To determine how many times a GPS satellite circles the Earth, it is important to understand the nature of GPS satellites and their orbits.

GPS satellites are part of a network used for global positioning system applications. These satellites are placed in medium Earth orbit (MEO) and are part of a constellation designed to provide global coverage. Let's analyze the details relevant to their orbits:

1. Orbit Period of GPS Satellites:
   GPS satellites are positioned at an altitude of approximately 20,200 kilometers above the Earth. This specific orbit is selected so that each satellite completes its orbit around Earth twice per sidereal day (approximately 23 hours and 56 minutes). This results in the satellite passing over the same spot on Earth twice every day.
2. Circling Time Around the Earth:
   The time taken by a GPS satellite to complete one full orbit around Earth is about 12 hours. Therefore, a GPS satellite circles the Earth twice in a 24-hour period.
3. Examining the Options:
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Once every 48 hours

1. : Incorrect, as satellites complete a full orbit every 12 hours, not 48.
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Once every 2 hours

1. : Incorrect given the known 12-hour orbit period.
   -

Once every 24 hours

1. : Incorrect, satellites orbit every 12 hours, thus twice in 24 hours.
   -

Once every 12 hours

1. : Correct, matches the known orbit time.

Based on the above consideration, we conclude that a GPS satellite circles the Earth once every 12 hours.