978-0078112829 Chapter 3 Solution Manual Part 1 | Course Paper

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Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Problem 3.1 If

f1

2tan x

21

6tan 3x

2

, then show that

df

dx 1

1cos x

 2

, thereby verifying the integral

in Equation 3.4.

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Problem 3.2 Find the three positive roots of the equation

10esin xx25x4

to eight significant

figures. Use:

(a) Newton’s method.

(b) Bisection method.

25xi410esin xi

xl

xu

xl

xu

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Problem 3.3 Find the first four non-negative roots of the equation

tan x

 tanh x

 

to eight

significant figures. Use:

(a) Newton’s method.

(b) Bisection method.

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 3

Problem 3.4 In terms of the eccentricity e, the period T and the angles



and



(in radians) find the

time t required to fly from point 1 to point 2 on the ellipse. C is the center of the ellipse.

Problem 3.5 Calculate the time required to fly from P to B, in terms of the eccentricity e and the period

T. B lies on the minor axis.

Problem 3.6 If the eccentricity of the elliptical orbit is 0.3, calculate, in terms of the period T, the time

required to fly from P to B.

Problem 3.7 If the eccentricity of the elliptical orbit is 0.5, calculate, in terms of the period T, the time

required to fly from P to B.

Problem 3.8 A satellite is in earth orbit for which the perigee altitude is 200 km and the apogee altitude

is 600 km. Find the time interval during which the satellite remains above an altitude of 400 km.

Problem 3.9 An earth-orbiting satellite has a perigee radius of 7000 km and an apogee radius of 10 000

km. (a) What true anomaly



is swept out between t = 0.5 hr and t = 1.5 hr after perigee passage? (b)

What area is swept out by the position vector during that time interval?

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