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Unformatted text preview: PX266 Geophysics (2010/11) Lecture 6 Handout – Gravity Due to Extended Bodies and Gravity Anomalies Dr. Gavin Bell Gravity due to a spherical shell Calculate gravitational potential at P – initially P is outside the shell. Area of strip = d b b sin 2 Mass of strip = d b t sin 2 2 Contribution to gravitational potential at P : l d b t G dV sin 2 2 Integrate to get V ( r ) (adding potential – scalar): 2 sin 2 ) ( l d b t G r V Cosine rule: cos 2 2 2 2 br b r l Differentiate cosine rule: br dl l d d br dl l sin sin 2 2 Plug this into the definite integral and change the limits carefully: b r b r b r b r l br b Gt br dl b Gt r V 2 2 2 2 ) ( b sin Spherical shell: thickness t , radius b, density P O b Circular strip, width = b d Q l |OP| = r d...
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This note was uploaded on 09/12/2011 for the course ECON 102 taught by Professor Gavinbell during the Spring '11 term at LSE.
- Spring '11