- #1

lizzyb

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## Homework Statement

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?

## Homework Equations

[tex]T^2 = (\frac{4 \pi^2}{G M}) r^3[/tex]

## The Attempt at a Solution

[tex]M_B = 2 M_A[/tex]

[tex]a_B = 2 a_A[/tex]

[tex]\frac{T_B}{T_A} = \frac{\sqrt{\frac{4 \pi^2}{G 2 M_A} 8 a_A^3}}{\sqrt{\frac{4 \pi^2}{G M_A} a_A^3}} = \sqrt{\frac{8}{2}} = \sqrt{ 4 } = 2[/tex]

but that was wrong. ?