Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Textbook Question

Chapter 12.3, Problem 12.110P

A space probe is to be placed in a circular orbit of radius 4000 km about the planet Mars. As the probe reaches A, the point of its original trajectory closest to Mars, it is inserted into a first elliptic transfer orbit by reducing its speed. This orbit brings it to point B with a much-reduced velocity. There the probe is inserted into a second transfer orbit by further reducing its speed. Knowing that the mass of Mars is 0.1074 times the mass of the earth, that r_A = 9000 km and r_B = 180 000 km, and that the probe approaches A on a parabolic trajectory, determine the time needed for the space probe to travel from A to B on its first transfer orbit.

Fig. P12.110

Chapter 12.3, Problem 12.110P, A space probe is to be placed in a circular orbit of radius 4000 km about the planet Mars. As the

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Chapter 12.3, Problem 12.109P

Chapter 12.3, Problem 12.112P

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A space probe is to be placed in a circular orbit of 5600-mi radius about the planet Venus in a specified plane. As the probe reaches A, the point of its original trajectory closest to Venus, it is inserted in a first elliptic transfer orbit by reducing its speed by ΔvA. This orbit brings it to point B with a much reduced velocity. There the probe is inserted in a second transfer orbit located in the specified plane by changing the direction of its velocity and further reducing its speed by ΔvB. Finally, as the probe reaches point C, it is inserted in the desired circular orbit by reducing its speed by ΔvC. Knowing that the mass of Venus is 0.82 times the mass of the earth, that rA = 9.3 × 103 mi and rB = 190 × 103 mi, and that the probe approaches A on a parabolic trajectory, determine by how much the velocity of the probe should be reduced (a) at A, (b) at B, (c) at C.

A spacecraft of mass m describes a circular orbit of radius ị around the earth. (a) Show that the additional energy AE that must be imparted to the spacecraft to transfer it to a circular orbit of larger radius r, is GMm(r2 – r¡) ΔΕ= where M is the mass of the earth. (b) Further show that if the transfer from one circular orbit to the other is executed by placing the space- craft on a transitional semielliptic path AB, the amounts of energy AE, and AEg which must be imparted at A and B are, respectively, proportional to r, and r¡: ΔΕΞ ΔΕΔΕ, ΔΕ

A space vehicle is in a circular orbit of 2200-km radius around the moon. To transfer it to a smaller circular orbit of 2080-km radius, the vehicle is first placed on an elliptic path AB by reducing its speed by 26.3 m/s as it passes through A . Knowing that the mass of the moon is 73.49 × 1021 kg, determine (a) the speed of the vehicle as it approaches B on the elliptic path, (b) the amount by which its speed should be reduced as it approaches B to insert it into the smaller circular orbit.

Chapter 12 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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Solution Summary: The author calculates the time needed for the space probe to travel from A to B on its first transfer orbit.

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