You probably already know that the Earth’s axis of rotation isn’t straight, but tilted. The angle varies slightly over time, but it’s usually somewhere around 22 degrees. Now, in our universe there is something known as *angular momentum*, which is basically just a fancy word for saying “amount of spinning”. A characteristic of angular momentum is that it is [preserved](https://en.wikipedia.org/wiki/Angular_momentum#Conservation_of_angular_momentum), meaning if no external forces act on the Earth, it will continue spinning the same amount and *in the same direction* i.e. the axis around which it spins will be pointing (roughly) the same way all the time. Take a look at this picture [here](https://www.abc.net.au/cm/lb/8856600/data/earth-seasons-data.jpg), and focus on the Tropic of Cancer. This is approximately where you’d find Hong Kong, The UAE, and it’s a bit north of Mexico City and Hawaii, though the argument works for any latitude.
During summertime, when the northern hemisphere is tilted towards the sun, a larger part of the Tropic of Cancer is illuminated at any given point. You can see this in the picture, and probably visualize it on a globe as well. Since the Earth rotates with a constant velocity, this means the Tropic of Cancer will spend more time in the sun – the days become longer. This is also why the effect is more pronounced near the poles. In Stockholm, Sweden, during the longest day in June, the sun rises at half past four in the morning and sets at ten in the evening. Remember that this doesn’t mean it goes completely dark! North of the Arctic circle, the Earth can keep on rotating without the sun setting, which is what gives rise to Arctic days where the sun don’t ever set, and Arctic nights, where the sun don’t rise.
Wintertime, you just replace sunlight with night time and the whole explanation still holds up. Or you could substitute the northern hemisphere for souther hemisphere, and it all just works out the same with only a six month time difference. Sphere are symmetrical, y’know.
Sidenote: Because of the preservation of angular momentum, the direction of the axis around which the Earth rotates is constant. However, since the Earth rotates around the Sun once per year while still pointing the rotational axis the same way, whether it points towards the sun or not changes every six months. Thus, it’s not really the change in the tilt of the Earth’s rotation axis, but the change *relative* to the Sun.
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