What does mosaic law say about sabbath observance?

Answer 1

The relevant verse is in Exodus ch.16, "Let no (Israelite) man go out from his place on the seventh day." Like many hundreds of other Torah-verses, this one is impossible to obey without an oral tradition (the Talmud). For those who prefer to create their own interpretation (such as the Karaites), it would be unclear as to whether they should take it to mean: Do not walk at all on the Shabbat, or-

Do not leave your room, or-

Do not leave your home, or-

Do not leave your town;

and also, whether this means men only, or not;

and, whether it is permanent, or applied only in the context of gathering the manna (Exodus ch.16).

It is the Israelite oral tradition, going all the way back, which specifies the exact method of keeping this command. There are a number of details, but the most basic is that we (Jews) may not leave our towns for a distance exceeding 2000 amah (about a kilometer) on the Shabbat or the Torah-festivals (of Leviticus ch.23).

Answer 2

In addition to what Dan Galilee's Expert Answer says, the Jewish tradition, which has followed the Israelite tradition, has banned all forms of transport other than walking (and under certain parameters necessary wheeled items like strollers or wheelchairs), such as riding an animal, driving, steering a boat, or flying an airplane.