While the seventh perek of Massekhet Arakhin dealt with a person who consecrated his ancestral field to the Temple while the yovel was in force, the eighth perek, which begins on today’s daf, discusses the laws at a time when the yovel was no longer kept. As we learned, someone who consecrated his field to the Temple during the time of yovel would redeem it based on a Biblical formula (see above, daf 24). When there was no yovel, however, the field was redeemed based on its market value as established in a public auction.
Tosafot emphasize that the need for a public auction only existed when the Temple was standing. With the destruction of the Temple, a field that was consecrated to the Temple served no real purpose and could be redeemed even with a symbolic peruta coin.
Keeping the Jubilee year and its attendant laws ended at the time of the exile of the tribes of Re’uven, Gad and half of Menashe, who made their ancestral homes on the eastern bank of the Jordan River, an event that took place many years before the destruction of the first Temple. The Rambam explains that the laws of the Jubilee year apply only when the Jewish people are established in the Land of Israel, and since that time this has not been the case. It is clear from a variety of sources that during the second Temple many of the laws relating to the Jubilee year were kept, a fact that led Rabbeinu Tam to assume that there was a biblical obligation to keep the yovel during that time. The Rambam does not accept this reasoning, and he states clearly that the laws of yovel did not apply during second Temple times (see the Mishneh Torah, Hilkhot Shemitta VeYovel 10:3). Some suggest that there was a Rabbinic injunction to keep some of the laws during the second Temple period.