Orbital Mechanics

The orbital velocity and escape velocity are given by the following formulas: where: - is the mass of the planet, - is the radius of the planet, - is the gravitational constant. For planet 'A', the orbital velocity at its surface is equal to the escape velocity from planet 'B'. Therefore, we have: Since the masses of the two planets are the same ( ), we can cancel the masses and the gravitational constant: Squaring both sides: Thus, the ratio of the radii of planets A and B is: So, the correct answer is option (2), .