Learn Hardcore German: Die Farbe des Himmels über der Stadt verändert die Stimmung vieler Menschen. - The color of the sky above the city changes many people’s mood.

Himmel is masculine (der Himmel = the sky).
Masculine singular genitive of the definite article is des, and the noun usually gets an -s:
- Nominative: der Himmel
- Genitive: des Himmels

The genitive here shows a relationship like English “the color of the sky”:

die Farbe des Himmels = the color of the sky

So des Himmels depends on Farbe and answers “the color of what?”

Why is it über der Stadt and not über die Stadt?

über is a two-way preposition (Wechselpräposition) that can take either:

dative (location, no movement), or
accusative (movement/direction).

Here it describes where the sky is, not a movement:

über der Stadt = above the city (static position → dative)

Compare:

Die Wolken hängen über der Stadt. – The clouds hang above the city. (location → dative)
Die Vögel fliegen über die Stadt. – The birds fly over the city. (movement across → accusative)

Since in your sentence it’s about the sky being above the city, not moving over it, über der Stadt (dative) is correct.

Is the verb in the right position? I thought German main clauses are “verb-second”, but verändert is not the second word.

German main clauses are indeed verb-second, but that means second element/constituent, not literally the second word.

In the sentence:

Die Farbe des Himmels über der Stadt – this whole chunk is one big subject phrase (first element).
verändert – conjugated verb, second element.
die Stimmung vieler Menschen – object phrase (rest of the clause).

So the structure is:

Subject: Die Farbe des Himmels über der Stadt
Verb: verändert
Object: die Stimmung vieler Menschen

The verb is correctly in second position as German grammar defines it.

Who is the subject and who is the object in this sentence?

Subject: Die Farbe des Himmels über der Stadt
- It is in the nominative and is the thing that does the changing.
Verb: verändert
Direct object: die Stimmung vieler Menschen
- It is in the accusative and is the thing that is changed.

Paraphrased:
The color of the sky above the city (subject) changes the mood of many people (object).

Why is it verändert and not ändert? What’s the difference between ändern and verändern?

Both verbs can mean “to change”, but there is a nuance:

ändern: to change something, often more neutral or small/partial changes.
- Das Wetter ändert sich. – The weather changes.
- Wir ändern den Plan. – We change the plan.
verändern: to alter/transform something, often sounds a bit stronger or more thorough, and slightly more formal.
- Die neuen Regeln verändern das Unternehmen. – The new rules transform the company.
- Die Stadt hat sich stark verändert. – The city has changed a lot.

In your sentence, verändert suggests that the sky’s color can significantly influence or affect people’s mood. You could say ändert die Stimmung vieler Menschen; it would still be correct, just with a slightly more neutral tone.

Is verändern a separable verb?

No. verändern is inseparable.

The prefix ver- is one of the classic inseparable prefixes in German (like be-, er-, zer-, etc.).
That means the prefix never splits off and you do not add ge- in the past participle.

Forms:

Infinitive: verändern
Present 3rd sg: er verändert
Simple past: er veränderte
Perfect: er hat etwas verändert (not geverändert and not er ändert…ver)

So in main clauses, you always keep verändern together:
Die Farbe des Himmels verändert die Stimmung vieler Menschen.

Why is it vieler Menschen and not viele Menschen or vielen Menschen?

vieler Menschen is genitive plural, dependent on Stimmung:

die Stimmung vieler Menschen = the mood of many people

Breakdown:

Menschen is the plural of Mensch.
In the genitive plural, nouns usually look like the dative plural (here still Menschen).
The quantifier viele gets the -er ending in the genitive plural: vieler.

So the pattern is:

Nominative plural: viele Menschen – many people
Genitive plural: vieler Menschen – of many people

You cannot just say die Stimmung vielen Menschen; without von, vieler is needed to mark the genitive plural.

Can I use von instead of the genitive, like die Stimmung von vielen Menschen or die Farbe vom Himmel?

Yes, but there are style differences:

die Stimmung vieler Menschen
- Genitive, sounds more formal/standard written German.
die Stimmung von vielen Menschen
- Using von
  - dative (vielen Menschen).
- Completely normal in spoken German, slightly more informal.
die Farbe des Himmels
- This is the most natural standard form in writing.
die Farbe vom Himmel (= von dem Himmel)
- Grammatically possible, but often sounds more colloquial or regional; many speakers would still prefer die Farbe des Himmels.

So:

For good written German: use the genitive (des Himmels, vieler Menschen).
In everyday speech: von
- dative is very common (die Stimmung von vielen Menschen).

Why is Stimmung singular when we’re talking about many people? Why not die Stimmungen vieler Menschen?

Both are possible, but they focus on slightly different ideas:

die Stimmung vieler Menschen (singular)
- Treats “mood” as a collective/general state.
- Focus is on the overall mood among many people.
die Stimmungen vieler Menschen (plural)
- Emphasizes many individual moods, perhaps different from each other.
- Less common in this kind of general, atmospheric statement.

In your sentence, the idea is that the sky’s color influences the general mood among people, so singular Stimmung is the natural choice.

What is the difference between Stimmung and Laune for “mood”?

Both relate to “mood”, but they’re used differently:

Stimmung
- Can be an individual’s mood or the general atmosphere.
- Often used for groups, places, times, events.
- Examples:
  - Die Stimmung im Zimmer ist gespannt. – The atmosphere in the room is tense.
  - Seine Stimmung war schlecht. – His mood was bad.
Laune
- More strongly about a person’s current mood (good/bad).
- You don’t normally use it for a crowd or a room.
- Examples:
  - Ich habe heute gute Laune. – I’m in a good mood today.
  - Sie ist immer schlechter Laune. – She is always in a bad mood.

In your sentence, Stimmung vieler Menschen is appropriate because it’s about a more general, shared mood among many people, not each person’s private “good/bad mood” moment.

Can I change the word order, for example: Über der Stadt verändert die Farbe des Himmels die Stimmung vieler Menschen?

Yes, that sentence is grammatically correct and means essentially the same thing.

Structure with fronting:

Fronted adverbial: Über der Stadt (first element)
Verb: verändert (still second element – verb-second rule)
Subject: die Farbe des Himmels
Object: die Stimmung vieler Menschen

So you get:

Über der Stadt verändert die Farbe des Himmels die Stimmung vieler Menschen.

This word order puts more emphasis on the location (Über der Stadt) and is quite natural in German. The original order is just a bit more neutral in focus.