Yes, as long as you have space for a runway in your yard that's exactly what you can do in the US. Lots of farmers and people who live out in the country do this. Usually they even register their airstrips with the FAA.
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In addition to the UK's civil and military aerodromes, there are hundreds of smaller, grass airfields set up by private individuals (termed 'farm strips'). If you own suitable land, it's possible to set up your own – of course, planning restrictions and practical considerations apply.
Landing and Handling FeesYou'll pay a fee for landing and using the airport facilities at your destination airport. The charge for this depends on the aircraft's weight. Smaller planes will have a lower fee. Yet they will vary considerably by airport, depending on its popularity, location, and facilities.
Under the 28-day rule, helicopter and fixed wing aircraft can be operated from appropriate sites for no more than 28 days in total in any calendar year.
So what can take off and land from where? A runway of at least 6,000 ft in length is usually adequate for aircraft weights below approximately 200,000 lb. Larger aircraft including wide-bodies will usually require at least 8,000 ft at sea level and somewhat more at higher altitude airports.
A private pilot license does not allow you to work for an airline or make money but is a good choice for hobbyists who want to fly small planes with friends and family as passengers. It is an important credential for aviation enthusiasts who wish to become a pilot of aircraft and experience the freedom of flight.
While no passenger or non-experienced pilot has ever successfully landed a commercial plane, occasionally someone without experience manages to land a smaller plane.