A recent high-precision determination of g has a quoted error of 6 parts in 10⁹. Estimate the increase in height at the Earth?s surface which gives a change in g equal to this error. If the dependence of g on geographical latitude at sea level is given by

g =g₀ (1 +? sin^2??).

where ? is the latitude and ? is a dimensionless constant with a value of 0.0053, estimate the northward displacement near latitude 45^o which gives a change in g equal to the quoted error.

8 = g0(1 + Bsin p).