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A binary star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses m and 2m and let their separation be l. Their time period of rotation about their centre of mass will be proportional to :
- a)l3/2
- b)m1/2
- c)l
- d)m–1/2
Correct answer is option 'A,D'. Can you explain this answer?
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A binary star is a system of two stars rotating about their centre of ...
The correct answers are: l3/2, m–1/2
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A binary star is a system of two stars rotating about their centre of ...
The time period of rotation about their center of mass can be calculated using Kepler's Third Law of Planetary Motion, which states that the square of the period of revolution is directly proportional to the cube of the semi-major axis.
In this case, the semi-major axis can be approximated as half of the separation between the two stars, denoted as "l/2". The period of rotation is denoted as "T".
By applying Kepler's Third Law, we have:
T^2 ∝ (l/2)^3
T^2 ∝ l^3/8
Taking the square root on both sides, we have:
T ∝ l^(3/2)
Therefore, the answer is (a) l^(3/2).
In this case, the semi-major axis can be approximated as half of the separation between the two stars, denoted as "l/2". The period of rotation is denoted as "T".
By applying Kepler's Third Law, we have:
T^2 ∝ (l/2)^3
T^2 ∝ l^3/8
Taking the square root on both sides, we have:
T ∝ l^(3/2)
Therefore, the answer is (a) l^(3/2).
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A binary star is a system of two stars rotating about their centre of ...
The correct answers are: l3/2, m–1/2
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