Why Eat

The Tur in siman 597 cites a machlokes Rishonim if there is an obligation to eat on Rosh Hashana. The debate would seem to center on if there is an obligation of שמחת יום טוב on RH or is that limited to the three regalim. However, the Shulchan Aruch rules one should eat on RH yet he also says in siman 582 that one does not say מועדים לשמחה in the prayers of RH, presumably since RH is not a day of simcha?  The Tur gives another reason to eat on RH besides being a fulfillment of שמחת יום טוב. The Tur evokes the Midrash that he cites in siman 581 that we dress up on RH since we show bitachon that Hashem we give us a favorable judgement.  based upon this, the Tur says one should eat as well. If so, there is no contradiction in the Shluchan Aruch for he holds it is not a day of simcha but nonetheless one should eat to show one's trust in a favorable judgment.  With this idea we can understand the comment of the Magen Avraham in the name of the Magid Masherim that one should not eat meat or have wine on RH.  But that is simcha?  Because we are not eating due to the law of simcha, rather to show bitachon in Hashem's judgement but that is nonetheless tempered by the severity of the day.  This may explain the opinion of Rav Natrunay Gaon (cited in the Tur) that one should not fast on the first day of RH but can on the second.  What is the difference, both days should have an obligation of simcha? (See Bach.) Because he holds we are not eating because of simcha, only to show that despite the severity of the din, we have bitachon in a favorable judgement. That demonstration is limited to the first day which is the main day of judgment but the second day is like the other days of the עשרת ימי תשובה where one may fast (even on Shabbos in his opinion.) (Based upon Minchas Asher, Yarech L'moadim siman 11-12.)