A satellite orbits a planet at radius

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Uncertainty in measurement

Mathematical Methods for Physics, Ch The derivative as a physical instrument

Problem

r = 4.216\times10^{7}\,\mathrm{m}

, measured with an uncertainty

\delta r = 1.0\times10^{5}\,\mathrm{m}

. For a given planet, Kepler's third law gives

T^2 \propto r^3

, so

T \propto r^{3/2}

. At this radius the period is

T = 8.640\times10^{4}\,\mathrm{s}

. ((a)) Find the fractional error

\delta r/r

. ((b)) Use the differential of

T \propto r^{3/2}

to estimate the fractional error

\delta T/T

, and hence the absolute uncertainty

\delta T

in the period, in seconds.

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