This occurred in 1955 when I was 13 years old.I went on a camping trip with a church group of 10 boys the same age, we had 2 adult sponsors with us.
We were camped on the banks of the Pecos river.
We had laid out bedrolls side by side on a grassy section which slowly sloped into the river.
As boys that age, we were running all over the area chasing each other, laughing and such.
About 9:30 p.m., I got tired and laid down on my bedroll, the other boys kept playing.
It was dark and in the West Texas desert 15 miles from a small town, there was little light pollution thus the stars were very bright.
In the night skies, there are always a sprinkling of stars brighter than the other stars.
As I layed there I happened to be staring a one of those stars which was directly above me, stationary.
It was completely still in the sky.
I stared at it for quite a while, I cannot say how long but I was staring at it while it remained stationary in the sky.
As I was looking at it, it began moving, it did not flash away.
It simply began moving, it did not get brighter or less bright.
It did not have a trail such as a comet would have.
I stopped some of the other boys and showed it to them.
They watched for a while but became bored and started playing again.
I continued to watch it until it went out of sight beyond the horizon.
It took about 2 minutes for it to go from a stationary position directly above in the sky to disappearing below the horizon.
This was before Sputnik or even any public idea about satellites.
At this time, there was a small airport in McCamey but only a very few light, fixed wing aircraft.