Concept explainers
(a)
The angular distance in arcseconds between the star 2M1207 and its planet, as seen from Earth, considering this star is 170 light years from Earth.
(a)
Answer to Problem 52Q
Solution:
Explanation of Solution
Given data:
The star 2M1207 is 170 light years from Earth.
Formula used:
Write the expression for the small angle formula.
Here,
Explanation:
Recall the expression for the small angle formula.
Substitute 55 au for
Conclusion:
Hence, the angular distance in arcseconds between the star 2M1207 and its planet is
(b)
The orbital period of the orbiting star 2M1207, whose mass is 0.025 times that of the Sun, by considering that the distance between the star and its planet is the semi-major axis of the orbit.
(b)
Answer to Problem 52Q
Solution:
Explanation of Solution
Given data:
The mass of star 2M1207 is 0.025 times that of the Sun.
Formula used:
Write the formula for the relation between orbital period and orbital distance according to Kepler’s third law.
Here,
Explanation:
The formula for the relation between orbital period and orbital distance for Sun, according to Kepler’s third law is written as,
Here, subscript ‘Sun’ is used for the respective quantities of the Sun.
The formula for the relation between orbital period and orbital distance for star 2M1207, according to Kepler’s third law is written as,
Here, subscript ‘2M1207’ is used for the respective quantities of the star 2M1207.
Divide equation (2) by equation (1).
Substitute 1 yr for
Conclusion:
Hence, the orbital period for star 2M1207 is
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