Explanation Draw the free-body diagram of the spacecraft with respect to earth as shown in Figure (1). Write the expression for the semi-major axis of ellipse. a = r max + r min 2 (I) Here, semi-major axis of ellipse is a , maximum radial distance is r max and minimum radial distance is r min . Write the expression for the radial distance of the spacecraft. r = b 2 + ( a − r min ) 2 (II) Here, radial distance of the spacecraft is r and minor axis is b . Write the expression for the radial velocity of the spacecraft. r ˙ = v cos α (III) Here, radial velocity of the spacecraft is r ˙ , velocity of the spacecraft is v and angle of the velocity of the spacecraft is α . Write the expression for the angular velocity of the spacecraft. θ ˙ = v sin α r (IV) Here, angular velocity of the spacecraft is θ ˙ . Apply the dynamic force equilibrium condition on the spacecraft along the radial direction. ∑ F r = m a r m g R 2 r 2 = m ( r ¨ − r θ ˙ 2 ) r ¨ = r θ ˙ 2 − g R 2 r 2 (V) Here, mass of the earth is m , radius of the earth is R , radial component of acceleration of the spacecraft is a r , angle made by the spacecraft with the axis is θ and radial acceleration of the spacecraft is r ¨ . Apply the dynamic force equilibrium condition on the spacecraft along the tangential direction. ∑ F θ = m a θ 0 = m ( r θ ¨ + 2 r ˙ θ ˙ ) θ ¨ = − 2 r ˙ θ ˙ r (VI) Here, tangential component of acceleration of the vehicle is a θ and tangential acceleration of the spacecraft is θ ¨ . Conclusion: Calculate the maximum radial distance. r max = 22300 mi + R Substitute 3959 mi for R . r max = 22300 mi + 3959 mi = 26259 mi Calculate the minimum radial distance. r min = 200 mi + R Substitute 3959 mi for R . r min = 200 mi + 3959 mi = 4159 mi Substitute 26259 mi for r max and 4159 mi for r min in Equation (I). a = 26259 mi + 4159 mi 2 = 15209 mi Calculate the angle made by the velocity of the spacecraft. α = tan − 1 ( b a − r min ) Substitute 10450 mi for b , 15209 mi for a and 4159 mi for r min . α = tan − 1 ( 10450 mi 15209 mi − 4159 mi ) = 43.4 ° Substitute 10450 mi for b , 15209 mi for a and 4159 mi for r min in Equation (II). r = ( 10450 mi ) 2 + ( 15209 mi − 4159 mi ) 2 = 15208

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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 3.5, Problem 91P

To determine

The radial velocity, angular velocity, radial acceleration and angular acceleration of the spacecraft.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.5, Problem 90P

Chapter 3.5, Problem 92P

Students have asked these similar questions

42 VOLTE 4G+ EV Suggested Que... Problem: You and your team are tasked with designing an around-coil system for an air- conditioning unit that will be installed in a hospital. The system must provide a controlled environment for the hospital's air-conditioning needs, ensuring that fresh air is brought in while exhaust air is expelled, without allowing contamination between the two airflow directions. The air-conditioning system will include two coils and two pumps (one duty pump and one standby pump) in a configuration that accommodates both exhaust and supply airflows. The system needs to comply with ASHRAE Standards, and ASME BPVC Section VIII, with attention to safety, reliability, and efficiency. The system will be used in a climate with moderate temperature variations, and its design will need to consider a range of operating and design specifications. Given data Desired Pressure in the Pipe: According to the (ASHRAE) standard for pressure drop limits. Pipe Diameter: Must comply…

compute the work done by a fuel-water interaction assuming that the 40,000 kg of mixed oxide fuel and 4000 kg of water expand independently and isentropically to 1 atmosphere. Assume that the initial fuel and water conditions are such that equilibrium mixture temperature achieved is 1945 K. Other water conditions are as follows: Tinitial = 400K, ro initial = 945 kg/m^3, cv = 4184 J/kg-K. Caution: Equation 6.9 is inappropriate for these conditions since the cooland at state e is supercritial.

If the W12x50 beam below is made of steel having an allowable bending stress of 36 ksi and an allowable shear stress of 15 ksi, determine the maximum cable force, P, that can safely be supported by the beam.

Chapter 3 Solutions

Engineering Mechanics: Dynamics

Ch. 3.4 - Prob. 1P Ch. 3.4 - The 50-kg crate is stationary when the force P is...Ch. 3.4 - At a certain instant, the 80-lb crate has a...Ch. 3.4 - A man pulls himself up the 15° incline by the...Ch. 3.4 - The 10-Mg truck hauls the 20-Mg trailer. If the...Ch. 3.4 - A 60-kg woman holds a 9-kg package as she stands...Ch. 3.4 - During a brake test, the rear-engine car is...Ch. 3.4 - Prob. 8P Ch. 3.4 - The inexperienced driver of an all-wheel-drive car...Ch. 3.4 - Prob. 10P

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.