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Unformatted text preview: et of mass m out of the gravitational ﬁeld of a planet with mass
M and radius R. Use Newton’s Law of Gravitation (see Exercise 29 in Section 6.4) and the fact that the initial kinetic
energy of 1 mv 2 supplies the needed work.
66. Astronomers use a technique called stellar stereography to determine the density of stars in a star cluster from the
observed (two-dimensional) density that can be analyzed from x2 1 dx 0.001 70. Estimate the numerical value of x0 e x2 d x by writing it as
the sum of x e d x and x4 e d x. Approximate the ﬁrst integral by using Simpson’s Rule with n 8 and show that the
second integral is smaller than x4 e 4 x d x, which is less than
0 x2 x2 71. If f t is continuous for t 0, the Laplace transform of f is...
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- Fall '07