Pluto’s mass and its radius are 500 times and 5.5 times less than the mass of the Earth and its radius, respectively.

Pluto’s mass and its radius are 500 times and 5.5 times less than the mass of the Earth and its radius, respectively. What is the ratio of the first cosmic velocities of Pluto and Earth

To find out the required ratio of the first cosmic velocities, consider the expression: k = Vs1 / Vpl1 = √ (G * Ms / Rs) / √ (G * Ms / Rpl) = √ (Rpl * Ms / (Mpl * Rs)), where Ms / Mpl – mass ratio (Mz / Mpl = 500 r.); Rz / Rpl – the ratio of the radii (Rz / Rpl = 5.5 p.).

Let’s perform the calculation: k = √ (Rpl * Mz / (Mpl * Rz)) = √ (500 / 5.5) ≈ 9.5 p.

Answer: c) The sought ratio of the first cosmic velocities is 9.5.