Concept explainers
(a)
The absolute magnitude of the star, HIP 72509, if the apparent magnitude of the star is
(a)
Answer to Problem 25Q
Solution:
Explanation of Solution
Given data:
The apparent magnitude of the star, HIP 72509, is
A parallax angle of the star, HIP 72509, is
Formula used:
The formula of the distance
The relation between the star’s apparent magnitude and absolute magnitude is written as:
Here,
Explanation:
The formula of the distance
The relation between the star’s apparent magnitude and absolute magnitude is written as:
Substitute
Substitute
Conclusion:
The absolute magnitude of the star, HIP 72509, is
(b)
The approximate ratio of luminosity of HIP 72509 to the Sun’s luminosity if the apparent magnitude of the star is
(b)
Answer to Problem 25Q
Solution:
Explanation of Solution
Given data:
The apparent magnitude of the star, HIP 72509, is
A parallax angle of the star, HIP 72509, is
Formula used:
The formula of the distance
Magnitude difference related to the brightness ratio:
Here,
The relation between luminosity of the stars from inverse-square law is:
Here,
Explanation:
The distance of star
Recall the expression that relates the magnitude difference to the brightness ratio for star HIP 72509 to the Sun.
The relation between luminosity of the star HIP 72509 and the Sun from inverse-square law is:
Rearrange for brightness ratio.
Combine the expression
Substitute
The distance of the Sun from Earth is
Substitute
Take anti log on both sides and solve as:
Conclusion:
The luminosity ratio of the star to the Sun is
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