Final answer:
To find the mass of the asteroid, Kepler's Third Law is applied using the given orbital period of 3.02 hours and the orbital radius of 2.0 km. The correct mass is calculated to be 1.2×1013 kg, which corresponds to option (a), making it a reasonable mass for an asteroid of this orbit size.
Step-by-step explanation:
To determine the mass of the asteroid, we can use Kepler's Third Law, which relates the orbital period of a satellite to the mass of the central body around which it orbits. The formula for Kepler's Third Law, when the satellite's mass is much smaller than the mass of the central body and hence can be neglected, is:
T2 = (4π²/GM)r3
where T is the orbital period, G is the gravitational constant (6.674×10-11 N(m/kg)2), M is the mass of the central body (mass of the asteroid in this case), and r is the radius of the orbit.
Now, plug in the given values: T = 3.02 hours (which is 3.02 x 3600 seconds), and r = 2.0 km (which is 2000 meters). Solving for M gives us the mass of the asteroid. Using the given information, we can calculate that the correct mass would be option (a) 1.2×1013 kg, considering the correct placement of decimal points and magnitude of scientific notation based on the astronomical context.
Given the radius of the orbit, the mass appears reasonable and aligned with what we would expect for a small satellite orbiting a nearby asteroid without drifting into it.