
(a)
The Sun’s orbital speed in meters per second considers that it moves in a small orbit of radius
(a)

Answer to Problem 45Q
Solution:
12.5 m/s
Explanation of Solution
Given data:
The Sun moves in a small orbit of radius
Formula used:
Write the expression for the circumference
Write the expression for the speed
Here,
Write the formula for the conversion of the unit of time from years to seconds.
Explanation:
Recall the expression for the circumference
The expression for the Sun’s orbital speed
Substitute
Conclusion:
Hence, the Sun’s orbital speed in meters per second is 12.5 m/s.
(b)
The angular diameter of the Sun’s orbit as seen by an alien astronomer from a hypothetical planet orbiting the star Vega, which is 25 ly from the Sun. Also explain whether, or not, the Sun’s motion is discernible if the alien astronomer could measure positions to an accuracy of 0.001 arcsec.
(b)

Answer to Problem 45Q
Solution:
Explanation of Solution
Given data:
The hypothetical planet is orbiting the star Vega, which is 25 ly from the Sun.
Formula used:
Write the small angle formula.
Here,
Write the expression for the relation between the diameter D and the radius r.
Write the expression for converting the unit of distance from light years to meters.
Explanation:
Recall the expression for the relation between diameter D and radius r.
Substitute
Recall the expression for the small angle formula.
Substitute
The above value tells that the motion would just barely be discernible if the alien astronomer could measure positions to an accuracy of 0.001 arcsec.
Conclusion:
Hence, the angular diameter of the Sun’s orbit is
(c)
The answer, same as explained in part (b), but by considering that the astronomer is located on a hypothetical planet in the Pleiades star cluster, 360 ly from the Sun. Then provide an explanation whether the Sun’s motion is discernible to this astronomer.
(c)

Answer to Problem 45Q
Solution:
No, because the value of
Explanation of Solution
Given data:
The astronomer is located on a hypothetical planet in the Pleiades star cluster, 360 ly from the Sun.
Formula used:
Write the small angle formula.
Here,
Write the expression for converting the unit of distance from light years to meters.
Explanation:
Recall the small angle formula.
Substitute
The above value of
Conclusion:
Hence, the Sun’s motion would not be discernible to this astronomer.
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Chapter 8 Solutions
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