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The atomic clocks on GPS satellites run about 38 millionths of a second a day faster than clocks on the ground, an effect predicted by Einstein's theories of relativity. Left uncorrected, the drift would put your position out by about 11 km within a single day.

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A GPS receiver, such as the one in your phone, works out where it is by timing signals from several satellites orbiting about 20,200 km up. Radio signals travel about 300 metres in a microsecond, a millionth of a second, so even tiny clock errors matter. Relativity pulls the clocks apart in two ways. Special relativity says moving clocks run slow: travelling at almost 4 km a second, the satellite clocks lose about 7 microseconds a day. General relativity says clocks in weaker gravity run fast: high above Earth they gain about 46. The net gain is about 38 microseconds a day. So before launch, each satellite clock is set to run slightly slow, at 10.22999999543 million cycles a second instead of 10.23 million, and in orbit it keeps step with clocks on the ground.

Türkçe oku
GPS uydularındaki atom saatleri, Einstein'ın görelilik kuramlarının öngördüğü gibi, yerdeki saatlerden her gün yaklaşık 38 mikrosaniye, yani saniyenin milyonda 38'i kadar ileri gider. Bu kayma düzeltilmese, bulunduğunuz yer tek bir günde 11 kilometre kadar yanlış hesaplanırdı.

Telefonunuzdaki gibi bir GPS alıcısı, yaklaşık 20.200 km yükseklikte dolanan uydulardan sinyal alır ve bu sinyallerin ne kadar sürede geldiğini ölçerek yerini bulur. Radyo sinyalleri bir mikrosaniyede, yani saniyenin milyonda birinde 300 metre kadar yol alır; bu yüzden saatteki en küçük hata bile önemlidir. Görelilik, uydu saatlerini iki yönden etkiler. Özel göreliliğe göre hareket eden saat yavaş işler: Saniyede 4 kilometreye yakın hızla giden uydu saatleri her gün 7 mikrosaniye kadar geri kalır. Genel göreliliğe göre ise kütleçekiminin zayıf olduğu yerde saat hızlı işler: Dünya'nın çok yukarısındaki bu saatler her gün 46 mikrosaniye kadar kazanır. Sonuçta günde yaklaşık 38 mikrosaniye ileri giderler. Bu yüzden her uydunun saati, fırlatılmadan önce biraz yavaş çalışacak biçimde ayarlanır: Saniyede 10,23 milyon yerine 10,22999999543 milyon salınım yapar. Böylece yörüngede yerdeki saatlerle aynı hızda işler.

Sources and further reading

Background reading: Time dilation
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