Question $3(20)$

A ship sails $1800km$ by great circle arc until it reaches $45N.$ At that moment its longitude is $40E$ and its azimuth is $40.$ What was its initial position and azimuth? $(14+6).$

Question $4(3+3+3+11)$

a$.$ What is the gravitational law for two point masses? $(3)$

b$.$ What is gravitational potential? $(3)$

c$.$ Define an equipotential surface and give one example $(3)$

d$.$ Gravitational acceleration at a given latitude $(g)$ is computed by:

$g_{}=g_0(1+si{n}^2+si{n}^2)$

where $g0$ is the value at the equator, of $978\mathrm{.}0318$ gals $(9\mathrm{.}780318\frac{m}{s^2}),$

$a=0\mathrm{.}0053024$

$=-0\mathrm{.}0000058$

Determine gravitational acceleration at the following latitudes and explain the change in results: $10,45$ and $90$

Question $5$

Given the ECEF coordinates of point C $($WGS$84,a=6378137\mathrm{.}00m$ and $b=6356752\mathrm{.}31m$ as follows:

$x_C=12,046\mathrm{.}58m,Y_C=-4,849,394\mathrm{.}08m,ZC=-4,553,160\mathrm{.}06m$

Compute geodetic coordinates. $(20).$