Physics

Problem

At a geophysical laboratory the surface acceleration due to gravity is measured as

9.806\,\text{m/s}^2

with an uncertainty of

\pm0.05\%

. The radius of the Earth is taken as

6.371\times10^{6}\,\text{m}

with an uncertainty of

\pm0.10\%

. An accepted value for the mass of the Earth is

5.972\times10^{24}\,\text{kg}

. Based on these data: a. (a) Calculate the product

GM_{\!E}

for the Earth, where

G

is the universal gravitational constant and

M_{\!E}

is the mass of the Earth. b. (b) Using the accepted mass of the Earth, determine a value of

G

implied by your result in part (a). c. (c) Estimate the percentage uncertainty in the value of

G

obtained in part (b) that arises from the stated uncertainties in

g

and

R_{\!E}

. (Assume the uncertainty in

M_{\!E}

is negligible in comparison.)