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Stationary -  means  -  not moving and  fixed at one point in space   as the time progresses.

The Sun is supposed to  be stationary while the planets revolve around the Sun.

Pasture :
   is a land green with a lot of grass good for grazing of animals. 
   Pasture --  used to indicate the good condition of a person or some thing.
           I have put  a horse to pasture.    The employee has been put out to pasture on attaining the retirement age.

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