Heating doesn’t happen instantly, there is a lag time. For really big things (like Earth itself) this lag time can be quite significant. Later in the summer the days may be getting shorter but the heat input is still enough to keep the temperature rising. If the summer days lasted for much longer then the average temperature would rise much higher before leveling off.
First off weather is complicated, certain years in certain places it may very well be the hottest day
But one big factor is that the days are still long enough and the sunlight is still intense enough that the earth doesn’t have enough time to cool all the way down overnight. So heat still build a up and you get hotter days.
Interestingly, the earliest sunrise and latest sunset do not occur on the summer solstice, the longest day. Earliest sunrise happens about a week before, latest sunset about a week after. This is due to a combination of the Earth’s axial tilt and elliptical orbit around the sun. Remember seeing that skinny figure 8 in the middle of the Pacific ocean on globes or maps? It’s called an analemma, it shows the sun’s daily motion in the sky over the course of a year. The sun runs a little early or late at various times of the year due to Earth’s tilt and elliptical orbit. It can get a bit complicated:
[https://en.wikipedia.org/wiki/Analemma](https://en.wikipedia.org/wiki/Analemma)
Imagine the Earth as a pizza and the Sun as an oven. If you place the pizza in the oven while it is preheating, the pizza will gradually warm as the oven gets up to temp (or Earth’s hemisphere begins to tilt towards the Sun). The Summer Solstice would be the peak moment that both the oven has reached the desired cooking temperature and hit the duration for cooking. If you turn off the oven but leave the pizza within, it will begin to get too hot and burn as the pizza continues to absorb the heat while the oven itself cools (or the Earth begins to tilt away/perpendicular to the Sun).
Edit: corrected that it is the tilt of the Earth and not distance as to the cause of the seasons.
Heat input from the sun is the slope of the average temperature, not the temperature itself. so you would see the steepest increase on that day, but the peak avg temp would actually be when the gain/loss from the sun equals out. Yay calculus.
Same reason why hottest time during the day does not occur at noon, but a bit before sunset.
Why isn’t your oven the hottest when it first ignites? It takes time for heat to build/absorb. In the case of weather, it’s the ground and structures absorbing heat. So it’s the weeks/months of high heat and lots of sun that allow highest temps to build over the summer vs. the single day with the longest amount of sun. It’s the longest day and all the following days with just slightly less sun continuing to warm everything over time.
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