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Date	November 2016	Marks available	3	Reference code	16N.3.HL.TZ0.9
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Estimate	Question number	9	Adapted from	N/A

Question

The global positioning system (GPS) uses satellites that orbit the Earth. The satellites transmit information to Earth using accurately known time signals derived from atomic clocks on the satellites. The time signals need to be corrected due to the gravitational redshift that occurs because the satellites are at a height of 20 Mm above the surface of the Earth.

The gravitational field strength at 20 Mm above the surface of the Earth is about 0.6 N kg^–1. Estimate the time correction per day needed to the time signals, due to the gravitational redshift.

[3]

Suggest, whether your answer to (a) underestimates or overestimates the correction required to the time signal.

[1]

Markscheme

$\frac{{\Delta f}}{f} = \frac{{gh}}{{{c^2}}}$ so $\Delta f = \frac{{0.6 \times 20000000}}{{{{\left( {3 \times {{10}^8}} \right)}^2}}} = 1.3 \times {10^{ - 10}}$