Concept explainers
(a)
Angular momentum per unit mass and energy per unit mass.
Answer to Problem 13.118P
We got
Angular momentum per unit mass
Energy per unit mass
Explanation of Solution
Given information:
Radius
Speed
Planet mass
Concept used:
Following formulae will be used.
Calculation:
Angular momentum per unit mass,
Energy per unit mass,
Conclusion:
We got
Angular momentum per unit mass
Energy per unit mass
(b)
Formula derivation.
Answer to Problem 13.118P
We got required formula as
Explanation of Solution
Given information:
Radius
Speed
Planet mass
Concept used:
Following formulae will be used.
Calculation:
Angular momentum per unit mass,
Energy per unit mass,
By solving of quadratic equation and rearranging,
Conclusion:
We got required formula as
(c)
The eccentricity of the trajectory.
Answer to Problem 13.118P
We got eccentricity as
Explanation of Solution
Given information:
Radius
Speed
Planet mass
Concept used:
Following formulae will be used.
Calculation:
We know when,
Also,
By comparing,
Conclusion:
We got eccentricity as
(d)
To show:
the trajectory shape depending on the energy type.
Answer to Problem 13.118P
Conditions have been shown below for different shape of trajectory at different eccentricity.
Explanation of Solution
Given information:
Radius
Speed
Planet mass
Concept used:
Following formulae will be used.
Calculation:
We know when,
For circular orbit
Conclusion:
Conditions have been shown above for different shape of trajectory at different eccentricity.
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Chapter 13 Solutions
Vector Mechanics For Engineers
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