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Summer is not the half of the year when we are nearer the sun. The seasons come from a tilt.

Astronomy Facts, sourced to NASA.

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The Earth's orbit is very nearly a circle, and what little difference there is runs the wrong way for the explanation people reach for first: the planet passes nearest the sun in early January, in the depth of the northern winter. What matters is that the axis leans by about twenty three degrees and keeps pointing the same way all year. Whichever hemisphere leans toward the sun gets longer days and a steeper, more concentrated beam.

The claim comes from NASA.

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