was poor with just 3 members
:( After a little chatting about various matters, Mike Swanson gave a
presentation on exoplanets. The Downloads section our web site has been updated
with the exoplanet presentation as well as the "Place the Planets" game used at
Astronomy day and a few other resources.
June's meeting will be an observing session at the Alivila site. We will meet at the Hospital conference room at 7PM and proceed from there to arrive at Alivila around 8PM. A reminder will be sent later this month.
Things to See This Month
June marks the beginning of what should be a great season for observing Mars.
The red planet will come closer to the Earth than it has in tens of thousands of
years allowing this tiny planet (about half the diameter of the Earth) to grow
to its largest apparent size during recorded history. While this all sounds
very dramatic and historic in nature, in more practical terms Mars makes a close
pass to the Earth once every two years with markedly closer passes every 15 or
16 years. This will be the best view you can get of Mars for at least the next
16 years. Currently Mars is still quite far from Earth and best viewed in the
early morning hours. Mars will get approach closer to us up through August,
after which it will begin to recede. Surface features (particularly the south
polar ice cap) are currently visible and more features become noticeable each
week. To help identify the features you are seeing in the eyepiece, visit the
Downloads section of our web site and download Mars Previewer II.
Several other celestial gems are scattered around the sky in the spring:
 M51  the Whirlpool Galaxy  the first galaxy in which astronomers detected spiral arm structure. A dark site and good transparency will provide stunning views of the arms, as well as M51's companion galaxy.
 M4, M5, M13, M92  a selection of great globular clusters visible in summer skies. M4, unlike most other globular clusters, even presents a great view in a set of tripodmounted binoculars.
 M57  the Ring Nebula  an exploded star, this planetary nebula looks distinctly like a donut in even small telescopes.
For more objects of interest and the locations of those listed above, download the latest chart from www.skymaps.com or visit www.SkyandTelescope.com and customize the online star chart for Okinawa's general location of 128 degrees East longitude and 26 degrees North latitude.
Useful Formulas for
Amateur Astronomers
Professional astronomy is heavily laden in mathematical simulations and complex
formulas. While the amateur astronomer can simply grab some gear or just use
their eyes to enjoy the night sky, there are several formulas that become useful
as your experience and equipment list grows. And, you don't need a college
mathematics background to make use of them. Please note that many of these
formulas are used in the Scope Calculator spreadsheet available on the Downloads
page of our web site.
Magnification of a Telescope
The most
commonly used formula in amateur astronomy is used to calculate the
magnification of a telescope:
magnification = focal length of telescope / focal length of eyepiece
Example: using a 10mm eyepiece in a telescope with a focal length of 1000mm results in a magnification of 100x (1000 / 10 = 100).
Maximum Magnification of a Telescope
Since we
can simply use different eyepieces to reach different magnification, the
temptation is to "pumpup" the power as high as possible. In theory and
practice, a telescope with excellent optics is limited to a magnification of
about 2 times the aperture (diameter of main object) measured in millimeters.
Example: an 80mm refractor is limited to a maximum magnification of about 160x
(80 x 2 = 160). Multiply inches by 25.4 to convert to millimeters.
Focal Ratio of a Telescope
The
focal ratio of a telescope is mostly used when considering exposure time for
astrophotography, but it is also a general characteristic of the telescope that
can be useful in other discussions.
focal ratio = focal length of telescope / aperture of telescope
The result is written as f/focal ratio. Example: an 80mm telescope with an 800mm focal length has a focal ratio of f/10 (800 / 80 = 10  note that both measurements must use the same unit, in this case mm).
Exit Pupil
The exit
pupil of an instrument is the cylinder of light leaving the eyepiece. If the
exit pupil is larger than the diameter of the fully opened (darkadapted) pupil
of your eye, some of the light will be wasted. Younger eyes typically have a
maximum pupil of about 7mm; older eyes may be limited to 5 or 6mm. Various
focal lengths and magnifications result in differing exit pupils.
exit pupil for binoculars = aperture of binocular in mm / magnification of binocular
Example: 10x50 binoculars have an aperture of 50 (the second number) and a magnification of 10 (the first number). The exit pupil of these binoculars would be 5mm (50 / 10 = 5).
exit pupil for telescope = focal length of eyepiece / focal ratio of telescope
Actually just a mathematical rearrangement of the formula given for a pair of binoculars, but this formula turns out to be much easier to work with. Example: using a 25mm eyepiece in a telescope with a focal ratio of f/10 results in an exit pupil of 2.5mm (25 / 10 = 2.5).
True Field of View
The true
field of view (TFOV) of an instrument is a measurement of the actual field of
view seen through the eyepiece. For example, the field of view might show about
1 degree of the sky at a time. A wider field of view is desirable for extended
objects such as large nebula and open clusters. Calculation of the TFOV
requires the apparent field of view (AFOV) of the eyepiece in use. This is a
statistic available from the eyepiece manufacturer, but it is useful to note
that most Plossls have an AFOV of about 50 degrees.
TFOV = AFOV of eyepiece / magnification given by eyepiece
Example: a 10mm Plossl with an AFOV of 50 degrees is used in a telescope of 1000mm focal length. The magnification given by this eyepiece is 100x (1000 / 10) so the TFOV is a half degree (50 / 100 = 0.5).
Resolving Limit
The
resolving limit of an instrument is an expression of the smallest detail that
can be detected by the instrument. The unit of measure is arcseconds (1/3600th
of a degree) and a common test is detecting separation in the components in a
very close double star. There are two commonly used calculations:
Rayleigh Limit = 5.5 / aperture of telescope in inches
Dawes Limit = 4.56 / aperture of telescope in inches
Example: the Rayleigh Limit for a telescope with a 6 inch aperture is approximately 0.9 arcseconds (5.5 / 6 = 0.92). To convert an aperture given in millimeters (mm) to inches, simply divide the millimeters by 25.4; for example, an 80mm aperture is 3.15 inches.
Light Gathering Power
This is
not really an absolute measurement but rather just a method of comparing two
optical instruments. The larger the light gathering power, the fainter the
objects that can be detected (also expressed by the limiting magnitude formula
below).
ratio of light gathering power = square of aperture of larger instrument / square of aperture of smaller instrument
Example: an 8 inch telescope gathers 4 times more light than a 4 inch telescope (64 / 16 = 4  note that both measurements must use the same unit, in this case inches). Another example: an 80mm scope gathers about 130 times more light than the naked eye (the maximum aperture of the naked eye is about 7mm so 6400 / 49 = 130.6).
Limiting Magnitude of an Optical Instrument
This one
is a little complicated. Limiting magnitude is the magnitude of the faintest
object that an average person with fully darkadapted eyes will be able to
detect.
limiting magnitude = 5 x LOG_{10}(aperture of scope in cm) + 7.5
LOG_{10} is "log base 10" or the common logarithm. This formula would require a calculator or spreadsheet program to complete. Example: considering an 80mm telescope (8cm)  LOG(8) is about 1.9, so limiting magnitude of an 80mm telescope is 12 (5 x 1.9 + 7.5 = 12). Be certain you multiply 5 times the LOG value before you add 7.5).
Clear Skies!
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