Final answer:
To find the centripetal force of asteroids Y and Z, we apply the formula Fc = mv²/r. Asteroid Y, moving at double the speed of asteroid X, exerts four times the force, which is 6000N. Asteroid Z, moving at triple the speed but at half the radius, exerts twelve times the force of asteroid X, or 18000N.
Step-by-step explanation:
The question involves calculating the centripetal force acting on asteroids orbiting a moon. Centripetal force can be calculated using the formula Fc = mv²/r, where m is the mass of the object, v is the linear velocity (speed), and r is the radius of the circular path.
Given that asteroid X orbits with a speed of 500 m/s and experiences a centripetal force of 1500N, we can infer that asteroid Y, orbiting at the same radius but at double the speed of asteroid X (1000 m/s), will experience a centripetal force four times greater, which is 6000N, because the force is proportional to the square of the velocity.
For asteroid Z, which orbits with a speed of 1500 m/s at half the orbital radius of asteroid X, we use the same formula with the new values for v and r. The centripetal force for asteroid Z can then be calculated to be 12 times that of asteroid X, namely 18000N, because while the speed is three times that of asteroid X, the radius is half, and the force is inversely proportional to radius.