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Analytical Mech Homework Solutions 66

# Analytical Mech Homework Solutions 66 - This is the same...

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This is the same expression as derived in Problem 6.3 for a particle dropped into a hole drilled through the earth. T 1.4 hours. 6.8 The 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 ( ) ( ) ,, xy a ε α = . The easiest way to solve this problem is to note that 1 60 = is small. The orbit is almost circular! 2 2 S GM m mv rr = and 2 S GM r = v with ra b =≈≈ when 0 4 310 S GM m v s  ≈=   More exactly cos rv v l β ×= = GG , but 2 ml k = (equation 6.5.19) Since S kG Mm = 2 S l GM = , hence () 1 2 cos S G M αβ == lv Or 1 2 1 cos S GM v = The angle can be calculated as follows: 22 1 yx ba += ( s e e a p p
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