There are two ways to reach Kamchatka from North America. The first option is to take Vladavia's twice-weekly flight from Anchorage to Petropavlovsk (departing on Mondays and Thursdays in season). This is relatively straightforward. However, it is an expensive ticket, and provides less flexibility in trip-planning since it only runs twice per week. You can book tickets or find out details of the schedule by contacting Red Star Travel.
It can be easier, and usually cheaper, to fly via Moscow instead. This also gives you the opportunity to see other parts of Russia, such as Moscow and St. Petersburg. There are daily flights from Moscow to Petropavlovsk-Kamchatsky, Kamchatka. If you book early enough, you can usually get a ticket via a consolidator that is significantly cheaper than flying via Anchorage. The cheapest ticket is usually on Aeroflot, especially if you book the entire ticket (US-Moscow-Kamchatka-Moscow-US) on that airline.
The flight will give you a sense of how incomprehensively huge
Russia is- the 7500km (4687 mile) 'great circle' route spans nine time
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