Solstice has nothing to do with the orbit of the sun or proximity to the sun.

It is about the angle of the earth relative to the sun. The earth leans a bit. For half the year, the southern hemisphere faces the sun more directly, the other half the northern hemisphere faces it more directly.

Summer/winter Solstice marks when the lean is most head on/most leaning away to the sun for each hemisphere.

This happens on the same day each year because the lean is constant.

The solstices are a function of Earth’s axial tilt, occurring when you’re pointed at the minimum and maximum angle.

This is independent of the Earth’s orbital characteristics, although the northern winter solstice does coincidentally occur near the Earth’s “perihelion” - the closest approach.

The solstice is a result of a planet's axial tilt (i.e. the planet does not spin perfectly straight "up"), and the perihilion (when the earth is closest to the sun) is not related to axial tilt but instead to where in the not-perfectly-circular orbit we are.

The solstices are tied to the tilt of the Earth's axis. They are the points when the axis is either tilted the most towards or away from the sun. This change of the orientation of the Earth's axis has a larger effect on the seasons and climate than the change in distance of the Earth to the Sun.

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Solstice relates to the tilt of the Earth not to distance from the Sun, occasionally the distance between the Earth and the Sun is slightly less, but that is like sitting 10 metres away from a burning log fire and moving 1 millimetre closer to the fire.

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The earth is closer to the sun during the northern hemisphere's winter than during its summer.

In fact, you can use the solstices/equinoxes to “calibrate” any given solar calendar system.

(Its lean is a characteristic of its orbit.)

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