This article may be useful as supplementary reading for physics classes, based on the DSE syllabus.
根據物理科文憑試課程綱要，本文或可作為有用的補充讀物。
Global
positioning systems (GPS) have
taken the world by storm since its development
in the 1970s. Its applications have extended from
purely navigational assistance to smart phone
gaming, spawning popular apps such as Pokémon
Go and its predecessor Ingress. In addition
to the complex technology of satel l ite
signalling, the GPS is often quoted as a device
that is directly affected by Einstein’s theory of
Special and General Relativity, but scientists have
managed to circumvent this problem entirely.
A GPS can be divided into three segments,
namely, specialised satellites, the control centre,
and the user device or receiver. Around 30
satellites containing atomic clocks orbit the earth.
At any given time, the GPS receiver must be
able to receive radio emissions from at least four
satellites to determine the location. The receiver
essentially calculates the distance between each
of the satellites based on the time required for the
transmissions to be received. In a process called
trilateration that somewhat resembles a Venn
diagram, the satellites create information in the
form of spheres. The intersections where these
spheres overlap pinpoint the location of the GPS
receiver. More satellites signals received equate to
more accurate of a location.
Since the location is determined by measuring
the time it takes for a signal to be received,
recording time accurately is crucial. In a nutshell,
Einstein’s theory of Special Relativity states that
a clock moving relative to an observer will be
slower than a clock that is stationary. The theory
of General Relativity then states that gravity also
has an effect on the way time ticks; the stronger
the gravitational field, the slower the clock ticks.
Satellites are in orbit around the earth at 14,000
km/hour at approximately 20,000 km above
ground. By the theory of General Relativity, the
clocks carried by the satellites would essentially
be running at a faster time to one on Earth (the
effect of general relativity due to less gravity in
orbit is greater than the effect of specific relativity
induced by higher movement speed), creating
an error of about 38 microseconds per day. When
this effect accumulates over time, the positioning
detected by the GPS would be so off that it would
be next to useless.
Yet, this is not the case. A commercial GPS
is able to pinpoint a location to an accuracy of
about 3 to 5 metres. Satellite clocks are already
adjusted for general and special relativity to
match the correct time on Earth, making up for
the discrepancy between the user location and
the satellites’. Additionally, the GPS receiver is
also capable of performing calculations that are
The GPS and Its Connection
to Relativity
全球定位系統
Satellite
Satellite
