Calculating Tb/Ta Ratio for Planets A & B

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To calculate the Tb/Ta ratio for planets A and B, apply Kepler's Third Law, which states that the square of the orbital period is proportional to the cube of the semi-major axis. Given that planet B has twice the mass of planet A and its semi-major axis is also twice as large, the relationship can be expressed as Tb^2/Ta^2 = (2a)^3/(a^3). Simplifying this leads to Tb/Ta = √(2^3) = √8, resulting in a ratio of Tb/Ta = 2√2. Understanding this relationship is crucial for solving the problem accurately.
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Tb / Ta = ?

i have a final question, which is how do i find this. i know what the question is askin i just don't understand how to get the answer

Two planets A and B, where B has twice the
mass of A, orbit the Sun in elliptical orbits.
The semi-major axis of the elliptical orbit of
planet B is two times larger than the semi-
major axis of the elliptical orbit of planet A.
What is the ratio of the orbital period of
planet B to that of planet A?
 
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HINT:Apply the 3-rd law of Kepler...

Daniel.
 
What is the equation which relates the semi-major axis of an orbit to the orbital period?
 

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