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Answer: It is an honor to learn Torah with people, all the more so with a soldier for whom Halacha is front and center. We will discuss principles and address some scenarios.
The gemara (Shabbat 19a) says that one may embark on a sea journey that will continue into Shabbat only if: A. He sails before the last three days of the week; OR B. His trip is for a mitzva. Rishonim (see Beit Yosef, Orach Chayim 248) present different possibilities about the relevant problem of being on the ship. These include: 1. Seasickness harms oneg Shabbat; 2. The violation of techum Shabbat. 3. The Rabbinic prohibition of sailing. 4. The Ba’al Hama’or (ad loc.) says that we presume that the danger will make it necessary to do melacha on Shabbat, and that it is forbidden to enter such a situation without a legitimate need at the time of the week that Shabbat should be on his mind. The Rivash (Shut 101), accepted by the Shulchan Aruch (OC 248:4), reasons that even those who explain the gemara differently, agree that there needs to be sufficient justification to put oneself into a situation that requires violation of Shabbat for pikuach nefesh.
Logically, making Shabbat early when the need to do melacha is expected during tosefet Shabbat is like setting up the need by entering the ship. It is unclear how high the chance of doing melacha needs to be for this to apply. In most cases, it depends if one has a shift or an operation at that time.
One pertinent question is why you are considering accepting Shabbat early. On a weekly basis, few men actively accept Shabbat early, in the way that [Ashkenazi] women do with candle lighting (see Shulchan Aruch and Rama, OC 263:10). Men do not accept Shabbat at that time (and must not if they need to daven Mincha). Some make a declaration of accepting Shabbat after Mincha, but this is not mainstream practice or required according to most poskim (see Yabia Omer VII, OC 34; Living the Halachic Process III, C-4). Rather, tosefet Shabbat is fulfilled by refraining from melacha at least a few minutes before bein hashemashot. It is detrimental to actively accept Shabbat when there is a good chance one would need to do melachot in those minutes.
The question is if soldiers want to accept Shabbat early to enable davening Ma’ariv (with a minyan), Kiddush, and/or a seuda before a shift? Based on the above, entering the situation requires that it includes facilitating a mitzva. What counts as a mitzva? The Tur (OC 248) cites Rabbeinu Tam that a business trip counts as a mitzva, whereas a pleasure trip is a non-mitzva. Many require a real mitzva, such as traveling to making aliya. The Shulchan Aruch (OC 248:4) rules like the stringent approach, but the Rama says that some follow Rabbeinu Tam, and they should not be criticized.
According to the approach that one needs a real mitzva, it is unclear whether doing the mitzvot of Shabbat during tosefet in a case that he can do the mitzvot in a non-optimal way (e.g., later, without a minyan, with cold food, while tired) counts. The policy of the IDF Rabbinate is that one should not accept Shabbat early if he can fulfill the mitzvot of the night after the shift. If not, one should eat his meal before the shift as a weekday meal and have a minor meal after returning from the shift. This reflects the correct general approach that one being exacting in avoiding melacha on Shabbat, even under extenuating circumstances, is more crucial than ideal fulfillment of the positive mitzvot of the day under such circumstances.
Such a general policy is for standard cases. Circumstances vary, both concerning halachic distinctions and practical concerns of the "army-on-Shabbat experience." We would expect an expert army chaplain (as a high-ranking one told me) to weigh the specifics of a given case to determine if it fits the general guidelines or whether accepting Shabbat early might be worthwhile.

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