(a)
The total orbital momentum of the Sun-Jupiter System.
(a)
Answer to Problem 2.6P
The momentum of the combined system is
Explanation of Solution
Write the expression for the reduced mass of the system
Here,
Write the expression for the total
Here,
Conclusion:
Substitute
Substitute
Thus, the momentum of the combined system is
(b)
The contribution of the Sun in the total orbital angular momentum.
(b)
Answer to Problem 2.6P
The contribution of the Sun in the angular momentum is
Explanation of Solution
Write the expression for the distance of Sun from the centre of mass
Here,
Write the expression for the Sun’s orbital speed.
Here,
Write the expression for the momentum of orbital motion of Sun
Here,
Conclusion:
Substitute
Substitute
Substitute
Thus, the contribution of the Sun in the angular momentum is
(c)
The contribution of the Jupiter in the orbital angular momentum and the difference with calculation of part (a) and part(b).
(c)
Answer to Problem 2.6P
The contribution of the Jupiter in the angular momentum is
Explanation of Solution
Write the expression for the distance of Jupiter from the centre of mass
Here,
Write the expression for the Jupiter’s orbital speed.
Here,
Write the expression for the momentum of orbital motion of Jupiter
Here,
Write the expression for the difference in momentum of part (a) and part (b).
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the contribution of the Jupiter in the angular momentum is
(d)
The angular momentum of Sun and Jupiter by using moment of inertia.
(d)
Answer to Problem 2.6P
The angular momentum by using mass moment of inertia, for the Sun is
Explanation of Solution
Write the expression for the angular momentum of the Sun
Here,
Write the expression for the angular momentum of the Jupiter.
Here,
Conclusion:
Substitute
Substitute
Thus, the angular momentum by using mass moment of inertia, for the Sun is
(e)
The part which is making largest contribution to the angular momentum of the Sun-Jupiter combines system.
(e)
Answer to Problem 2.6P
The Sun is making largest contribution to the angular momentum of the Sun-Jupiter combines system.
Explanation of Solution
From part (d) and part (c) it is clear that Sun has the highest contribution in the angular momentum of the Sun-Jupiter combined system. Since the value of the angular momentum is
Conclusion:
Thus, the Sun is making largest contribution to the angular momentum of the Sun-Jupiter combines system.
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