Concept explainers
(a)
The orbital period of a star, revolving around Sagittarius
(a)
Answer to Problem 42Q
Solution:
Explanation of Solution
Given data:
Orbital velocity of the star is
Formula used:
The expression for the orbital period of a star:
Here,
Conversion from
Conversion from seconds to year,
Explanation:
Recall the expression for the period of an orbiting object.
Substitute
Conclusion:
Therefore, the orbital period of the star is
(b)
The sum of the masses of Sagittarius A* and the star in terms of solar mass. It is given that the star orbits around Sagittarius
(b)
Answer to Problem 42Q
Solution:
Explanation of Solution
Given data:
Orbital velocity of the star is
Formula used:
Write the expression for Newton’s form of Kepler’s third law.
Here,
From the previous subpart, the orbital period of the star is
Conversion from
Conversion from mass (in kg.) to solar mass,
Explanation:
In the previous subpart (b), the orbital period of the star was calculated as
Recall the expression for Newton’s form of Kepler’s third law.
Rearrange the expression in terms of the masses of the star and Sagittarius A*,
Substitute
The sum of masses in terms of solar mass of the star and Sagittarius A*.
Conclusion:
Hence, the sum of masses in terms of solar mass of Sagittarius A* and the star is
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Chapter 22 Solutions
Universe
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