Question

Planet A and planet B are in circular orbits around a distant star.

Answer 1

Answer:

$\frac{v_A}{v_B}=0.402$

Explanation:

The speed that planets must have in order for their orbit to be stable, is given by:

$v=\sqrt{\frac{GM}{r}}$

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:

$r_A=6.2r_B$

So, the ratio of their speed is:

$\frac{v_A}{v_B}=\frac{\sqrt{\frac{GM}{r_A}}}{\sqrt{\frac{GM}{r_B}}}\\\frac{v_A}{v_B}=\sqrt{\frac{r_B}{r_A}}\\\frac{v_A}{v_B}=\sqrt{\frac{r_B}{6.2r_B}}\\\frac{v_A}{v_B}=\sqrt{\frac{1}{6.2}}\\\frac{v_A}{v_B}=0.402$