Learn Hardcore Portuguese (Portugal): No observatório da cidade, há um telescópio grande que pode ser usado pelo público. - At the city observatory, there is a large telescope that can be used by the public.

Using just de cidade would sound wrong here; it would be like saying observatory of city in English, missing the. In Portuguese, we usually keep the definite article in this type of phrase:

o mapa da cidade = the map of the city
o centro da cidade = the city centre
o observatório da cidade = the city observatory

How should I understand há in this sentence? Why not use tem?

In this sentence, há means there is (or there exists).

há um telescópio grande ≈ there is a big telescope

In European Portuguese, há (from haver) is the standard way to say there is / there are.

Tem (from ter) is very commonly used with this meaning in Brazilian Portuguese (e.g. tem um telescópio grande), but in European Portuguese it sounds more natural and neutral to use há or existe:

Há um telescópio grande…
Existe um telescópio grande…

Also, note that há can also mean ago when used with time:

Há dois anos = two years ago

Why is it um telescópio grande and not um grande telescópio? Does the position of grande change the meaning?

In Portuguese, most descriptive adjectives normally come after the noun:

um telescópio grande = a big telescope

Putting grande after the noun is the neutral, descriptive form: you’re just saying the telescope is physically large.

You can say um grande telescópio. That is correct, but it usually shifts the nuance a bit:

um telescópio grande = a telescope that is big (size)
um grande telescópio = a great / impressive / very good telescope (more evaluative than purely size)

So in your sentence, um telescópio grande is the more straightforward way to describe its size.

What is que doing in um telescópio grande que pode ser usado pelo público? Can I leave it out like in English sometimes?

Here, que is a relative pronoun meaning that / which. It introduces the relative clause describing the telescope:

um telescópio grande [que pode ser usado pelo público]
= a big telescope that can be used by the public

In Portuguese, you cannot normally omit que in this kind of sentence. In English you can say:

the telescope [that] the public can use
the telescope the public can use

But in Portuguese, you need the que:

✅ o telescópio que o público pode usar
❌ o telescópio o público pode usar (sounds wrong / incomplete)

How does pode ser usado work grammatically? Why do we need ser?

Pode ser usado is a passive construction built from three parts:

pode – 3rd person singular of poder (can / may)
ser – infinitive of ser (to be)
usado – past participle of usar (used)

So:

pode ser usado = can be used

It works just like English: you need be to form the passive:

English: can be used, not can used
Portuguese: pode ser usado, not pode usado

The subject of the sentence is um telescópio grande, and usado agrees with telescópio (masculine singular).

Why is it usado and not usada / usados / usadas? How does agreement work here?

Usado is a past participle used in the passive voice, and it must agree in gender and number with the thing being used.

Here, the thing being used is um telescópio grande:

telescópio is masculine singular, so the participle is usado (masc. sing.)

Some variations:

um telescópio → pode ser usado (masc. sing.)
dois telescópios → podem ser usados (masc. plural)
uma câmara → pode ser usada (fem. sing.)
três câmaras → podem ser usadas (fem. plural)

Verb + participle + agreement:

pode ser usado (he/she/it can be used – masc. sing. subject)
podem ser usadas (they can be used – fem. plural subject)

What does pelo mean in usado pelo público, and how is it formed?

Pelo is a contraction of:

por = by / through
o = the (masculine singular)

So:

por
- o → pelo → by the

Usado pelo público = used by the public

Other forms of this contraction:

por
- o → pelo (by the – masc. sing.)
por
- a → pela (by the – fem. sing.)
por
- os → pelos (by the – masc. pl.)
por
- as → pelas (by the – fem. pl.)

Examples:

usado pelo público = used by the public
feito pela empresa = made by the company
controlado pelos cientistas = controlled by the scientists
organizado pelas escolas = organized by the schools

Could I say para o público instead of pelo público? What’s the difference between por and para here?

Yes, you could say para o público, but it changes the meaning slightly.

usado pelo público = used by the public
- Focus: who uses it (the public are the users / agents).
para o público = for the public
- Focus: for whom it is intended (the public is the target audience or beneficiary).

So:

um telescópio que pode ser usado pelo público
= a telescope that the public can (actually) use.
um telescópio para o público
= a telescope for the public (intended for them, maybe in theory).

In your original sentence, pelo público emphasizes the idea “the public themselves use it”, which fits well.

Why is the comma after cidade there? Is it obligatory?

The comma after cidade separates an introductory phrase from the main clause:

No observatório da cidade, há um telescópio grande…

In Portuguese, when you start a sentence with an adverbial/prepositional phrase (time, place, etc.), you can use a comma to mark that separation. It’s common and completely correct here.

Without the comma, it would still be grammatically acceptable:

No observatório da cidade há um telescópio grande…

Using the comma slightly highlights the location as a separate frame for what comes next. In many styles, especially in written language, the comma is preferred here, but it's not absolutely mandatory.

Can I change the word order, like Há um telescópio grande no observatório da cidade? Does that sound natural?

Yes, that is natural, and very common:

No observatório da cidade, há um telescópio grande…
(Location first: emphasis on where.)
Há um telescópio grande no observatório da cidade…
(Existence first: emphasis on the fact there is one.)

Both are correct European Portuguese. The difference is mostly in emphasis and style:

Starting with No observatório da cidade sets the scene (place).
Starting with Há um telescópio grande focuses first on the telescope’s existence.

In both cases, que pode ser usado pelo público clearly refers back to um telescópio grande.

How do you pronounce observatório, telescópio, and público in European Portuguese, and what do the accents tell me?

The accents show where the stress is and often whether the vowel is open or closed.

Approximate European Portuguese pronunciation (stress in CAPS):

observatório → ob-ser-va-TÓ-ri-o
- stress on TÓ, open ó; roughly: ob-zair-vah-TÓ-ree-oo
telescópio → te-les-CÓ-pi-o
- stress on CÓ, open ó; roughly: tel-esh-CÓ-pee-oo
público → PÚ-bli-co
- stress on PÚ; roughly: POO-bli-koo

Accents:

ó (acute) usually marks an open stressed o sound.
ú (acute) marks a stressed u sound.

So the accents help you know which syllable is stressed and how to shape the vowel.

Why do we say pelo público with o público and not just por público?

In Portuguese, general or generic nouns (like the public, the student, the doctor) usually take a definite article when you talk about them in a general sense.

So you normally say:

o público = the public (in general)
os estudantes = the students (students in general)
os médicos = doctors (as a group)

Therefore:

pelo público = by the public
❌ por público sounds incomplete / unnatural in this meaning.

You can sometimes see por público especializado, where público is more like a modifier of especializado (specialized audience), but in your sentence público is the main noun, so the article is expected:

pelo público = used by the public (in general).