Final answer:
The correct answer is a) (R, a), where R stands for the radius of the asteroid, and a represents the prince's acceleration while in orbit. Calculations related to gravity and motion involve formulas like G∗(M/r²) for gravitational acceleration and F = ma for net force and acceleration.
Step-by-step explanation:
The radius of the asteroid and the magnitude of the acceleration of the prince while he is in circular orbit at the surface of asteroid B-612 should be given as an ordered pair with the asteroid radius first, followed by the magnitude of the prince's acceleration. This corresponds to option a) (R, a) from the choices provided. The radius is denoted as R and the expression for acceleration, in this case centripetal acceleration, would be a.
For the other queries, the acceleration due to gravity on the surface of the Moon and Mars can be calculated using the formula G∗(M/r²), where G is the gravitational constant, M is the mass of the celestial body, and r is its radius.
The net force on a rogue asteroid by a pair of space tractors requires the vector addition of the two given forces, F₁ and F₂, to find the total force exerted on the asteroid; then, the acceleration can be found using Newton's second law F = ma.
For an object like a piece of dust on a spinning CD, the total distance traveled can be found by calculating the circumference of the CD (2πr) and multiplying it by the number of revolutions per minute and the number of minutes.