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Telescopes: basic parameters

It happens quite often to ask if a specific telescope can “show” a certain object with given magnitude. For this reason, it is useful to keep in mind a few simple relations giving the basic properties of telescopes.In this post, I explain three parameters: Limiting magnitude, resolving power, and the magnification.

Limiting magnitude is the magnitude of the faintest object one can see through a telescope. The larger the telescope aperture, the larger the light gathering power (w.r.t. the human eye), and the larger the limiting magnitude. It is given by the following relation:

Limiting Magnitude = 2.7 + 5 Log(D)

where D is the diameter of the telescope objective (lens or mirror) in mm. To have a more realistic estimate, you may subtract 0.5 from the given values. This is due to dirty optics and old coatings. For many small telescopes, you can see the numerical result in the below table.

Another important property of any telescope is its resolving power. The Rayleigh limit tells us if two stars are apart by an angle α, we can resolve them marginally if it satisfies the following relation:

α [arc second] = 1.22 λ [m] / D [m] * 206265.

where λ is the wavelength of observation, e.g., take 500 nm, and D is again the diameter of the objective.  Note that due to atmospheric turbulence, the resolving power is bound by atmospheric seeing. When seeing is good, i.e., the atmosphere is stable and has not too much turbulence, the resolution can be as low as one arc seconds. However, a typical value of 2-3 arc seconds is normal for many observing sites. Actually, this is one of the key parameters when professional astronomers try to find a good site for a new telescope. The reason the Hubble space telescope with a 2.4 m mirror captures sharpest ever images, way sharper than, e.g., 10m Keck telescopes, is due to atmospheric turbulence. For small amateur telescopes, the seeing effect can be traced with the amount of wobbling a bright star or planet shows in the eyepiece.

Magnification is defined as the ratio between the apparent angular size of an object in the telescope (through the eyepiece) , and its real angular size on the sky. It is calculated from the ratio between the objective focal length and the eyepiece focal length. In my opinion, one of the least important parameters in a telescope is its magnification. I put a rather conservative low to normal magnification, I personally use in the last column. Larger magnifications can be reached by using eyepiece with smaller focal length. However, again due to seeing effects, there is a practical limit, regardless of the size of the telescope, which is about 500x. When we use large magnification for faint or diffuse objects, not only focusing gets very hard, but also the surface brightness falls down. Hence, a large magnification is only recommended for planets and multiple stars.

I plan to discuss optical aberrations  of telescopes in a separate post.

Total lunar eclipse of June 15, 2011

A great total lunar eclipse is coming !

While total eclipses of the sun are rare at any location on the Earth, eclipses of the Moon can be observed without the need to travel. A lunar eclipse is visible from the whole hemisphere of the Earth for which the Moon is above the horizon.

As seen in the Moon path below, it almost goes through the center of the Earth’s umbra. That means the Moon will be specially dark during the totality period. The brightness of lunar eclipses is often described in terms of the Danjon scale:

0: very dark eclipse. Moon defficult to see, appears steely dark.

1: dark. features like maria or craters are difficult to distinguish.

2: dark red eclipse.

3: eclipsed Moon quite bright, reddish. Maria easily visible.

4: very bright eclipse, with Moon appearing coppery red-orange.

The last total lunar eclipse I have observed falls in the category 3 or 4. I can remember its cooper red color. I hope the upcoming eclipse will be way darker.

In the eclipse of June 15, 2011, the Moon starts moving into the Earth’s penumbra at 17:25 UT while it enters the umbra at 18:23 UT.

The Moon will be in the shadow completely between 19:22 and 21:03 UT. At that time, it starts leaving the Earth’s umbra.

This eclipse will be observable from Africa, south/west Asia, as well as east Asia, and Europe. For western European observers, the eclipse starts while the Moon is rising. While observers from south America can watch part of the event, north America observers have no chance.

For more detailed information, you can check this file (the file is downloadable from Nasa/Eclipse webpage as well).

How to buy an auto in Germany?

1) Find an auto.  Depending on the amount of money you want to spend, you can buy guaranteed second hand autos from dealers. These are usually cars with an age less than five years and in good situations. They are significantly cheaper than the new ones but are not really cheap.

A second option is to search auto handlers, or Internet, like

http://suchen.mobile.de/fahrzeuge/auto/

or

http://autoscount24.de

or

http://auto.de

In a previous post, I have explained in detail what was my criteria.

2) Suppose you found the auto you like to buy. It is time to see the auto before any further step. Make an appointment with the dealer/owner and check the auto.  Needless to say, it is helpful to keep an experienced driver with you. Check all the aspects like engine, pollution (very important), body, etc. Ideally, go to a workshop and ask an expert mechanic to check the auto for you.
That costs, of course, but is way better than buying something which is not worth the price.

Nowadays, there are many cities which are called environmental zone (Umweltzone).  If you live in such an environmental zones, you must have a green pollution sticker (Schadstoffplakette). Also check the history of auto from repair papers. You are allowed to ask to see the auto papers (Fahrzeugschein, Fahrzeugbriefe) along with inspection results (Hauptuntersuchung). This is to proof of insurance and proof of ownership of the car (Kfz-Brief).  This way, you are sure that the information you have gathered about the auto is not fake.

2-1) Beside checking the auto itself, make sure that you see the original license and the  HU/AU papers before making any decision, or payment. What is written there is far more important than what is written in advertisement.

2-5) Is the price reasonable? There are books, tables, and internet pages you can check which auto, with what mileage, age, etc is worth how much. try this:

http://www.dat.de/

2-9) Tricks:  There is a level of cheating that always happens. For example, it is announced that the auto has a green environmental plaket and its pollution is in Euro 4 class. In reality, it is written in the TüV report that it is Euro 3 and green.That means you have to pay more tax than what you thought. Another example: It is said that this auto has Radio. Well, it has, but the antenna is broken ! So make sure you are very careful in the selection procedure.

While you are not satisfied with the auto/price, repeat the above two steps.

3) Write a contract. It must include names and addresses of both sides,  details of the auto, details of damages you observe like accidents, and the  amount and type of payment.

4) Pay the price and get all the original papers. In this step you have four papers: Fahrzeugschein, Fahrzeugbriefe, Hauptuntersuching (TÜV), and the payment bill itself.

5) Insurance. You could actually do this step before writing the contract. Having a copy of auto papers is enough along with your driving license. Depending on how long you had driving license, owned an auto without accident, and how far you can convince the insurance guy, it can be drastically different. If you are a beginner, by default it is 200% of the normal prince. And unfortunately depending on your nationality, it can increase up to many ten percents ! My bet suggestion is the following:

https://www.huk24.de/

6) Now you need the permission and auto-ID. Go to the city hall (Stadthaus), and ask for them. You have to keep all the above documents, you insurance, and the EC card of your bank account.

6-1) If you buy an auto from a different city, you perhaps do not want to go back and forth just to get the paper work and a Kennzeichen. The solution is a temporary Kennzeichen: it works only a few days, and includes also insurance, so you get it for like 85-120 Euro.

The kfz-Steuer (tax) depends on the age of auto, the engine capacity, and the pollution class. You pay that in cash right there. There are web pages where you can calculate it online like:

http://www.kfz-steuer.de/

Then, you will be asked about if you have special demand for the characters of your auto-ID. You get an auto-ID on a paper (permission). At the end of this process, which takes some 5 min, you have:

Fahrzeugschein and Fahrzeugbriefe in your name (congratulation !), and all other papers you had provided. In addition, you get the
pollution label for the front plate of your auto.

After that, you go to an Autoschilder and ask them to build the metal platers of the auto-ID. It takes like 1-2 min.
Finally, you need to attach two inspection and one pollution stickers on you auto ID. Go back to Stadthaus and do it.

Done.
You can attach the auto-ID to your auto and start to drive it. For me, it worked like this. If you know a better way, let me know.