SVG 319 Theory Questions: Solutions to Geodetic Potential Theory Problems

300 Level Survey and Geoinformatics Department exam questions and detailed answers. Download the answers in document format. Correct, detailed, and straightforward answers.

Questions:

(a) Show that the solution to the Laplace equation in geodetic coordinates is ∇2V=0∇2V=0.

(b) Given the following parameters of a homogeneous sphere, calculate the mass and density of the sphere:

• Acceleration due to gravity (a) = 981 m/s2981m/s2,

• Radius (R) = $6378\text{Km}$,

• Gravitational Constant = 6.67×10−11 m3/kg/sec26.67×10−11m3/kg/sec2.

(c) Taking values along the x, y, and z axes as -5 to +5 at step increases of +1 along each axis, plot a graph to show that density in a homogeneous sphere is maximum at the center and minimum at the surface if:

• Gravitational Constant = 6.67×10−3 m3/kg/sec26.67×10−3m3/kg/sec2,

• Potential of the sphere = $981$.

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