What is the angular velocity of the Earth as it rotates about the Sun?

The angular velocity of the Earth as it orbits the Sun can be calculated based on the fact that the Earth completes one full revolution around the Sun in one year, which corresponds to an angle of (2\pi) radians.

To find the angular velocity, we can use the formula for angular velocity, which is given by the number of radians per revolution divided by the time in seconds taken for that revolution. Over the course of a year, there are approximately (31,536,000) seconds (365 days).

Thus, the angular velocity ( \omega ) can be expressed as:

[

\omega = \frac{2\pi \text{ radians}}{T}

]

where ( T ) is the time in seconds for one complete rotation (which is one year). Plugging in the numbers:

[

\omega = \frac{2\pi \text{ radians}}{31,536,000 \text{ s}} \approx 1.99 \times 10^{-7} \text{ rad/s}.

]

This approximates to about (1.99 , \text{rad/s}), indicating the rate at which the Earth is moving in its circular path around