Analytical Mech Homework Solutions 78

Analytical Mech Homework Solutions 78 - a(1 2 1 cos and the...

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6.27 (See Figure 6.10.1) From equation 6.5.18a 2 (1 ) 1c o s a r ε θ = + and the data on ellipses in Figure 6.5.1 ) pa = so ) o s rp + = + For a parabolic orbit, 1 = The comet intersects earth’s orbit at ra = . 2 o s p a = + 2 cos 1 p a =− + 6.28 (See Figure 6.10.1) T along the comet’s trajectory inside earth’s orbit d = t From equation 6.5.4, 22 d rr dt l == ± so 2 rd dt l = 2 T l = From equation 6.5.18a 2 ) o s a r = + and the data on ellipses in Figure 6.5.1 ) = so ) o s + = + From equation 6.5.18b, with 1 = for a parabolic orbit: 2 o s p r = + At 2 π = the distance to the comet is 2 2 o s 2 p α = + From equation 6.5.19, 2 ml k = , where kG M m = , so
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