8454 —הַתְאֲמָתַת קוֹטֶר הַשֶּׁמֶשׁ עַל פִּי הָרַמְבַּ"ם עִם אַסְטְרוֹנוֹמְיָה מוֹדֶרְנִית

Shalom u'Vrachah! [Rosh Chodesh Tammuz 5722] ... What is written in Shaar HaYichud VeHaEmunah chapter 7, that the sun is "about 167 times the size of the earth," is based on the ruling of the Rambam in Hilchos Yesodei HaTorah 3:8 (and more precisely in his introduction to Pirush HaMishnayos: "166 and three-eighths times").

It seems your honor was challenged by those who claim that modern scientists have found otherwise — that it is four or five million times larger, or even more. As with other such 'scientific' questions, the questioner is not truly knowledgeable even in science! The figure of four or five million and more refers to volume, while Rambam speaks about diameter.

The value for these diameters given in current astronomy books is about 110 (not 167) — but this measurement includes only certain layers of the sun, not all. The outermost layers (according to current astronomers) change greatly over time (contracting and expanding), are not all visible (only their effects are 'seen'), etc., making them difficult to measure. They also do not include protuberances, but sometimes these expansions were observed and measured so that then the sun’s diameter was more than 167 times that of earth, and later contracted again, etc., but this is not the place for full discussion.

This was printed in Likkutei Sichos vol. 10 p. 180. This letter is to Rabbi Ephraim Eliezer Yales. Additional letters to him appear above — letter #2888, and as referenced in notes there.

Summary

The Rebbe clarifies that differences between Rambam’s figures and modern science stem from measuring different aspects (diameter vs. volume) and varying definitions of what constitutes the sun’s boundaries.