OrbitickGPS Clock Correction / Gravitational Time DilationSticker

Orbitick sets every clock wrong, on purpose.

A GPS satellite circles about 20,200 km up, carrying atomic clocks whose time signals tell receivers on the ground how far away it is. Light covers about 30 cm in a nanosecond, so the clocks must agree with the ground to within nanoseconds. Relativity says they won’t.

Two effects pull in opposite directions. Higher up, in weaker gravity, a clock runs faster: about +45.7 microseconds a day. Moving at nearly 3.9 km/s, it runs slower: about −7.1 microseconds a day. The net is +38.6 μs a day, which would soon wreck positioning if left alone. The first line on this page combines them, with the potential measured from the geoid, whose effective potential includes Earth’s rotation term. Neil Ashby notes that leaving that term out made the original factory offset wrong for about eight years.

So the fix is to make the clock wrong before launch. Its fractional rate in orbit is +4.4647×10⁻¹⁰, so the specified factory offset is −4.4647×10⁻¹⁰: the 10.23 MHz reference is set to 10.229 999 995 43 MHz, the dial in Orbitick’s hand. In orbit, gravity and motion bring it back to 10.23 MHz as seen from the ground. In practice, Ashby adds, rubidium clocks are often left un-offset and their rates are corrected from orbit through the navigation message instead. A smaller wobble from the slightly eccentric orbit is corrected in the receiver.

Orbitick is a pre-emptive liar whose lies are cancelled exactly by gravity and speed. Every time a phone finds its blue dot, her arithmetic is at work somewhere overhead.

Wrong on purpose. Right in orbit.