Concept explainers
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
(a)
The velocity of the probe should be reduced at point
Answer to Problem 12.105P
The velocity reduction at point
Explanation of Solution
Given information:
Initial velocity corresponding to a parabolic orbit,
Angular momentum of a unit mass,
If the trajectory is an elliptical orbit,
Calculation:
Initial velocity corresponding to a parabolic orbit,
Since,
Then consider the first transfer elliptical orbit,
Applying angular momentum equation,
Therefore the velocity reduction at point
(b)
The velocity of the probe should be reduced at
Answer to Problem 12.105P
The velocity reduction at point
Explanation of Solution
Given information:
Angular momentum of a unit mass,
If the trajectory is an elliptical orbit,
Calculation:
Consider the first transfer elliptical orbit,
Then consider the second transfer elliptical orbit,
Since,
Applying angular momentum equation,
Therefore, the velocity reduction at point
(b)
The velocity of the probe should be reduced at
Answer to Problem 12.105P
The velocity reduction at point
Explanation of Solution
Given information:
Angular momentum of a unit mass,
Initial velocity corresponding to a circular orbit,
Calculation:
Consider the second transfer elliptical orbit,
Then consider the circular orbit at
Since,
Therefore the velocity reduction at point
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Chapter 12 Solutions
Vector Mechanics For Engineers
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