ASTRONOMICAL FORMULAE
where d is the aperture of the objective where M is the magnification
At prime focus (ground glass), magnification is
1x for
where M is the magnification The scotopic (dark-adapted) aperture of the human
pupil is
(by substituting F/f for M) By substituting d=7 (the scotopic aperture of the
human pupil)
(by substituting 6 mm for d and taking the reciprocal)
(by substituting 0.63 mm, the minimum diameter to
which the where M is the maximum theoretical magnification
(158x per mm
where m is the approximate limiting visual magnitude
where the larger the relative brightness value,
the better
(the second formula is based on Lambda = 0.00055
for yellow)
where r is the linear radius (one-half the linear
diameter)
where Theta is the smallest resolvable angle in
" Atmospheric conditions seldom permit Theta < 0.5".
The Dawes
where M is the magnification required About the closest star separation that the eye can
distinguish
where Resolution is the smallest resolvable lunar
feature in km
where Light Grasp is times that received by the
retina To compare the relative light grasp of two main lenses
used at the
where f/ is the f-number of the system (objective)
where f/ is the f-number of the system The diameter of the first image equals the film
diagonal
where f/ is the f-number of the system
where f/ is the f-number of the system
(the ratio of intensities of illumination is squared where Exposure Compensation is the exposure compensation
where Exposure Compensation is the exposure compensation
(the light-recording power is directly proportional
to the where Power is the light-recording power of the
system Example: a 200-mm f/8 system compared with a 100-mm
f/5 system
where Efficiency is the efficiency of the lens for
where Print EFL is the print's effective focal length
where Guidescope M is the magnification needed Experience indicates that the minimum guiding magnification
needed Guidescope M = Guidescope EFL / Print EFL where Guidescope M is the guidescope's magnification
(should be >=
where Guiding Tolerance is in mm
where S is the error ("slop") in " The slop is derived from the formula Theta = k*(h/F),
where EFL is the effective focal length in mm
where Resolving Power is the resolving power of a
photographic
where Maximum Resolution is the resolution for a
perfect lens Most films, even fast ones, resolve only 60 lines/mm;
the human
where Minimum Resolution is the min resolution necessary
where h is the linear height in mm of the image at
prime focus The first formula yields image size of the sun and
moon as The second formula can be used to find the angle
of view (Theta) The third formula can be used to find the effective
focal length
where Length is the length in mm of the star trail
on film
where T is the exposure time in minutes for a length
of 24 mm
where T is the maximum exposure time in seconds without
a star F is the focal length of the lens in mm The earth rotates 5' in 20 s, which yields a barely
detectable N.B. The above formulae assume a declination of 0o.
For other
where i is the linear image size in mm of the image
at prime focus h is the linear height of the object in units corresponding to D D is the distance of the object in units corresponding to h F is the effective focal length (focal length times
Barlow The last formula gives the focal length necessary
to photograph a
where e is the exposure duration in seconds for an
image size of f is the f-number (f/) of the lens S is the film's ISO speed B is the brightness factor of the object (Venus 1000,
Moon 125, Thus, a 2-minute exposure at f/1.4 is equivalent
to a 32-minute
where B is the surface brightness of the (round) extended object M is the magnitude of the object (total brightness
of the object), D is the angular diameter of the object in seconds
of arc (D^2 is
where e is the exposure duration in seconds
where H is the hour angle The Hour Angle is negative east of and positive west
of the
where n is the serial order of the planets from the
sun (Mercury's
where Theta is the object's apparent angular size
in units h is the linear height of the object in units corresponding to D D is the distance of the object in units corresponding to h Theta is the object's angular height (angle of view)
in units k is a constant with a value of 57.3 for Theta in
degrees, 3438 in A degree is the apparent size of an object whose
distance is 57.3 Under ideal conditions, the human eye can resolve
anything
where h is the linear height of the meteor in km
where cos(Latitude)=1 on lines of constant longitude
Penny, 4 km distant .......................................
1"
Big Dipper, from cup to handle Little Dipper, from cup to handle
D = diameter of aperture in mm Minimum useful magnification ....................
0.13*D 0.2*D for better contrast |