12th Edition

ISBN: 9781260663778

Author: BEER

Publisher: MCG

Concept explainers

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Textbook Question

Chapter 13.2, Problem 13.117P

Using the answers obtained in Prob. 13.108, show that the intended circular orbit and the resulting elliptic orbit intersect at the ends of the minor axis of the elliptic orbit.

13.108 A satellite is projected into space with a velocity v₀ at a distance r₀ from the center of the earth by the last stage of its launching rocket. The velocity v₀ was designed to send the satellite into a circular orbit of radius r₀. However, owing to a malfunction of control, the satellite is not projected horizontally but at an angle α with the horizontal and, as a result, is propelled into an elliptic orbit. Determine the maximum and minimum values of the distance from the center of the earth to the satellite.

Fig. P13.108

Chapter 13.2, Problem 13.117P, Using the answers obtained in Prob. 13.108, show that the intended circular orbit and the resulting

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.2, Problem 13.116P

Chapter 13.2, Problem 13.118P

Students have asked these similar questions

A space probe is to be placed in a circular orbit of radius 4o00 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 ra= 9004 km and rg= 180 004 km, and that the probe approaches A on a parabolic trajectory, determine the time needed for the space probe to travel from A to Bon its first transfer orbit. Approach trajectory Second transfer orbit В 4000 km First transfer orbit The time needed for the space probe to travel from A to B on its first transfer orbit is |h.

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.

In Prob. 13.109, a space vehicle was in a circular orbit at an altitude of 225 mi above the surface of the earth. To return to earth it decreased its speed as it passed through A by firing its engine for a short interval of time in a direction opposite to the direction of its motion. Its resulting velocity as it reached point B at an altitude of 40 mi formed an angle fB = 60° with the vertical. An alternative strategy for taking the space vehicle out of its circular orbit would be to turn it around so that its engine pointed away from the earth and then give it an incremental velocity DvA toward the center O of the earth. This would likely require a smaller expenditure of energy when firing the engine at A, but might result in too fast a descent at B. Assuming that this strategy is used, use computational software to determine the values of fB and vB for an energy expenditure ranging from 5 to 100 percent of that needed in Prob. 13.109. 13.109. A space vehicle is in a circular…

Chapter 13 Solutions

VECTOR MECH. FOR EGR: STATS & DYNAM (LL

Ch. 13.1 - Block A is traveling with a speed v0 on a smooth...Ch. 13.1 - A 400-kg satellite is placed in a circular orbit...Ch. 13.1 - A 0.5-lb stone is dropped down the bottomless pit...Ch. 13.1 - A baseball player hits a 5.1-oz baseball with an...Ch. 13.1 - A 500-kg communications satellite is in a circular...Ch. 13.1 - Prob. 13.5P Ch. 13.1 - In an ore-mixing operation, a bucket full of ore...Ch. 13.1 - Determine the maximum theoretical speed that may...Ch. 13.1 - A 2000-kg automobile starts from rest at point A...Ch. 13.1 - An athlete is holding 30 lb of weights at a height...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Solution Summary: The author illustrates how the circular orbit and the resulting elliptic orbit intersect at the ends of the minor axis.

Concept explainers

Videos

Want to see the full answer?

Chapter 13 Solutions