The sun appears to move across the sky because the Earth spins on its axis. To a person standing on Earth, the sun subtends an angle of θ = 9.28 × 10^-3 radians. How much time (in seconds) does it take for the sun to move a distance equal to its own diameter?

To determine the time it takes for the Sun to move across the sky, we assume that its apparent motion is due to the rotation of the Earth. Since the Earth rotates 360 degrees (or 2π radians) in 24 hours (or 86400 seconds), we can calculate how long it takes for the Sun to move across an angle equivalent to its diameter.

Given that the Sun subtends an angle of θ = 9.28 × 10^-3 radians, we can set up a proportion to find the time (t) it takes for the Sun to move this angle, based on the Earth's rotation:

(θ radians) / (t seconds) = (2π radians) / (86400 seconds)

Now, solving for t:

t = (θ radians * 86400 seconds) / (2π radians)

Plugging in the value for θ and using the approximate value of π as 3.14159, we get:

t = (9.28 × 10^-3 * 86400 seconds) / (2 * 3.14159)

t ≈ (9.28 × 10^-3 * 86400) / (6.28318)

t ≈ (800563.2 × 10^-3) / 6.28318

t ≈ 800.5632 / 6.28318

t ≈ 127.441 seconds

So it takes approximately 127.441 seconds for the Sun to move a distance equal to its own diameter across the sky from the perspective of a person on Earth.