Is it permissible to sweep a floor with a broom on Shabbat?
The Shulhan Aruch (Orah Haim 337:2; listen to audio recording for precise citation) rules that it is permissible to sweep finished floors on Shabbat, meaning, floors that are marbleized, tiled and the like. Long ago, many people did not have an actual floor in their home; the ground itself was their floor. The Shulhan Aruch rules that one may not sweep the ground, as this will inevitably result in "Ashvuyeh Gumot" – filling in holes in the ground with dirt, which constitutes a Shabbat violation. And although one who sweeps a floor has no intention to fill the holes in the ground, sweeping is nevertheless forbidden because of the inevitability of this result. The Halacha of "Pesik Resheh" establishes that one may not perform an action on Shabbat that will inevitably result in a Shabbat violation, even if one has no intention to cause this result through his action. Therefore, even though a person who sweeps the ground has no intention to fill the holes in the ground, it is forbidden to sweep ground on Shabbat since this will inevitably result in filling holes.
Of course, our homes today are generally properly floored with tiles or other surfaces, and it is therefore entirely permissible to sweep floors on Shabbat, as mentioned. If, however, a person has an unfinished section of his home, he may not sweep in that part of the house on Shabbat. Similarly, if a person has an unpaved section of his backyard which he wants to clean, he may not sweep that area on Shabbat.
Is it permissible to ask a gentile to sweep ground on Shabbat?
Although it is generally forbidden to ask or instruct a gentile to perform an activity forbidden for a Jew on Shabbat, it would be permissible to ask a gentile to sweep the ground in one’s backyard or an unfinished part of his home. Hacham Ovadia Yosef writes that the prohibition of "Amira Le’nochri" (asking a gentile to perform forbidden activity on Shabbat) does not apply to activities that are forbidden by virtue of the rule of "Pesik Resheh." Situations of "Pesik Resheh" are forbidden only by force of Rabbinic enactment, and the Sages did not go so far as forbidding asking a gentile to perform an action involving a "Pesik Resheh." Therefore, since sweeping the ground is forbidden only due to a "Pesik Resheh," as the person clearly has no intention to fill the holes in the ground, one may ask a gentile to sweep the ground on Shabbat.
Summary: It is permissible to sweep floors inside one’s home on Shabbat, but one may not sweep the ground outside one’s home or in an unfinished area of one’s home on Shabbat. One may, however, ask a gentile to sweep ground on Shabbat.
