In a halachically public area (reshut ha'rabim) with no eruv, on Shabbat you may move a stationary object up to 4 amot (6'9 1/2", or about 2 meters) from the place where you find it. If you are already transporting the object when you realize it, do whichever one of the following applies:
Situation You are walking on Shabbat in a public domain (reshut ha'rabim) that does not have an eruv and find something in your pocket.
What To Do

• If you were walking and are still walking, go back to the most recent private domain and leave the item there. (If you cannot reasonably get back to where that was, continue to your destination and drop the item inside the first private domain you reach.)
• If you have already stopped walking, drop the item where you are.
• If you had stopped walking and then resumed walking, drop the item where you are.

On Shabbat (or Yom Kippur), you may not transfer an object between and among domains unless there is a city eruv (which allows carrying within the borders of the eruv).

The International Dateline (IDL), which is 180 degrees away from Greenwich, England, crosses the Pacific ocean from north to south and divides a region of safek/doubt as to which day is Shabbat. This region's eastern boundary is a line 180 degrees east of Jerusalem, which lies between Hawaii and the US mainland; the western boundary is east of Shanghai. All countries in this region of IDL safek/doubt are island countries.
 
In a region of doubt, such as Tasmania, keep normal Shabbat (Shabbat d'rabanan) on local Saturday and keep Shabbat d'oraita on:

• West of mainland USA, but
• East of the IDL, and
• Not attached to the mainland.

• West of the IDL, but
• East of Shanghai, and
• Not attached to the mainland.

Note In all cases, you must still observe regular Shabbat on Friday night/Saturday.
Situation
You are in a place near the International Dateline (IDL) in which you are not sure which day of the week it is halachically: Shabbat or, if you are east or west of the IDL, Friday or Sunday.
What To Do
On the Friday or Sunday in question, there is no shvut (d'rabanan prohibitions, including muktza), so you may do all melacha d'rabanan WITHOUT a shinui. You may:

• Ask or tell a non-Jew to do anything, including a melacha d'rabanan or d'oraita.
• Ride in a cab or car driven by a non-Jew.

• Use electricity--except for heat or light—including turning on a fan or air conditioner (heat and light are forbidden by the Torah).
• Use the telephone. (Using a cellphone may be permissible--ask a rabbi).

• Carry from a private domain (reshut ha'yachid) to another private domain, even through a public domain (reshut ha'rabim); but you may not stop walking in the public domain and you may not put the object down in the public domain unless you use a shinui.
• There is no practical way to light candles, even using a shinui, but a non-Jew may light them for you and and you may say the blessing on the candles.
• Swim, surf, scuba dive, climb, and play all games that do not use melacha. You may not wring out clothes and if you are swimming or scuba diving, your swimsuit or wetsuit must be clean.
• Walk any distance (there is no techum Shabbat d'oraita).
• Kinyan. You may acquire items.

• Fly, including check in and getting on plane if:
  • The pilot is non-Jewish, and
  • You don't do any melacha d'oraita (including any writing) without a shinui.
• Use a computer if it automatically goes to sleep after less than 24 hours of not being used.
• Shower. However:
  • You may not use an “instant on” hot water system in which the water is heated as you use it; you may only use the hot water if it has a holding tank.
  • You may use only liquid soap; hard soap is forbidden.
• Ingest medicine (but you may not smear it on skin).
• Use some make up, such as rouge, mascara, eye shadow. You may not use lipstick.
• Open a refrigerator with light (and all other psik reisha d'la neicha lei).

• You may buy necessities on Friday or Sunday as long as:
  • The store owner is not Jewish (or if he/she is Jewish, does not write or print a receipt),
  • You do not write, and
  • There is no reshut ha'rabim.

You may also do melacha d'oraita if:

• You use a shinui (non-normal way of doing that action--this is forbidden d'rabanan on Shabbat but is allowed on the Friday or Sunday in question), OR
• Two or more people do the melacha together.

 
D'oraita, you may not:

• Cook food.

• Turn on lights (but you may turn them off).
• Carry from domains.
• Boneh – building any permanent structure.
• Write two or more letters of the alphabet.
• Drive--there is no practical way to drive using a shinui.
• Shave--there is no practical way to shave using a shinui.
• Use toothpaste (but you may use tooth-cleaning powder).
• Use skin cream--you may dab it on without smearing it.

However, you may do these following actions with a shinui on the Friday or Sunday in question, as follows:

• Cook food. You must put food in the cooking utensil first, then turn on the heat with shinui. You may turn off the heat even without a shinui.
• Turn on lights (such as with your elbow).
• Stop along the way when carrying from a private domain (reshut ha'yachid) to another private domain, even through a public domain (reshut ha'rabim). As a shinui, you may carry the object in your mouth (as long as it is not food), etc.

Note Carrying something in your pocket is NOT a shinui.

• Tear paper (such as putting toilet paper across knees and moving the knees apart).
• Write (such as with the opposite hand).

Flying East From Australia on Sunday If You Cross IDL from Friday into Saturday