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Calculate of the questión? coordinate manifold of a gravitational field, with coordinates 2.5. In the 0 X 1, X 2, X-(r, r,6, φ), selected Christoffel symbols are known to be c2 , and 22 33 non-zero. Here, f=_2MG1c2r, where are 12 33/ 13J' 23 G ating object. Let M be the mass of the sun in the following calculation. 667 X 10-11 m3/kg sec2, c 3 x 108 m/sec, and M is the mass of the gravi- (a) A radially oriented vector segment (Ax) which has unit length at the surface of the sun (r = rs) is parallel-translated radially outward to the earth's orbit, at SE.Calculate the shift in coordinate measurement of the length of this vector at the completion of this transport. [Neglect effect of change in (x1) on its contri- bution to x, and consider only the gravitational field of the sun, neglecting that of the earth. b) Carry out a similar calculation for a time interval (x) which measures one sec- ond in length at rs, and is then parallel-translated radially to rsE

Answer 1

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SE V CE vi dn ves)= (Ax' ) given and Lee- v'(E)= (4x% inside the in terus We can/ fake vi 느△x, as swtgested in tne question SE VO ho = 2.948 Km SE de

SE d Jxm PSE ose an yo SE. Ln I:o 600 0214 m

SE SE 0 1 on iv 트 )((42) 0 99999 286 S