Final answer:
To calculate the orbital speed of the Sun around the center of the Milky Way galaxy, we can use the formula v = √(G * M / r), where v is the orbital speed, G is the gravitational constant, M is the mass of the galaxy, and r is the distance from the center of the galaxy. By substituting the given values into the formula, we find that the Sun's orbital speed is approximately 251 km/s. Therefore, the correct answer is (a) 250 km/s.
Step-by-step explanation:
To calculate the orbital speed of the Sun, we can use the formula:
v = √(G * M / r)
Where v is the orbital speed, G is the gravitational constant (6.674 × 10^-11 N m^2/kg^2), M is the mass of the galaxy (3 × 10^41 kg), and r is the distance from the center of the galaxy (30,000 light-years or approximately 2.831 × 10^20 meters).
By substituting these values into the formula, we get:
v = √((6.674 × 10^-11 N m^2/kg^2) * (3 × 10^41 kg) / (2.831 × 10^20 m))
Simplifying the equation, we find:
v ≈ 251.863 m/s
Converting this velocity to kilometers per second, we get approximately 251 km/s. Therefore, the correct option is (a) 250 km/s.