Learn French: Peut-être l'astronome a-t-il eu du mal à voir l'éclipse. - Perhaps the astronomer had trouble seeing the eclipse.

This is called complex inversion. When a sentence begins with certain adverbs like Peut-être, formal French requires subject-verb inversion. Because the subject is a noun (l'astronome) rather than a pronoun, you must leave the noun in front of the verb and insert the matching pronoun (il) immediately after the verb.

Do I always have to use this complex inversion after Peut-être?

No, complex inversion is primarily used in formal or written French. In everyday spoken French, you can avoid the inversion by adding que after the adverb, which allows you to use standard word order: Peut-être que l'astronome a eu du mal...

Why is there a -t- inserted in a-t-il?

This is a pronunciation rule for inversion. When the verb ends in a vowel (like a) and the inverted pronoun starts with a vowel (like il, elle, or on), French adds a -t- between them. This prevents two vowel sounds from clashing awkwardly.

Why do we use à in à voir instead of de voir or just the infinitive?

The phrase for having trouble doing something is avoir du mal à followed by an infinitive. It is a set expression, so you must always use the preposition à here, even though English translates it with an -ing verb like seeing.