The last time one may pray the afternoon service, minkha, according to Rebbeinu Tam TB Zevakhim 56

 The Torah sets different time limitations for different sacrifices. A shelamim, a well-being sacrifice, may be eaten for the time period over two days and one night. The time allotted for a Kohen to eat a khatat, a sin offering, is over one day and one night. The Paschal lamb is only eaten at night until midnight. There’s also a time limitation for the sprinkling of the blood on the altar. A person has all day until sunset to sprinkle the blood on the altar. If he doesn’t, the blood is considered notar (נותר), past its expiration date, and must be disposed of properly. Daf TB Zevakhim 56 wants to know how we know this halakha.

“Rav Yitzḥak bar Avudimi says: From where is it derived that the blood of offerings becomes disqualified at sunset and can no longer be presented on the altar? This is as it is stated in the verse: “But if the sacrifice of his offering be a vow, or a gift offering, it shall be eaten on the day that he sacrifices his offering [zivḥo], and on the morrow” (Leviticus 7:16). This means that on the day that you slaughter [zove’aḥ] the offering you sacrifice it on the altar and present its blood. But on the day that you do not slaughter the offering you may not sacrifice it and present its blood.” (Sefaria org translation)

This discussion actually has practical application today. According to one rabbinic source, the morning prayers, shakharit, and the afternoon prayers, minkha, are all replacements for the morning and afternoon daily sacrifices temidim. Obviously, there are time limitations for the services like they were time limitations for the daily temidim. It is too late to pray minkha after the sun sets and night begins.

Tosefot ד"ה מִנַיִן לְדָם cites Rebbeinu Tam’s approach in determining when night begins. He understands the setting of the sun as a process. Sheki’at hakhama

(הַחַמָּה שְׁקִיעַת) is when the sun sets below the horizon. Maysheki’at hakhama (מֵשְקִיעַת הַחַמָה) describes a much longer period of time. Twilight (bein hashamasot-בּין השמשות) begins 58 ½ minutes after the sun just begins to set. Twilight only last 13 ½ minutes. According to Rebbeinu Tam night (tzait hakokhavim-צאת הכוכבים) occurs 72 minutes after the initial sunset. This means that one who holds by Rebbeinu Tam’s opinion has a longer time to squeeze in minkha and has to wait a longer time before Shabbat ends.