p01_035 - 35(a When is measured in radians it is equal to...

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Unformatted text preview: 35. (a) When is measured in radians, it is equal to the arclength divided by the radius. For very large radius circles and small values of , such as we deal with in this problem, the arcs may be .. .. approximated as . R Sun ......................................................................... .......... ...... . .. ... . .. ....... .... ...... .. ......... ...... .. ... ......... . . .... .... .. . straight lines ... ... ... ....... ......... .... .. ..... ......... ... ... .... ... ........ ........ . .. ... ..... .. . ... ......... .. .... .. .. ......... ... .. .. ......... .... .. .... .. . .... .. .. which for our . .. ......... ... .. ......... .... .. . . .. . . ......... . ......... . ... .. . ... .. . . . .. . . . . ... .. ... .. . . . . .. purposes corre. . . . ... .. ... .. . . .. d D .... . .... .. . . . . ... .. .. ... . . . . .. .... . . ... .. . . . spond to the di... .. . . .. ... . . ........ .. .... . ........ . . ... .. . .. ........ ........ . .. ... .. .. ... . ........ ........ .. .... .. .. ... .. .. ........ ........ .. . ameters d and ... .. .. .. ... ........... ... ........... .. .. .... ...... .. .. ... ... .. . ... .. ..... ....... ... ....... .. ....... ... .. ..... ..... ... ... R Moon .................... D of the Moon ................... and Sun, respectively. Thus, = which yields D/d = 400. (b) Various geometric formulas are given in Appendix E. Using rs and rm for the radius of the Sun and Moon, respectively (noting that their ratio is the same as D/d), then the Sun's volume divided by that of the Moon is 3 4 3 rs 3 rs = = 4003 = 6.4 107 . 4 3 rm rm 3 (c) The angle should turn out to be roughly 0.009 rad (or about half a degree). Putting this into the equation above, we get d = RMoon = (0.009) 3.8 105 3.4 103 km . d R Moon = D R Sun = R Sun D = R Moon d ...
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This note was uploaded on 06/11/2008 for the course PHY 035 taught by Professor Furlan during the Spring '08 term at UniFor.

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