Concept explainers
Find the resulting values of angle
Answer to Problem 13.111P
The resulting values of angle
Explanation of Solution
Given information:
The altitude of the space vehicle in a circular orbit
The altitude of the surface of the earth from the center of the earth
The radius of the earth (R) is
The velocity at B forms an angle
The acceleration due to gravity (g) is
Assume the energy is used with only 50 percent of the energy expenditure used in Problem 110.
Calculation:
Convert the radius of the earth (R) from kilometer to meter:
Here,
Substitute
The expression for the geocentric force acting on the spacecraft when it is on the surface of earth
Here, G is the universal gravitational constant, M is the mass of the earth and m is the mass of the space vehicle.
The expression for the force acting on the spacecraft on the surface of the earth due to gravity
Substitute
Substitute
Calculate the altitude of the point A from the center of the earth
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Calculate the altitude of the point B from the center of the earth
Substitute
The expression for the normal acceleration
The expression for the geocentric force acting on the space vehicle when it is on the surface of earth (F) as follows:
Here, G is the universal gravitational constant, M is the mass of the earth and m is the mass of the space vehicle.
Calculate the velocity in circular orbit
Substitute
Substitute
The expression for the kinetic energy at point A
Here, m is the mass of the satellite.
Calculate the gravitational potential energy at point A
Substitute
The expression for the kinetic energy of the satellite at point B
Calculate the gravitational potential energy at point B
Substitute
The expression for the principle of conservation of energy at the point A to point B as follows:
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Calculate the energy expenditure
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Calculate the energy used
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Consider the additional kinetic energy at the point A:
Substitute
The expression for the kinetic energy at point A
The expression for the principle of conservation of energy at the point A to point B as follows:
Substitute
Substitute
The expression or the principle of conservation of angular momentum at point A to the point B as follows:
Substitute
Therefore, the resulting values of angle
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Chapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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