I have been into astronomy for... well as long as I can remember really. I think it started when my Dad got me a CAD print out of the space shuttle Columbia, OV-102. This was about the time I was getting into radio as well, and as a 7 year old typed a letter out on a typewriter to NASA asking about their Deep Space Network system. I didn't get much info about the DSN, but I got a ton of images from from Hubble and other deep space probes they had sent out over the years.
Sadly I wasn't really able to do much in the field with it because of a lack of money and my poor understanding of optics at the time. So it just kind of sat in the background, coming out as more of a obsession with all things NASA, ESA, and AMSAT.
This all changed when recently a member of our pod gave me a pair of telescopes she no longer had need for. This got me going viewing celestial object directly again, and after a few viewings of Jupiter and its moons, Saturn and it's Rings, and trying to find Apollo landing sites on the moon I was hooked again!!!
On top of this my cash flow had been increasing due to some contract jobs I was doing and this gave me a chance to improve my equipment. But after looking at what is out there the question was raised, "what do I really need, and what do I really get for this stuff?" OFF TO RESEARCH!!!!
After my optical principle research frenzy I came back with some very good info! Which I was able to distill down into this GDoc Spreadsheet.
The Basics:
Now before you go and run off to look at the spreadsheet, I would like to explain a few things here, just to fill you in on the details.
The basic idea of an optical telescope is that it gathers light from distant sources use its Objective optical device, a parabolic mirror or convexed lense, and focuses that light on to a focal plane. This inverted image of the distance object is then magnified via the eyepiece and then sent to your eye. This basic system allows you see objects that are normally too dim for your eyes to see. Or for objects that you can see, it allows you to resolve more detail on those objects. Now there is a lot of math and such that can get involved here, but I want to start out with the practical details first, then we can get to the meat of it. ;)
Terms:
So lets getting a few terms down before we move forward:
Focal length: Distance between the Objective Optical device and the focal Plane, In millimeters.
Eyepiece Focal length: The distance between the focal plane and the the end element of the eyepiece, in millimeters.
Apparent View: How big the magnified chunk the sky looks to your, in degrees.
Actual view: The chunk of the sky that is being magnified. Most the time measured in Degrees.
Magnification: A relative number that tells you how much more you are seeing then your naked eyes.
Arcseconds: A polar measurement of an area of the sky. one arcsecond=1/3600th of a degree.
The Math:
Now, let dig into to this, first lets hit magnification. To get an idea of magnification we need to know how much you can see with your eye. Most humans have an effective view of view of 114 degrees, or about 410,400 arcseconds of the sky. Reference:Wikipedia:Field_of_view You can resolve down to about 60 arcseconds with your eye, or about 0.016 degrees.Reference: darkskydiary:arcminutes-and-arcseconds
Magnification:
So the idea here is that the telescope should be able to give use some degree more resoultion and hence a small field of view. The math for this is basic, it the focal length of the telescope over the focal eyepiece of the telescope. So you can say that magnification is inversely proportional to focal length of the eyepiece. So if your telescope has a focal length of 1100mm, and you are using a 15mm eyepiece. 1100/15=73.3 But this doesn't really give us much info, how much of the sky can you now see, what kind of resolution can you expect?
Field of View:
Lets now go through the math for figuring out the field of view now. Each eyepiece you buy for you telescope will have a spec called "apparent field of view". This is the field of view that it will magnify the chunk of the sky to so you can see. Because your field of view and resolution of vision is fixed. From this number and the magnification we can figure out the "actual field of view", which is size of the area of the sky you are actually looking at. So if we use our example above we should be able to figure out how much we can see with our 1100mm telescope and 15mm eyepiece. Now, lets assume our eyepiece has a 52 degree apparent field of view. We take this number and divide it by the magnification, in other words our actual field of view is inversely proportional to the magnification. (52/73.3=0.709 degrees) We can convert this into arcseconds to get 2,553.8.
Now, what does this number really mean?? Well we can compare this the apparent diameter of different celestial objects.
| Celestial body | Angular diameter | Relative size (10 pixels per arcsecond) |
|---|---|---|
| Sun | 31.6′ – 32.7′ | 28.7–29.7 times the maximum value for Venus (orange bar below) / 1896–1962″ |
| Moon | 29.3′ – 34.1′ | 26.6–31.0 times the maximum value for Venus (orange bar below) / 1758–2046″ |
| Venus | 9.565″ – 66.012″ | |
| Jupiter | 29.800″ – 50.115″ | |
| Saturn | 14.991″ – 20.790″ | |
| Mars | 3.492″ – 25.113″ | |
| Mercury | 4.535″ – 13.019″ | |
| Uranus | 3.340″ – 4.084″ | |
| Neptune | 2.179″ – 2.373″ | |
| Ceres | 0.330″ – 0.840″ | |
| Vesta | 0.20" – 0.64" | |
| Pluto | 0.063″ – 0.115″ | |
| R Doradus | 0.052″ – 0.062″ | |
| Betelgeuse | 0.049″ – 0.060″ | |
| Eris | 0.034" – 0.089″ | |
| Alphard | 0.00909″ | |
| Alpha Centauri A | 0.007″ | |
| Canopus | 0.006″ | |
| Sirius | 0.005936″ | |
| Altair | 0.003″ | |
| Deneb | 0.002″ | |
| Proxima Centauri | 0.001″ |
Source: Wikipedia:Angular_diameter
So if we compare this to the sun, with an angular diameter of 32.7 arcminutes, or 1,962 arcseconds, we can see our view with this setup will be 1.3 times greater in size. Or to put it a different way, if you centered the sun(while using a sun filter on your telescope, not doing that could damage your eyes) in your telescopes view with the 15mm eyepiece there would be 295.9 arcsecond on each side of the your view. So the sun would fill up a little over half your view.
Now if you tied to look at Pluto, with an apparent diameter of only 0.115 arcseconds you would have a hard time see it as it would only be .004% of your view. That is far below the resolution of the human eye and you would need a shorter focal length eyepiece for that.
How to pick the right eyepiece for the job.
So now that we have some of our basic math down, how do you know which eyepiece to use? We that depends on what you are doing. Using the chart from above you can figure out the size of the object you want to view. If the object is not on the list there are many sites out there that can help you figure out what it's angular diameter is. Once you figure that out, go to the spreadsheet, Telescope/Eyepiece combo info, and fill in the info for the eyepieces you have and your telescope. BINGO, you have the area each of your eyepieces can see! But what if it's not enough? There is a device for that!
The Barlow.
A Barlow is a device that multiples the magnification of you eyepiece. Your place the device in between your eyepiece and your telescope. So if you put it between the 1100mm telescope and our 15mm eyepiece it would be the same as using a 7.5mm eyepiece. Now on the spreadsheet, Telescope/Eyepiece combo info, I have a second sheet that includes a column for a Barlow. Now the effect on the actual view is not proportional to the barlow, so second sheet will help you figure out how much area you can see by putting the Barlow in.
Conclusion.
I hope this post has helped fill in some of the gaps about the practical details of what you need to get a good view of the sky. I also hope the spreadsheet will help speed things up. Now I have filled it in with examples, just replace those with your values.
If you have any questions or comments please leave them below.
I also want to thank Jay Reynolds Freeman for his page http://old.observers.org/beginner/eyepieces.freeman.html
It was the main inspiration for this post and the source of the math in the spreadsheet and this post. He has a lot of good practical info on the page, you should really check it out.
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