This is the same expression as derived in Problem 6.3 for a particle dropped into a hole drilled through the earth. T1.4≈hours. 6.8The Earth’s orbit about the Sun is counter-clockwise as seen from, say, the north star. It’s coordinates on approach at the latus rectum are ( ) ( ),,xyaεα=−. The easiest way to solve this problem is to note that 160=is small. The orbit is almost circular! 22SGM mmvrr∴=and 2SGMr=vwith rab=≈≈when 0≈4310SGMmvs≈=⋅More exactlycosrvvlβ×==GG, but 2mlk=(equation 6.5.19) Since SkGMm=2SlGM=, hence ()12cosSGMαβ==lvOr 121cosSGMv=The angle can be calculated as follows: 221yxba+=(seeapp
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