more about Mars magnification

In article , Mick wrote:
At present Mars should be over 1/2 degree at 100 X's, which is a full moon
disc. At 200 X's, Mars should appear
as the moon would at 100 X's. This just doesnt happen because the moon
takes up the whole field in the EP at 100X's

So there is some optical trick occuring that eludes me...

For Mars to have the same apparent size in the eyepiece at 200x that the
Moon has at 100x it would have to be 900 arc seconds wide instead of
20 arc seconds wide.

"Mick" wrote in message ...
At 200 X's, Mars should appear as the moon would at 100 X's.
This just doesnt happen . . .
So there is some optical trick occuring that eludes me...

No optical trick - let's review the math:

The naked-eye angular diameter of the Moon at its mean distance is
1865 arcseconds, or ~31.1 arcminutes.

Magnification = apparent field / true field M = AF_deg / TF_deg

See http://www.twcac.org/Tutorials/apare...true_field.htm for a
diagram of the apparent and true fields.

For photographs illustrating the apparent and true fields, see the
bottom of web page:

http://www.astro.com.sg/chpt3.htm Apparent field is on the left;
true field on the right.

If the Moon just fills the eyepiece at 100x, it sounds like you are
using Possel eyepiece that has a 52 degree apparent field of view:

M = AF_deg / TF_deg
~100x = 52 deg / 31.1 arcminutes
= 3120 arcminutes / 31.1 arcminutes
= 187200 arcseconds / 1866 arcseconds
= ~100x

At its closest distance to Earth, Mars will have a naked-eye extended
apparent angular size of 25.1 arcseconds, or ~0.42 arcminutes.

At what power will Mars fill your Possel eyepiece with a 52 degree
apparent field of view?

M = 52 degs / 25.1 arcseconds
= 187200 arcseconds / 25.1 arcseconds
= 7458 power

This is considerably higher than observing Mars at 200x, as you have
been experimenting with.

It is probably impractical to try to construct equal sized images of
the Moon and Mars in the apparent field of your eyepiece.

Take a 36x eyepiece to look at the Moon - probably one of the lowest
powers in your eyepiece rack. In the eyepiece, the Moon would then
have a apparent angular size in your 52 degree apparent field-of-view
eyepiece of:

M = AF_deg / TF_deg
36 = AF / 31.1 arcminutes rearranging -
AF = TF x M
= 31.1 arcminutes x 20
AF = ~1120 arcminutes
= ~18.6 degrees

= 18.6 deg / 52 deg
= ~36% of the FOV

This means that the Moon takes up 18.6 degrees of your 52 degree
Possel eyepiece's apparent field of view or about 36% of the eyepiece
field of view.

With Matt Wier's online telescope simulator you can simulate how the
Moon would appear:

http://www.stic.net/mattwier/

In the online simulator, move the Eyepiece Focal Length bar in the
simulator to its maxmimum (55mm). This will simulate the view of the
Moon at 36x. The default apparent field of view in the simulator is 50
degrees. Move the FOV slider bar 52 degrees.

To view an equal-sized Mars in the eyepiece - that is to have the same
apparent field size (18.6 degrees or 36% of the FOV) in the 52 degree
apparent field of your Possel eyepiece - what magnification would you
use?

M = AF_deg / TF_deg
M = 18.6 degrees / 25.1 arcseconds
= 66960 arcseconds / 25.1 arcseconds
= 2667 power

This 2667 power probably exceeds the highest power eyepiece in your
rack by 4 to 10 times.

The online telescope simulator also contains the Object Data "Mars" to
simulate viewing the red planet. (But it cannot be made to simulate
2667 power easily, if at all! - ) Set the simulator to "Mars." Set
the magnification to 200x by moving the Eyepiece focal length to 20mm.

Viewing Mars at 200x using the 52 degree Possel apparent field of view
eyepiece gives:

M = AF_deg / TF_deg
200 = AF / 25.1 arcseconds rearranging -
AF = TF x M
= 25.1 arcseconds x 200
AF = 5020 arcseconds
= ~1.4 degrees
= 1.4 deg / 52 deg
= 2.7% of apparent FOV

This is about what is seen of Mars in the simulated (and your real)
eyepiece - a small distinct red disk with no detail.

You need about 800x to get a reasonably sized image in the Possel's 52
degree apparent field of view:

M = AF_deg / TF_deg
800 = AF / 25.1 arcseconds rearranging -
AF = TF x M
= 25.1 arcseconds x 800
AF = 20080 arcseconds
= ~5.6 degrees
= 5.6 deg / 52 deg
= ~11% of apparent FOV

At 800x and 11% apparent FOV, you get a blurry disk with detail
begining to resolve.

To set the online telescope simulator to 800x, hit the 2x Barlow
button. Then move the Eyepiece focal length slider to the left until
the magnification field reads about 800x (at about 5mm). You may have
to brighten the image up a bit by increasing the simulated telescope's
aperture size.

In another thread, message
... Peter Lawerence
has posted a number of pictures of Mars that his web site states were
taken using a Vixen FL-102 f9 refractor, a 20mm eyepiece lens, and a
2x Barlow - all coupled to a digital camera set at a zoom of 10x.

See his web site at http://www.pbl33.co.uk/

All put together, this gave Peter about ~920x:

fl_obj = 102mm x 9f = 918mm
M = fl_obj / fl_eyepiece
M = 918 mm / 20 mm = ~46x then add in the Barlow:
2M = 46 x 2 = 92 then the zoom camera
10(2)M = 10 x 2 x 46 = 920 power

You can use the simulator at http://www.stic.net/mattwier/ to emulate
920x. (Use the 2x Barlow button. In the Eyepiece focal length box,
type in 4.35mm. Brighten the image by increasing the aperture.) The
resolution of Mars in the online simulator resembles what Peter was
able to accomplish (with additional brightness being added by image
stacking instead of a larger aperture).

But I always get more of charge out of light coming from the real
thing than light received by "internet astronomy." -

Hope the above helps in better understanding how light moves through a
telescope. I know its confusing. Just stick with it.

Regards - Kurt

Some web sites for studying field of view:

http://www.twcac.org/Tutorials/apare...true_field.htm
http://www.spacegazer.com/basics.htm#field
http://www.astro.com.sg/chpt3.htm
http://www.stic.net/mattwier/

"PrisNo6" wrote in message
om...
"Mick" wrote in message
...
At 200 X's, Mars should appear as the moon would at 100 X's.
This just doesnt happen . . .
So there is some optical trick occuring that eludes me...

No optical trick - let's review the math:

The naked-eye angular diameter of the Moon at its mean distance is
1865 arcseconds, or ~31.1 arcminutes.



Oh..I do like the simulator however...

"Mick" wrote in message ...
At 200 X's, Mars should appear as the moon would at 100 X's.
This just doesnt happen . . .
So there is some optical trick occuring that eludes me...

Well, if at 200 X's, Mars really would appear as the moon would at
100 X's, then Mars would, from the Earth, appear half as large
as the Moon. And this would imply several things:

1. To the naked eye, Mars would appear as a disk and those with
a sharp vision would even be able to distinguish some of Mars'
largest surface features -- without a telescope!

2. Mars real diameter would be at least some 160 times the Moon's
diameter -- that's some 40 times the Earth's diameter, or some
4 times larger than Jupiter !!!!

These things too does not happen.

Thus, at 200X, Mars will appear much smaller than the Moon does at 100X.

--
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