* The von Rheticus Model Telescope; This is a terrestrial instrument, so you see things right side up in a wide field of view when you use it.

* There are two buttons, a bigger one and a smaller one, located on the eyepiece, for adjusting the power of the telescope. Pressing either button displays the current magnification as a red number at the edge of your field of view for half a second and then gradually changes it until you stop pressing the button; the bigger one increases it by moving the outer eyepiece lens farther away from the inner one, and the smaller one decreases it by moving the outer eyepiece lens nearer to the inner one.

* The magnifying power ranges from a minimum of 10 to a maximum of 250.

* Changing the power generally requires changing the focus. There is a knob on the left side of the wider tube near the eyepiece that changes the focus by sliding the eyepiece tube into and out of the objective lens tube. There is also a feature called autofocus, which focuses on the nearest object in your field of view as long as the focusing knob is pushed in. This feature enables you to focus more quickly, but it can have certain disadvantages: you may not want to look at the nearest object that happens to be in your field of view, and it only focuses correctly if you are neither short-sighted nor far-sighted. If for any reason you want to disable the autofocus feature, pull the focusing knob out. There are two more buttons on this telescope that will be discussed in a later lesson.

* The von Rheticus telescope is small enough to fit into your pocket: it’s about 15 centimeters (six inches) long and the objective lens is about 2.5 centimeters (one inch) wide, but its resolution is as good as a much bigger Muggle-built telescope.

* The resolution of a telescope is the smallest angular distance between two points of light, as observed by the naked eye, that can be seen through the telescope as two distinct points of light rather than one, or, equivalently, the smallest angular size of a disc, as observed by the naked eye, that can be seen through the telescope as a disc rather than a point of light. The wider the objective lens of a Muggle-built telescope is, the smaller the resolution will be. A Muggle-built telescope with a 2.5-centimeter-wide objective lens has at best a resolution of about five arcseconds.

* Uranus and Neptune always look smaller than that, so these planets, like stars, appear to be points of light rather than a disc. Your telescope would have to be at least 12.5 centimeters wide to achieve a resolution of one arcsecond. But the von Rheticus model can achieve a resolution of one arcsecond, even with an objective lens only 2.5 centimeters wide. How? Magic, of course.

* As a general rule, the greatest magnifying power of a telescope that is useful is about 250 divided by the resolution in arcseconds, or about 20 times the width of the objective lens of a Muggle-built telescope; increasing the power beyond that amount makes things look bigger but doesn’t improve the resolution, so objects just look blurred.

* The greatest useful magnifying power of the von Rheticus telescope is about 250, its maximum power.

* A Muggle-built telescope that’s anywhere near 12.5 centimeters wide can’t be used without being attached to a tripod or other type of support. The telescope shown is only five centimeters wide, but it still requires a tripod. It’s too heavy to be held in your hand, and the unavoidable shaking of your hand would make the objects you’re looking at appear to dance around.

* The tube is sensitive to the shaking of your hand and compensates for it. It cannot compensate for the movement of the air using adaptive optics like the big modern Muggle-built telescopes, which is why it is limited to 250 power; there are magical telescopes that can do that, but they’re too expensive to be used in this course.

* Telescope lenses are fragile things – they are easily scratched and broken. There are two charms that protect the objective lens: the Scratch-Resistant Charm and the Break-Resistant Charm. Note, however, the word “resistant.” It’s harder to scratch or break the lens than it would be without those charms, but it can still be done. If that happens to your telescope, bring it to me, and I’ll cast the Repairing Charm on the lens.

* There is a cap that fits over the objective lens and a string, one end of which is attached to the cap and the other to the tube by means of the Sticking Charm, which prevents the cap from getting lost.

* There are two celestial bodies that you mustn’t look at through your magical telescope: the Sun and the full Moon. They both have enough magical power to destroy all the charms that were cast on your telescope, making it no better than a one-inch-wide Muggle-built one, so if you wanted to continue in this course, you’d have to buy a new one. In addition, looking at the Sun through any telescope will instantly blind you in one eye unless you use a sun filter (which must be placed over the objective lens instead of the eyepiece – otherwise the sunlight, focused on the filter, might crack it and blind you). The lens cap will protect the lens against accidental breaking or scratching and also against the light of the Sun or the full Moon hitting it, so you must always keep the lens cap on whenever you’re not using your telescope.

* The night of a full or nearly full Moon is a bad time for stargazing, as it washes out the image of any stars that appear close to it. Additionally, you would be unable to use your von Rheticus telescope, and even Moon viewing would be at its worst due to the absence of shadows cast by the mountains and the rims of craters. So how can you tell which nights to avoid? There are Muggle resources you could look up, but there are two magical tools that you can use as well. Both of these tools serve to let you know what phase the Moon will be in at a future date - that is, its apparent shape and how much of it appears to be lit in the sky.

* One of these is a lunascope. It’s not really a telescope (you don’t look at the Moon through it, which is a good thing because you may want to use it indoors or at a time when the Moon isn’t visible), but it looks like a telescope because it’s a tube with a hole in one end to look through. You punch the day, month, and year into the three buttons on the side of the tube and look through the hole; then you will see a picture of the Moon in the phase it will be in on the day you have chosen.

* The Moon Chart; It’s a piece of parchment that shows ten consecutive dates side by side, over each of which is a picture of the Moon in the phase it will be in on that date. Touching a spot on the right side of the parchment makes it show the next ten dates, and touching a spot on the left side makes it show the previous ten dates. It’s less expensive than a lunascope, but it takes longer to turn to a date in the distant future.

* A celestial globe is like a terrestrial one except that instead of showing the countries and oceans on the surface of the Earth, it shows the stars and constellations in the sky, as well as the names of some of those stars and constellations. Some of these globes appear to show the mirror image of the constellations as you would typically see them, because looking up at the sky from the Earth is like viewing the inside of the globe, rather than the outside. Other globes invert the image so that the constellations appear the same way as they do from Earth.

* This is a useful astronomical tool, but it can’t show the Sun, the Moon, or the planets, because they move with respect to the stars (the stars move too, but slowly enough that a celestial globe is useful for quite some time). This is where magic comes in: like the Marauders’ Map, a clever piece of parchment which shows the position of everyone in Hogwarts castle and their names, the magical version of the celestial globe does show the Sun, Moon, and planets and their names, and you can even make it show where they were or will be on any given day. This makes it easier to locate the planets in the sky, and it is also a valuable tool for astrology.

There are other astronomical tools used by Muggles and wizards alike. One of these is the orrery, which is a model of the solar system, with the planets moving around the Sun. While the Sun and planets are shown as being larger or smaller than the other bodies as they are in life, they are not to scale: otherwise, to make the smallest planet, Mercury, visible (say one millimeter big), the orrery would have to be enormous (Neptune would have to be nearly 100 meters from the Sun). The time taken by the planets to revolve around the Sun are to scale, but of course they are much shorter in the model than they are in the sky; otherwise you couldn’t see the motion of even the fastest planet, Mercury. In the Muggle-built version, the planets are attached to the sun by metal rods and made to move by electrical motors. In the magical version, the sun and the planets float in the air and are enchanted to move, making for a much nicer aesthetic, in my humble opinion. This tool is used mainly for educational rather than research purposes.

A star chart too is used by both magical people and Muggles. It is a flat map of the sky with no magical properties, but it helps you locate stars and constellations in the sky. Unlike the celestial globe, it won’t help you find the planets unless you already know where they are, but it’s much lighter to carry around when you’re outside stargazing. Star charts will be discussed in more detail in a later year.

When you go outside at night to stargaze, there is always the danger of tripping over something you can’t see, which could damage your telescope as well as your knees, and you might want to read your star chart, so you need a source of light that’s bright enough to read it. However, exposure to bright light would ruin the adaption your eyes make to see in the dark, and it takes about half an hour to restore it fully. Interestingly, red light reduces your dark adaption less than white light of the same brightness, but only if it’s pure red rather than light that looks red but contains other colours. The tool used by astronomers, both magical and Muggle, to solve this problem is called an astronomer’s lamp, which emits a pure red light whose brightness you can control so that you can choose the dimmest light that still enables you to do what you want to do. It takes a brighter light to read a star chart than it does to see objects that are big enough to trip over; but here’s a trick that will let you read a star chart without diminishing your dark adaption in the eye you’ll be using to look through your telescope: close that eye while the astronomer’s lamp is on!

Do not try to locate an object with your telescope set to high power, because otherwise you will see so little of the sky that it would be hard to even find the Moon. The Muggle-built telescope shown earlier in the lesson has another little telescope attached to the top of it, called a telescopic sight, which points in the same direction. Astronomers first use the sight to locate the object they want to see, and only then do they look at it through the eyepiece. If you don’t happen to have a telescopic sight with you, all you have to do to turn your scope into a sight is set it to the lowest power until you’ve located what you want to see, and then you can crank up the power.

Your telescope may have better resolution than a Muggle-built telescope of the same size, but it doesn’t gather any more light. However, there is a way that you can see stars that are slightly too dim to see when you look straight at them. If you look away from the centre of the viewing field, a star may pop into view. This is because the middle of your eye, or rather, the middle of the retina called the fovea centralis, although it is more sensitive to colour and has better resolution than any other part of the eye, is less sensitive to dim light than the other parts. The reason for this is related to the anatomy of the eye: the fovea centralis consists of colour-sensitive cones, whereas the periphery of the retina consists of colour-blind but more light-sensitive rods. If you’re interested in the anatomy of the eye, you may be able to find a book on the subject in the Hogwarts library, but if not, there are plenty of Muggle sources on the subject.

Suppose you want to look at a planet and you know approximately where it is in the night sky. You look up and you see some points of light near where you think the planet should be. How do you know which of those points of light is the planet and which of them are stars? Stars twinkle because of the movement of the air. Planets don’t twinkle because they have a larger angular size - the star with the biggest angular size is Betelgeuse (0.044 arcseconds), whereas the planet with the smallest angular size is Neptune (2.2 arcseconds at the minimum). That’s big enough that the effect of the movement of the air on the various parts of the planet’s disc cancel each other out, which is why no planet twinkles, not even Neptune.

Now suppose that you want to estimate how many degrees two celestial bodies are apart. There’s an easy way to do so which requires no magic at all. Hold your hand out at arm’s length and compare the apparent distance between the two celestial objects with the apparent size of a part of your hand. The picture below shows the apparent angular size of various parts of your hand when held out at arm’s length. Of course, these numbers are only approximate and differ from person to person, but they’re good enough for a rough estimate.