Why GPS must correct for special and general relativity
PAPER VII — ENGINEERING · QUESTION 32 OF 32
In plain terms: The free authoritative review giving the exact numbers the question asks for, from the physicist who worked them out for the system.
The question as set
Why must a GPS receiver correct for both special and general relativity? Quantify the daily error of neglecting each, and say which dominates.
The question in Paper VII · Its section on the reference page
The question in context
This is question 32 of the 32 set in Paper VII — Engineering of The Truly Hardest Exam in the World, the examination of The College of All Minds. In the College’s subject index it is filed under Geodesy and navigation. Like every question of the College, it carries three references of record, verified live at publication and described twice — technically, and in plain terms — so the ground can be judged before it is walked. The response required is an argument, not a survey, of at most three thousand words, as technical as the question demands and no more.
The references of record
Relativity in the Global Positioning System
Both corrections quantified: time dilation of −37 µs/day at orbital speed against +45 µs/day of gravitational blueshift, netting +38 µs/day.
In plain terms: The free authoritative review giving the exact numbers the question asks for, from the physicist who worked them out for the system.
GPS — the official system record
The error budget of record, against which a 38-microsecond daily drift — some eleven kilometres of ranging error — may be scaled.
In plain terms: The free official statement of how accurate the system is, so the cost of neglecting relativity can be judged.
Time and frequency — the standards
The clock physics beneath the correction: caesium and rubidium standards, their stability, and the definition the corrections preserve.
In plain terms: The free official source on the clocks whose disagreement the corrections repair.
Background: Global Positioning System · Gravitational time dilation