Concept explainers
(a)
The semi major axes of the orbits of stars
(a)

Answer to Problem 41Q
Solution:
The S0-2 star has a semi-major axis of
Explanation of Solution
Given data:
The black hole in Sagittarius
Formula used:
Write the expression for Newton’s form of Kepler’s third law.
Here,
Conversion from
Conversion from seconds to years is done as:
Conversion from mass (in kg.) to solar mass is done as:
Explanation:
Recall the expression for Newton’s form of Kepler’s third law.
Rearrange the expression in terms of semi major axis.
For
Further calculate as,
Now, for
Substitute
Further calculate as,
Conclusion:
Therefore, the semi major axes of the orbits of stars
(b)
The angular size of the semi major axes of the orbits of stars
(b)

Answer to Problem 41Q
Solution:
The angular size of the orbit of S0-2 star is
Explanation of Solution
Given data:
Sagittarius
Formula used:
Write the small-angle formula.
Here, α is the angle subtended by the object (in arcseconds), d is the distance between the observer and the object and D is the linear size of the object.
Conversion formula for 1 pc to au is,
Explanation:
The linear size of an orbit can be taken as twice its semi major axis.
The angular size of the orbit of star
Substitute
Similarly, the angular size of the orbit of star
Substitute
These angle are quite small. To study the motion of such stars with very small angular sizes, high resolution infrared imaging is adopted because for the observation of far off tiny objects, radiation of large wavelengths must be used.
Conclusion:
The angular size of each orbit of stars
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Chapter 22 Solutions
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