Size matters, but how?

Hello again! Talking about telescopes, is size important? Well, as always, it depends on what you want to do: Planetary or Deep Sky Objects (DSO)

Some maths!

This, like many other things, can be solved using maths. So let's define a couple of formulas

Maximum magnifications:
As the name says, it is the maximum magnifications you can reach with your telescope. For this we need to know the aperture of the telescope:

maximum_mag = 2 * telescope_aperture 

maximum_mag_newtonian = 1.8 * telescope_aperture

I do the distinction between Newtonian telescopes and others because on Newtonians the factor is more close to 1.8 to 2.

Magnification with eyepiece/sensor:
Different eyepieces/sensors give us different magnifications. For calculating these magnifications we just need to know the focal length of the telescope and, for eyepieces, the focal length of the eyepiece; for sensors, we need to know the length of the diagonal:

magnifications_eyepiece = telescope_focal_length / eyepiece_focal_length

magnifications_sensor = telescope_focal_length / sensor_diagonal_length

Speed of light capturing:
A telescope which "captures" light fast is considered a fast telescope.  This "speed" of capture is expressed as the f-ratio or f-number (f/). The lowest the f-ratio is, the faster the telescope is. To calculate this number we only need to know the focal length and the aperture of the telescope:

f = focal_length / aperture

Some of the formulas I wrote are not physically exact and correct, but they give us very approximated values!

Okay! Now let's talk about what we want to see!

Planets

Okay, as I mentioned in this other post, if we want to see planets, we need to reach at least 180x magnifications, which are the needed magnifications to see details on planets. Well, using the functions above we need nothing more!
  1. We have a lower limit of magnifications, less than 180x won't work so, at least, we need a telescope with 90mm of aperture:
    maximum_mag = 2 * telescope_aperture
    180 = 2 * telescope_aperture
    180 / 2 = telescope_aperture
    90 = telescope_aperture

  2. Considering the classical 6mm eyepiece, which comes with almost all beginner telescopes, we need to find a focal length for getting a 180x magnification at least:

    magnifications_eyepiece = telescope_focal_length / eyepiece_focal_length
    180 = telescope_focal_length / 6
     180 * 6 = telescope_focal_length
    1080 = telescope_focal_length

  3. And that's all! We know that a good planetary telescope to see planets with a minimum eyepiece of 6mm (which is also the size of the diagonal of some planetary sensors), you need a telescope 90/1080 at least.
But, do I really need a 1080mm, well, that's not really necessary, luckily we have Barlow lenses.

A Barlow lens is a lens you put between the telescope and the eyepiece that duplicates the focal length of your telescope.

Skywatcher x2 Barlow Lens

This means that using a 90/540 telescope with a Barlow x2 will be like using a 90/1080 telescope! But this has its cons, like everything.


Using the same example as above, a 90/540 telescope is a f/6 telescope. Using a Barlow it will become a f/12 telescope. An x2 Barlow not only multiplies the focal length 2 times, but it also reduces the speed of your telescope at half of its normal speed.

For planetary, f-number is not so relevant as in DSO since planets and Sun are really bright in the sky. But that's something to take into account.

Okay! Now we know the minimum telescope we need to see planets and their details, but, is this good enough? Well, we said it is the minimum telescope, but not best. As I said in my previous post, to see planets we want big apertures to capture more details, and we want a long focal length to reach bigger magnifications easier.


So let's consider a 127/1500, this telescope has a 254x magnifications, so it is good for planets. Using the same eyepiece as in the last case, a 6mm, we will have 250x magnifications! This is more than enough, this is perfect! More than this would head us to a non-nitid image, eg: Using the 127/1500 with an x2 Barlow and a 6mm eyepiece will give us 500x magnifications, far above the 250x limit.


Good! We the specifications for a telescope for seeing planets, now, a 1080mm reflector/refractor is a huge and unmanageable telescope, it will work well if you are going to use it always at the same place, but what if you need to move? For these cases, there are very good models of models Maksutov-Cassegrain and Schmidt-Cassegrain, which will give us really long focal lengths and apertures in a compact space.

Skywatcher Maksutov-Cassegrain Mak 127

 The 127/1500 telescope I used as an example is a Maksutov-Cassegrain from Skywatcher, the Mak 127.

Now we know enough about telescopes to see planets but... Howe planets would see using these Telescopes? Luckily we have an excellent software to check this, it is called Stellarium and it's free!

To see how these telescopes work I will use Saturn at its opposition in 2020. I will emulate the 90/540, the 90/1080 and the 127/1500 using a 6mm eyepiece.

Telescope 90/540 - No Barlow

Well... Barely a bright point. If you see well you could badly see the ring. As you can see... below the numbers we calculated, planets are not a big thing. But what if I use a Barlow?


Telescope 90/540 - x2 Barlow

This is another thing! As we calculated before, we need at least a 1080mm focal length telescope to see details. Using an x2 Barlow with the 90/540 will give us that focal length. AS you can see, now the rings are more detailed and nitid.

Telescope 90/1080 - No Barlow

Well, using a 90/1080 is the same as using the 90/540 with an x2 Barlow (The slightly different os size it's because of the way I trimmed the image). In this case, it has no sense to try the 90/1080 with an x2 Barlow because we will be exceeding the maximum magnifications limit for this Telescope and eyepiece. But let's move to serious business!

Telescope 127/1500 - No Barlow

You might feel disappointed with this, but look better, in this case, you can see very well the rings, the division of Cassini and the storms on the planet, and that's impressive! Of course, there are other telescopes that will work very well for planets such as the Celestron SCT 8", with which we would see this:

Celestron SCT 8" - 203.2/2032

Quite impressive, right?

But what if I'm using a camera? As I said before, the formula for the eyepiece works also for the sensor if you change the focal length of the eyepiece by the length of the sensor's diagonal. Suppose we are using the 127/1500 telescope with a ZWO ASI 224MC, which has a diagonal size of 6mm, using this webpage we can emulate the magnification and overlap it with the field of view (FOV) of the sensor, and it looks like this:

FOV overlapped with Eyepiece

Of course, the FOV of the camera has a square shape, but the magnifications are the same.

So, retaking our original, bigger telescopes are better for planets? The answer is yes

Deep Sky Objects

Okay, for planetary bigger is better, is the same for DSO? Well, despite DSO are faint in the sky, many of them are tremendous huge! Let's take the famous Heart Nebula and the Moon as examples:
Moon has an apparent diameter of 31 arc-minutes when is full; Heart nebula has an apparent size of 150 arc-minutes, almost 5 times bigger than the full moon! When we say "apparent size" doesn't mean the real size of the object, it means how big we see it from the earth. A man at 2km away has an apparent size of a couple of millimeters, but it doesn't mean the man is a couple of millimeters tall on real.

And you could think "Why if the Heart nebula is bigger than the full moon I cannot see it at the naked eye?". Well, the answer is simple, because human eyes are not sensitive enough! For this reason, in this section, I'll use sensors instead of eyepieces because, since you can practice visual DSO, most of the time you will use a camera to see something more than a "cotton-like" object in the sky.

So, as I said, many of the most famous DSO are huge compared to the small planets. I'm going to use some of the previous telescopes combined with a Canon EOS 1000d sensor to compare how objects would see. Let's go!

Let's start with our amazing 90/540 telescope with the EOS 1000d sensor, which has around 27mm of diagonal. This will give us ~20x magnifications, and this is how Andromeda Galaxy (m31) would look like

90/540 with Canon EOS 1000d

Not bad at all!! The whole Galaxy would fit into our sensor (red square). Also, a 90/540 is an f/6 telescope, which means it is fast enough for DSO!

The next telescope is the 90/1080. It would be a waste of time to consider this one since it is an f/12 telescope, it is really slow so it won't work for DSO. The same happens with the 127/1500. But what if I have a 180/1080 telescope? it is another f/6! Let's check...

180/1080 with Canon EOS 1000d

Do you see it? With a bigger telescope, we will have better details of the core/center of the Object, but it won't fit in our sensor.

Of course, for small objects, we might want to use a bigger telescope, but at the beginning, we will want to focus on big and "easy" objects.

So, for DSO, size matters too but, contrary to Planetary, bigger doesn't mean better.

Conclusion

Everything depends on what you want to see/capture. For planets, bigger telescopes work better. For DSO it really depends on the target you have in mind. Since this is a beginner post, I would recommend a "small" telescope for DSO so it can be used with the most common and bigger targets, such as Andromeda, Orion's Nebula, Heart Nebula, etc. Also, a small telescope is more manageable and would make learning easier.

Personally, I've found the Newtonian 150/750 very polyvalent. With an x2 Barlow will have a 1500mm focal length, which makes it pretty decent for planetary. For DSO has a healthy f/5, which is quite fast, but it is true that some big DSO such as Andromeda Galaxy or the Heart Nebula won't completely fit in the sensor.

So these are the concepts about telescopes, sizes, and targets you need to know for getting started!!

As always that you for reading me and clear skies!

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