Final answer:
To find the orbital period of a space probe in a circular orbit around asteroid Vesta, we can use Kepler's third law. However, this calculation is marginally useful at best due to various real-world factors.
Step-by-step explanation:
To find the orbital period of a space probe in a circular orbit around asteroid Vesta, we can use Kepler's third law which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. The semi-major axis of the orbit is the sum of the radius of the asteroid (520 km) and the radius of the orbit (10.0 km), which is 530 km. We can then calculate the orbital period using the formula T = 2π√(a^3/GM), where a is the semi-major axis, G is the gravitational constant (6.674 × 10^-11 Nm^2/kg^2), and M is the mass of the asteroid (2.67 × 10^20 kg). Plugging in the values, we get T = 4.6 hours.
This calculation is marginally useful at best because it assumes a perfect circular orbit and neglects other factors such as the gravitational influence of other bodies and the irregular shape of the asteroid. In reality, the orbit of a space probe around an asteroid would be affected by various factors, making the calculated orbital period only an approximation.