بسم الله الرحمن الرحيم
“by the stars when they set” 
There are three opinions regarding this verse, the first is that Allah swore by the stars when they set like the sun on the horizon, the second is that Allah swore by the constellation Pleiades (a seven star cluster) when it sets like the sun, and the third is that Allah swors by the Qur’an when Gabriel takes it down to Muhammad in instalments (nujuman), because the word star in arabic can also mean instalments or something given in parts so the verse would then read ““by the instalments of the Quran”.
Once we consider why Allah is taking this oath, mentioned in the next verses, it becomes clear Allah is referring to both the stars when they set and the Quran coming down in instalments. Even if the Pleiades is meant because Allah uses the general name of stars instead, the constellation in its role to guide at night would represent all stars because Allah mentions the star sirius by name later in this surah rather then generally. In the verse Allah refers to the verses of the Quran being given to the prophet (saws) with the descriptive imagery of the stars as they are setting like the sun, He is tying the two pictures together, had Allah wanted He could have stated the Quran being sent down in more literal and clear terms but chose this specific phrasing instead.
“Ibn ‘Abbas said regarding the interpretation of Allah’s saying (By the Star when it setteth): ‘(By the Najm when it setteth) He says: Allah swears by the Qur’an when Gabriel takes it down to Muhammad in instalments (nujuman): one, two, three or four verses at a time. There was a 20 years interval between the first and last verses. When this verse was revealed, ‘Utbah Ibn Abi Lahab heard that the Prophet (pbuh) swore by the revelation of the Qur’an in instalment and so he said: “Tell Muhammad that I disbelieve in the instalments of the Qur’an”. When the Prophet (pbuh) was informed of this, he prayed: “O Allah! Set on him one of Your wild beasts”. Later, Allah set on him a lion near Harran that snatched him from among his friends and took him to a place nearby. It tore him apart from head to foot but did not eat him because of his impurity, just as the Prophet (pbuh) had prayed against him.” (Tanwir al Miqbas min Tafsir Ibn Abbas, 53:1)
It may seem clear from the hadith the verse is referring to only the Quran yet of 47 translations of the Quran only two refer to the Quran in instalments, the rest mention the stars, which is the opinion of the mufasireen, the commentators of the Quran.
Allah continues, “Your comrade erreth not, nor is deceived; Nor doth he speak of (his own) desire. It is naught save an inspiration that is inspired, Which one of mighty powers hath taught him” (53:2-5)
Allah takes an oath by the setting of the stars that the prophet (saws) did not make a mistake and wasn’t deceived by what he was receiving, so the topic here is inspiration and right judgment, Allah then stresses this subject with the next verse by saying the prophet doesn’t even speak from his own desire and emphasis it again by literally saying it is inspiration that is inspired in him by the Angel Gabriel.