Your reasoning would only work if Earth rotated on the spot for 1 sidereal day, and then jumped forward in its orbit.

Instead, it is a smooth process, with it rotating as it orbits.

A similar jump can be seen in the model as well.

Do you mean in the model you are trying to present or the actual model?

Because in the actual model it can't.

There is no sudden jump.

How come noon "N" is lagged by 4 minutes in the sunshine after the completion of 360 degrees rotation of the earth while orbiting the sun when N has already completed its quota of 6 hours in the sunshine and 12 hours in the nighttime in the first three quarters? Shouldn’t it be 1 minute in the sunshine?

I wouldn't say it has completed its quota of 6 hours in sunshine. It has spent more than that, but the important part is that it is not the full 12 hours.

No, it shouldn't be 1 minute. Why do you think it should be?

It would be 1 minute if you were doing a 90 degree rotation from when day started.

But instead you are doing a 360 degree rotation from it starting at noon.

Below is the full detail.

Which leaves out the times, and just results in confusion.

Especially with you placing the solar day before the sidereal day.

After a 90 degree rotation, N has spent 359 minutes in the sun, and still isn't out. Due to the orbit, you have to wait another minute to reach B.

So after 6 hours (1 minute more than a 90 degree rotation), it has reached point B.

After a 180 degree rotation FROM THE START it has spent 6 hours in the sun and only 358 minutes in night.

1 minute of this was used to reach point B while still in the day.

You need to wait an addition 2 minutes to reach point M.

This also makes sense as considering it from point B.

You have a 90 degree rotation and 1 minute to reach point B, and then an additional 90 degree rotation and 1 minute to reach point M, so that is a total of 180 degrees and 2 minutes.

A 180 degree rotation from point N is NOT the same as a 90 degree rotation from point B. You have used an extra minute to reach point B, and that minute is taken away from the rotation from point B towards point M. So after a 180 degree rotation and 1 minute you have reached the point that is a 90 degree rotation from point B. You then need to take an extra minute (or a total of 180 degrees and 2 minutes) to reach point M.

Then the same applies to reach point A, where it is 3 minutes from a 270 degree rotation from N, with 1 minute to reach B 1 minute to reach M and 1 minute to reach A.

Or it is just a 1 minute delay from a 90 degree rotation from M.

And finally to reach point N again, it is an extra 4 minutes from a 360 degree rotation, or 1 minute from a 90 degree rotation from A.

These 4 minutes can be summarised as 1 extra minute in day to reach point B, 1 extra minute in night to reach point M, 1 extra minute in night to reach point A and 1 extra minute in day to reach point M.

And the first 3 of these minutes puts it in the same location as a 90 degree rotation from A.

We can also see how much it has spent in day and night.

It spent 359 minutes, i.e. the first 90 degree rotation in the day. It then had to spend another minute to reach point B, bringing a subtotal to an initial 360 minutes in the sun.

It then rotates for another 90 degrees for 359 minutes in night and needs to spend another minute to reach point M, bringing the time in night to 360 minutes and the total time to 720.

It then rotates for another 90 degrees for 359 minutes in night and needs to spend another minute to reach point A, bringing the time in night to 720 minutes and the total time to 1080.

After a 360 degree rotation, it has been 1436 minutes. 720 of these have been at night, leaving 716 minutes in the day. It needs to wait another 4 minutes to reach M which will be entirely in the day. That brings the total daytime to 720 hours.

The 1 minute extra only applies if you have the initial time be a 90 degree rotation from the previous point.

If you increase the angle, you increase the time.

For 180 degrees it is 2 minutes, 1 minute for the first 90 degree rotation, and then another for the second.

Or, the timeline, in order:

time | Position |

0 | Starts at N |

359 | 90 degree rotation from N |

360 | Reaches point B |

718 | 180 degree rotation from N |

719 | 90 degree rotation from B |

720 | Reaches point M |

1077 | 270 degree rotation from N |

1078 | 180 degree rotation from B |

1079 | 90 degree rotation from M |

1080 | Reaches point A |

1436 | 360 degree rotation from N |

1437 | 270 degree rotation from B |

1438 | 180 degree rotation from M |

1439 | 90 degree rotation from A |

1440 | Reaches point N |

And this timeline really makes it clear where the issue is.

If you just want to look at the last 90 degree rotation and extra minute, you have that 90 degree rotation from A bringing you to t=1439 minutes, where you need 1 more minute.

But if you do a 360 degree rotation from N, then all the time is taken away from the last section.

You are trying to treat a 360 degree rotation as ending up at time t=1439 minutes, but it is only 1436 minutes.

We can also consider what should happen if your suggestion was true.

If it requires a 90 degree rotation and 1 extra minute to reach point B, but then it is only a 360 degree rotation and 1 minute to reach point N again, then you can break it down into:

A 90 degree rotation + 1 minute to reach point B.

A 90 degree rotatoin to reach point M.

A 90 degree rotation to reach point A

A 90 degree rotation to reach point N.

You have Earth being slow for the first 90 degree rotation + 1 minute, and then faster for the rest.

If instead we have it take the same each time that means:

A 90 degree rotation + 1 minute to reach point B.

A 90 degree rotation + 1 minute to reach point M.

A 90 degree rotation + 1 minute to reach point A.

A 90 degree rotation + 1 minute to reach point N.

This gives a total of a 360 degree rotation and 4 minutes to reach point N.

You can also consider an analogous problem.

Consider a car driving along a track at 60 km/hr.

The track is 244 km long.

After 1 hour, the car has reached 60 km. It needs to spend another minute to reach the quarter mark.

After 2 hours, the car has reached 120 km. It needs to spend another 2 minutes to reach the half way point.

But if we consider it 1 hour after it reached the quarter mark, that 2 hours and 1 minute from the start so it only needs 1 extra minute.

After 3 hours, it needs 3 more minutes.

And after 4 hours, it needs 4 more minutes.