Answer:
[tex]\frac{v_A}{v_B}=0.402[/tex]
Explanation:
The speed that planets must have in order for their orbit to be stable, is given by:
[tex]v=\sqrt{\frac{GM}{r}}[/tex]
Here v It is called orbital speed, G is the gravitational constant, M is the mass of the star and r is the radius of the orbit. In this case we have:
[tex]r_A=6.2r_B[/tex]
So, the ratio of their speed is:
[tex]\frac{v_A}{v_B}=\frac{\sqrt{\frac{GM}{r_A}}}{\sqrt{\frac{GM}{r_B}}}\\\frac{v_A}{v_B}=\sqrt{\frac{r_B}{r_A}}\\\frac{v_A}{v_B}=\sqrt{\frac{r_B}{6.2r_B}}\\\frac{v_A}{v_B}=\sqrt{\frac{1}{6.2}}\\\frac{v_A}{v_B}=0.402[/tex]
