Interplanetary Trips The simplest way to travel between the planets is to let the Sun's gravity do the work and take advantage of Kepler's laws of orbital motion. A fuel efficient way to travel is to put the spacecraft in orbit around the Sun with the Earth at one end of the orbit at launch and the other planet at the opposite end at arrival. These orbits are called ``Hohmann orbits'' after Walter Hohmann who developed the theory for transfer orbits. The spacecraft requires only an acceleration at the beginning of the trip and a deceleration at the end of the trip to put it in orbit around the other planet. Let's go to Mars! The relative positions of Earth and Mars must be just right at launch so that Mars will be at the right position to greet the spacecraft when it arrives several months later. These good positionings happen once every 780 days (the synodic period of Mars). The spacecraft must be launched within a time interval called the ``launch window'' that is just few of weeks long to use a Hohmann orbit for the spacecraft's path. The Earth is at the
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