Geography: How is the time of sunrise calculated at the twilight line? I hope you can explain it in detail.

Answer 1

The twilight line was a line on Earth used to describe the direction of the sun's movement in the sky. It was made up of the day and dusk line (where the sun's rays passed) and the twilight line (where the sun's rays did not pass). The division of the twilight line was based on the time between sunset and sunrise. This period of time was the twilight line, and vice versa was the day line.

Calculating the position and time of the twilight line required determining the position of the sun first. In the process of the Earth's revolution, the sun was always in the orbit of the Earth's revolution and kept moving away from the Earth as the radius of the revolution changed. We can determine the position of the twilight line by calculating the position of the sun in the sky.

Assuming that the sun is revolving on the equator and ignoring the rotation of the earth, the position of the sun in the sky can be expressed as:

C = R × (T/3652422)

C is the position of the sun in the sky, R is the radius of the earth, T is the time it takes for the earth to orbit once, which is 3652422 days.

Substituting the expression of C into the above formula, we can get:

R × (T/3652422) = 360 × π × (R/3652422 × T) × (1 + (R/3652422 × T)^3)

Pi is pi, R is the radius of the earth, and T is the time it takes for the earth to make one revolution.

We can simplify the above formula to:

R = 3652422 × T / (360 × π × (T/3652422 × T) × (1 + (T/3652422 × T)^3))

Substituting the expression of R into the above formula, we can get:

The position of the twilight line = 360 × pi × (3652422 × T / (360 × pi × (T/3652422 × T) × (1 + (T/3652422 × T)^3))

The position of the twilight line = 360 × pi × (3652422 × T / (360 × pi × (T/3652422 × T) × (1 + (T/3652422 × T)^3))

Here, he used mathematical multiplication and division operations to express the position of the sun in the sky as an exponential. By continuously adjusting the value of T, we can calculate the twilight line at different positions.

When the sun is on the equator, T = 3652422 days can be substituted into the above formula:

The position of the twilight line = 360 × pi × (3652422 × T / (360 × pi × (T/3652422 × T) × (1 + (T/3652422 × T)^3)) = 360 × pi × (3652422 × T / (360 × pi × (T/3652422 × T) × (1 + (T/3652422 × T)^3))

When the sun is above the polar circle, T = 3652422 × 23/7 = 7946576 days can be substituted into the above formula:

The position of the twilight line = 360 × pi × (3652422 × T / (360 × pi × (T/3652422 × T) × (1 + (T/3652422 × T)^3)) = 360 × pi × (3652422 × T / (360 × pi × (T/3652422 × T) × (1 + (T/3652422 × T)^3))

By calculating, we can get the position and time of the twilight line at different positions.