Final answer:
The angular velocity of Earth's orbit around the Sun is calculated using the period of one orbit, which is approximately one year. The resulting angular velocity is approximately 1.99 x 10^-7 rad/s.
Step-by-step explanation:
To calculate the angular velocity of the Earth in its orbit around the Sun, we need to know the period of one orbit, which is one year. Given that a year is approximately 365.25 days and that each day has 86400 seconds, the period T is 365.25 × 86400 s. The angular velocity, ω, is given by ω = 2π / T.
Converting days to seconds for the period T we get: T = 365.25 × 86400 s = 3.156 × 107 s. Now, calculating the angular velocity:
ω = 2π / (3.156 × 107 s) ≈ 1.99 × 10-7 rad/s
Therefore, the correct answer is a) Approximately 1.99 × 10-7 rad/s.