Explanation Given: The maximum and minimum distance from center of the planet is shown in Figure (1). The mass of the planet M = 0.6 ( 5.976 × 10 24 kg ) . The gravitational constant is G = 66.73 × 10 − 12 m 3 / kg ⋅ s 2 From Figure (1) write the value for minimum distance r p . r p = 6 Mm 10 6 m 1 Mm = 6 ( 10 6 ) m From Figure (1) write the value for maximum distance r a . r a = 100 Mm 10 6 m 1 Mm = 100 ( 10 6 ) m Write the expression for the minimum distance from the centre of Planet. r a = r 0 2 G M ( r 0 υ 0 2 ) − 1 (I) Here, minimum distance from the center of planet is r 0 and the initial speed of the rocket υ 0 and the gravitational constant is G and mass of the planet is M . From Figure (1) write the equation for the h . h = r p υ p = r a υ a h = r p υ B = r a υ A ' (II) Here, h is constant at any positions of the orbit , the speed of the rocket at apogee is υ a , the speed of the rocket at perigee is υ p , r p is the minimum distance from the center of planet or perigee and r a is the orbit maximum distance from the center of planet or apogee. Write the expression for period of elliptical orbit. T = π r p υ p ( r p + r a ) r p r a (III) Here, period is T , r p is minimum distance from the center of planet or perigee and r a is the maximum distance from the center of planet or apogee. Write the expression for time required to travel from A to A ' . t = T 2 (IV) Here, period is T and time is t . Conclusion: Since, r 0 = r p and υ 0 = υ p . Substitute r p for r 0 and υ p for υ 0 in Equation (I). r a = r 0 2 G M ( r 0 υ 0 2 ) − 1 r a = r p 2 G M ( r p υ p 2 ) − 1 2 G M e ( r p υ p 2 ) M = r p r a + 1 2 G M ( r p υ p 2 ) = r p + r a r a υ p = 2 G M r a r p ( r p + r a ) (V). Since, υ p = υ B . Substitute υ B for υ p , [ 100 ( 10 6 ) m ] for r a , [ 6 ( 10 6 ) m ] for r p , 66

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Conservation of Energy

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

Question

Chapter 13.7, Problem 130P

To determine

The required free-flight speed rocket must have at A' and the time t required for the rocket to land, going from A' to B' .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.7, Problem 129P

Chapter 13.7, Problem 131P

Students have asked these similar questions

The resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {r

Please solve this problem as soon as possible My ID# 016948724

The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear 5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft? TS I y 18T 32T This a 12 x 18T C 48T 5

Chapter 13 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 13.4 - The 10-kg block is subjected to the forces shown....Ch. 13.4 - The 10-kg block is subjected to the forces shown....Ch. 13.4 - Determine the initial acceleration of the 10-kg...Ch. 13.4 - Prob. 4PP Ch. 13.4 - Prob. 1FP Ch. 13.4 - If motor M exerts a force of F = (10t2 + 100) N on...Ch. 13.4 - A spring of stiffness k = 500 N/m is mounted...Ch. 13.4 - Prob. 5FP Ch. 13.4 - Block B rests upon a smooth surface. If the...Ch. 13.4 - The 6-lb particle is subjected to the action of...

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.

The required free-flight speed rocket must have at A ' and the time t required for the rocket to land, going from A ' to B ' .

Solution Summary: The author determines the required free-flight speed rocket must have at A' and the time t required for the rocket to land.

Concept explainers

Videos

The required free-flight speed rocket must have at A' and the time t required for the rocket to land, going from A' to B' .

Want to see the full answer?

Chapter 13 Solutions