A star sized object circled the sky and then shot straight out of sight at very great speed.

It was in the summer and I am not  sure of the year. It could have been l958 or 59.  I was outside and looked at the sky, which was full of stars.  I noticed that one of the stars was moving in a very large circle around the sky.  For as high as it must have been, it must have been moving at a great speed. It continued this for  awhile and then it shot off straight out of sight at a much greater speed.  It was about the size of one of the stars, but brighter.  Other people outside saw it also.  I called the Civil Defense call line and found that it was busy for quite awhile.  When I finally got through, they said that they had many calls about the same thing.  I am a high school teacher
Date is approximate.  PD