Concept explainers
(a)
The escape speed from the surface of the present-day Sun.
(a)

Answer to Problem 46Q
Solution:
Explanation of Solution
Given data:
For present-day Sun,
Formula used:
Write the expression for the escape speed.
Here,
M is the mass of the Sun
R is the radius of the Sun
G is a constant having value
Explanation:
Recall the equation for the escape speed.
Substitute
Conclusion:
Therefore, the escape speed for the present-day Sun is
(b)
The escape speed from the surface of the Sun when it becomes a red giant with the mass as of the present-day but having a radius 100 times larger than of present-day.
(b)

Answer to Problem 46Q
Solution:
Explanation of Solution
Given data:
For a red giant Sun,
Formula used:
Write the expression for the escape speed.
Here,
M is the mass of the red giant Sun
R is the radius of the red giant Sun
G is a constant having value
Explanation:
Recall the equation for escape speed.
Substitute
Conclusion:
Therefore, the escape speed when the Sun becomes a red giant with a radius 100 times that of the present-day Sun is
(c)
The reason that a red giant can lose mass more easily than a main-sequence star based on the results obtained in (a) and (b).
(c)

Answer to Problem 46Q
Solution: In the case of the red giant, the matter can escape more easily because, in the red giant, the matter has to travel at one-tenth of the speed required to escape the present-day Sun. Hence, the red giant will lose mass more easily.
Explanation of Solution
Introduction:
The escape velocity is the minimum speed required to escape the gravitational attraction of a planet or a star.
Explanation:
The escape speed for present-day Sun is
Conclusion:
A red giant will lose mass more easily as compared to the present-day Sun.
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