Sunset is defined as the instant that the top of the sun disappears below the horizon ...

Sunset is defined as the instant that the top of the sun disappears below the horizon. How long is it from the time when the bottom of the sun hits the horizon until the instant of sunset assuming that you are standing on the equator on March 21 ( the orbital radius of earth is 1.5 x10^ 11 ,the radius radius of sun is 6.99x10^8 m).

Solution

The duration between the moment the bottom of the sun touches the horizon and the instant of sunset at the equator on March 21 can be estimated as follows:

Let's consider the Earth as a sphere with a radius of 6.371 x 10^6 meters, and the Sun as a sphere with a radius of 6.99 x 10^8 meters.

On March 21st, the Earth is at the equinox, which means that the Sun is directly overhead at the equator. The distance between the center of the Earth and the center of the Sun is 1.5 x 10^11 meters.

The apparent size of the Sun as seen from the Earth is about 0.5 degrees. So, the apparent size of the Sun from the Earth can be used to calculate the time it takes for the bottom of the Sun to disappear below the horizon.

Time = (2 * (Earth's radius + Sun's radius) * sin(Sun's apparent size / 2)) / (speed of light)

Plugging in the numbers, we get:

Time = (2 * (6.371 x 10^6 + 6.99 x 10^8) * sin(0.5 / 2)) / (3 x 10^8)

Time = (2 * (6.371 x 10^6 + 6.99 x 10^8) * 0.25) / (3 x 10^8)

Time = (2 * (7.0061 x 10^8) * 0.25) / (3 x 10^8)

Time = (1.7015 x 10^8) / (3 x 10^8)

Time = 0.567 seconds

So, it takes approximately 0.567 seconds from the moment the bottom of the Sun touches the horizon until the instant of sunset.

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