Titan

I am seeing a_very_small disk for Titan tonight just as I did a few nights
back. Using my 12.5 inch newtonian at 400x seems to bring out a somewhat
brownish tint to the moon.

Martin

"Martin R. Howell" wrote in message hlink.net...
I am seeing a_very_small disk for Titan tonight just as I did a few nights
back. Using my 12.5 inch newtonian at 400x seems to bring out a somewhat
brownish tint to the moon.

Martin

In the past few weeks with the optimum placement of both jupiter and
Saturn for viewing, the question has come up a few time about which
moons can be seen and with what scopes and further what does it take
to resolve the moons. I put this together from a series of replies I
gave to those questions on the CN planetary forum and the Amart Equip
forum. There are further discussions on the CN planetary forum
related to Transit Shadows and Seeing Encke. edz

Disk vs. Airy Disk

How can I tell if I'm seeing moons resolved as a disk?
A perfect way to observe the difference would be when the extended
object is in the field of view of a star. Focus precisely and then
compare the difference between the disk and the star.

Assuming for the moment that this star would be moderately bright,
let's say for example 5th mag, then the star will provide you with the
near perfect size Airy disk. The central bright spot in the middle of
the Airy disk will be nearly equal to the Rayleigh limit calculation
for your scope. The size of that spot does vary slightly with the
magnitude of stars, so although the Airy disk is always the same size
in the scope, the central bright spot varies with magnitude.

All stars produce the same size Airy disk in your scope. Only the
central bright visible spot within the Airy disk varies slightly.
However, extended objects have an infinite number of points that give
off light. So all the edges around a moon disk produce an Airy disk in
your scope. The image formed from a moon disk is the result of a
circle of an infinite number of Airy disks.

Continue with the assumption that you can see a moderately bright star
near the moon disk. For a moon disk, the image in the scope will be
larger than the Airy disk of a star. The scope will show the moon disk
fattened up by producing the Airy disks all around the edges. The
image size is slightly smaller than the sum of the Rayleigh Limit plus
the object diameter. A little further on we'll discuss specifically
how big the image is.


Seeing Saturn's Moons

At close approach Saturn is just over 8 AU from Earth. Currently it is
9+ AU from Earth. These calcs are based on 9AU

Titan is 5150km (3193 miles) mag 8.4, 0.78 arcsec diameter
Rhea is 1528km (947 miles) mag 9.7, 0.23 arcsec
Iapetus is 1436km (890 miles) mag 8.6 to 11.5, 0.22 arcsec
Dione is 1120km (694 miles) mag 10.4, 0.17 arcsec
Tethys is 1046km (650 miles) mag 10.3, 0.16 arcsec
Enceladus is 512km (317 miles) mag 11.8
Mimas is 421km (255 miles) mag 12.9
Hyperion is 360km (223 miles) mag 14.2

You can see here most of the angular dimensions are very tiny. For any
scope up to 20" aperture every moon except Titan shows up almost as a
point source.

Titan is just barely resolvable to a disk with an 8" under the best
possible conditions. The image disk will be larger than an Airy disk,
making the need for magnification a little less than if it were a
point source, but the faint magnitude will require additional
magnification to see Titan resolved. I believe magnification on the
order of 275x would be required to see Titan as a disk in an 8". It is
not resolved with anything smaller. Under good conditions it could
probably be resolved at 250x with a 10".

I have seen four moons with my G5 125mm SCT. I have seen 5 with my
CR150. The 5th was Enceladus. I have never seen Iapetus or Mimas.
Hyperion is beyond my scope capabilities.

Seeing Jupiter's Moons as Disks

Jupiter is 88,700miles in diameter. At 5AU it's disk would appear
39.3 arcsec.
The sizes (at 5AU) and the magnitudes of Jupiter's moons a
Ganymede 3,270 = 1.45 arcsec, mag 4.6
Callisto 2,980 = 1.32 arcsec, mag 5.6
Io 2,260 = 1.00 arcsec, mag 5.0
Europa 1,940 = 0.86 arcsec, mag 5.3

Ganymede, at 3,270 miles in diameter, at a distance of 5 A.U., would
appear 1.45 arcseconds across. This will vary slightly as Jupiter gets
closer or further away from Earth. Jupiter varies from about 4.25AU
to about 6AU.

Dawes Limit is an inappropriate criterion to measure whether an object
will appear larger or smaller than the Airy disk produced by the
scope. Dawes Limit is simply an empirical measure at which two
components of a double star can be noticed as double because a notch
identifies them. Dawes is not equivalent to Airy disk size. The
correct measure for the radius of the Airy disk for your scope is
Rayleigh Criterion, 5.45/Dinches or 138/Dmm.

Rayleigh Criteria gives the radius of the Airy disk. The central
bright spot, or the visible disk portion of the Airy disk, for a
moderately bright star (assumed 5th-6th mag) is approximately one half
the Airy disk diameter. The Airy disk radius for a 80mm scope is
138/80 = 1.72 arcseconds. The Airy disk for ALL 80mm scopes is 1.72
radius, therefore diameter = 1.72 x 2 = 3.44 arcseconds.

If the light is only moderately bright, such as from a 5th - 6th
magnitude star, then the central bright spot, or the visible disk
within the Airy disk, is about one half of the full diameter of the
Airy disk. Therefore, in a 80mm scope, the diameter of the central
bright disk for a moderately bright star would be 1.72 arcseconds,
equal to the Rayleigh Limit.

If the object is brighter, say 4th or 3rd magnitude, there is more
light in the visible central disk, maybe on the order of 60% to 75% of
all the light, up to a maximum of 84% for the brightest stars.
Therefore the central bright disk may be on the order of 60% to 75% of
the diameter of the Airy disk for fairly bright objects. It may be
less than 50% of the diameter of the Airy disk for a faint star. How
much of the light falls into the central disk and how much is thrown
into the diffraction rings is dependant on the magnitude.

For an object to be resolved, the angular dimension of the object must
be larger than the angular dimension of the Airy disk. Otherwise the
scope will simply fatten up the image and make it appear larger than
it truly is. The special condition of a disk as an extended object
slightly changes the size of the "unresolved" image.

Ganymede's moon disk is 1.45 arcsec across. It is smaller than the
1.72 arcsec Airy disk, the resolution limit of the 80mm scope, so it
will not be resolved. But it will form an image in the scope larger
than the Airy disk. Only a point source will produce an image the size
of the Airy disk. A moon disk is an extended object. All points on
the 1.45 arcsec moon disk may be considered point sources. Each point
source gives off light that forms an Airy disk.

The image in the scope of a true Airy disk, from a star too far away
to have any perceptible dimension, is the Airy disk. The airy disk has
dimension. Ganymede, a moon disk, has an infinite number of Airy
disks that can be considered to emanate from everywhere on the 1.45
arcsec moon disk, including centered on all the edges. If the light
from each point is equal and near 5th magnitude, then each point
produces an Airy disk with a bright central visible disk 1.72 arcsec
diameter. With the center of a visible diffraction disk on the very
edge of the moon's disk, half of each visible diffraction disk extends
beyond the moon disk. Therefore, at first pass, Ganymede will produce
an image in the scope equal to the width of Ganymede's disk plus
Rayleigh Limit (the Airy disk).

Rather than an Airy disk of 1.72 arcsec, Ganymede will produce an
apparent image disk of 1.45 + 1.72 or 3.17 arcseconds. This object
itself, the disk of Ganymede, is too small for the resolution of the
80mm scope and still is not resolved. But the image due to the special
condition of the extended object is wider than an Airy disk. But the
size of this image will be further qualified by integrated magnitudes.

Two stars very close together will have an integrated magnitude
brighter than each of the individual stars. It is reasonable to
assume that the integrated light of the moon disk is made up of an
infinite number of points, each having less light than the full
integrated magnitude of the moon disk itself. The visible spot
portion of the Airy disks, including those formed at the edges of the
moon disk, if truly formed by fainter light, may be somewhat smaller
than predicted above. Since it is difficult to know exactly what the
brightness of components of the integrated magnitude really are, how
small is difficult to determine, but it is reasonable to assume the
overall dimension of the image disk is smaller than 1.45 + 1.72
arcsec, maybe smaller by only 10% to 20% of the Airy disk radius.

A reasonable assumption is for a faint component, 40% of the energy
resides in the central bright spot. For a scope with a Rayleigh Limit
of 1.72 arcsec, 40% of the energy in the central disk would result in
a central bright spot with a diameter of 1.38 arcsec. It is
reasonable to assume the Airy disks formed by an infinite number of
points are all somewhat smaller and fainter than would be the Airy
disk for the integrated magnitude of all the points. In fact the
light overhanging the edges may be even smaller and fainter than the
40% energy value I claculate here. This would result in an image 1.45
+ 1.38 = 2.83 arcsec wide in an 80mm scope.

Said a different way, for any scope to be able to resolve an extended
object, the scope must have a resolution smaller than the object.
Otherwise, the scope will simply show the object fattened up by
producing the Airy disks all around the edges. The image size is
slightly smaller than the sum of the Rayleigh Limit plus the object
diameter.

None of Jupiter's moons can be resolved with a 80mm scope. Ganymede,
and possibly Callisto, but no others, may be resolved with a 100mm
scope.


Jupiter's moons in a 6" scope

An f8 150mm refractor has a Rayleigh Limit of 5.45/6 or 138/150 = 0.92
arcseconds. It is capable of resolving moderately bright doubles as
close as 0.9 arcsec. I have confirmed that it is capable of doing so.
With my CR150 I have "cleanly split" 4 different doubles, all with
components between mag5 and 6, three at 0.9 and one at 0.8 arcsec. One
was seen at 300x split, one at 370x and two required 480x to see a
clean split between the two components. I have detected a 0.7 arcsec
double, but not seen a split in anything below 0.8.

The sizes (at 5AU) and the magnitudes of Jupiter's moons a
Ganymede 3,270 = 1.45 arcsec, mag 4.6
Callisto 2,980 = 1.32 arcsec, mag 5.6
Io 2,260 = 1.00 arcsec, mag 5.0
Europa 1,940 = 0.86 arcsec, mag 5.3

The magnitudes are very well placed for assuming none are too bright
or too faint to fit the normal (Rayleigh Limit) amount of light in the
central visible bright spot of the Airy disk. Ganymede may be just a
bit bright, and this might just enlarger the central spot a little.

Ganymede at 3,270 miles in diameter, at a distance of 5 A.U. would
appear 1.45" arcseconds across. 3270/5AU = y/x = tangent theta =
0.0004029 degrees = 1.45"
Jupiter can range from less than 4.5AU to just over 6AU from Earth.
These calculations are based on a distance of 5AU from Earth.

Even though I have acuity of 150 arcsec, I find I need a much larger
apparent size to see objects near the resolution limit. It has been
well documented that as doubles approach the Rayleigh Limit, it
becomes more difficult to see them. Take note of the magnifications it
took to see doubles of 0.9 and 0.8. In all but one, It took 370x to
480x. It took 480 x 0.8 = 384 apparent arcsec size to see a 0.8 arcsec
double. It took 370 x 0.9 = 333 apparent arcsec to see a 0.9 arcsec
double. As a comparison, it takes only about 130x to 150x to see
doubles of about 2 arcsec (260-300 arcsec) and only 75x to 100x to see
doubles near 2.5 arcsec (187-250 arcsec).

The images of the moons in the scope are all wider than the moon
disks. Since the edges of the moon disk give off light and create
Airy disks in the scope image, the dimension of the image is nearly
the width of the moon disk plus the Airy disk (half airy disk
overhanging the edges). Because the images are larger than an Airy
disk, they will be easier to see.

Based on that, I estimate magnifications to see these as disks in the
6" f8 refractor.
200x to see Europa 0.86 arcsec, image disk about 1.6
190x to see Io 1.0 arcsec, image disk about 1.7
150x to see Callisto 1.32 arcsec, image disk about 2.1 and
140x to see Ganymede 1.45 arcsec image disk about 2.2.

edz

"edz" wrote:

Titan is just barely resolvable to a disk with an 8" under the best
possible conditions. The image disk will be larger than an Airy disk,
making the need for magnification a little less than if it were a
point source, but the faint magnitude will require additional
magnification to see Titan resolved. I believe magnification on the
order of 275x would be required to see Titan as a disk in an 8". It is
not resolved with anything smaller. Under good conditions it could
probably be resolved at 250x with a 10".


Thanks for the incredibly thorough response from which I extracted the above
snip. It was very informative and should give others the impetus to try for
Titan's disk when they might otherwise not have.

I would be interested in the color others may perceive Titan to be and the
size of scope used to tease that color out of the planet's disk. While it
is inclined towards to a brownish hue to my eyes, some state it to appear
orange.

For more on the color of the 3,000 mile plus diameter moon (second biggest
in the solar system), go to:
http://www.eoascientific.com/prototy...rn/saturn15.ht
ml

This site labels Titan orange while showing a photo in which, at least to my
eyes, it appears more brown.


Respectfully,


Martin R. Howell