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Do those few thousand kilometers of difference going around the earth significantly affect the amount of thermal energy the moon receives from the sun to warm up its surface?

Also, are there more significant differences between these variables when the earth goes from perihelion to aphelion and vice-versa?

Moon's orbit around earth around Sun, not to scale.

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    $\begingroup$ I’ll wait for someone with greater expertise to provide an answer, but my guess is the dominant factor will be the orbit around the Sun rather than proximity to Earth. There’s a few million km difference between perihelion and aphelion. $\endgroup$ – Chappo May 24 '18 at 6:45
  • $\begingroup$ Is there any way I can bump the question? I don't think it receives enough attention. (If this comment is considered off topic I'll delete it) @Chappo $\endgroup$ – Peter Johnmeyer May 25 '18 at 1:20
  • $\begingroup$ Your edit is an effective bump - the question is currently coming up top in “hottest today” on the app, and 2nd in “active”. Just gotta hope someone has the time & inclination to answer. It should be a relatively easy task to calculate the difference in solar radiation between aphelion & perihelion, which will be several orders of magnitude greater than difference between apogee & perigee. $\endgroup$ – Chappo May 25 '18 at 1:33
  • $\begingroup$ It might be more interesting to calculate the change in heat received from the Earth (only) . Unlike the solar calculation, you now have to deal with an extended source. $\endgroup$ – Carl Witthoft May 25 '18 at 14:54
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Roughly speaking, the moon's orbit has a semi-major axis of about 400,000 km. The semi-major axis of the Earth's orbit is 149.6 million km. The intensity of sunlight received by the Moon depends on the inverse of the square of the distance, so the difference amounts to $((1.496e8 + 4e5)/(1.496e8 - 4e5))^2$ = 1.011, or about 1%. So, not very much.

The variation in Earth's distance from the Sun is about five million km, so that's going to have more of an effect than the lunar orbit itself (as Chappo pointed out in their comment). That works out to a variation of about 6.9% in insolation from perihelion to aphelion. The maximum possible variation -- full moon at aphelion versus new moon at perihelion -- would be $((1.521e8 + 4e5)/(1.471e8 - 4e5))^2$, which works out to about 8.1%.

The difference in insolation from new moon to full moon at perihelion is about 1.09%, versus a difference of 1.06% at aphelion.

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