How do the Craft and Holy Royal Arch degrees relate to Geometry & Astronomy?

Geometry forms the foundational science upon which Speculative Masonry is erected, standing synonymous with the Craft itself in medieval manuscript charges 15. The Old Charges record geometry as the fifth science, which encompasses all measurement of lines, surfaces, and solids, while astronomy ranks as the seventh, teaching the motions, magnitudes, and distances of the luminaries and stars 5. All seven liberal sciences were held to be contained under geometry, as no craft, agriculture, or navigation could subsist without measurement 5.

In the Fellowcraft degree of the Craft, geometry is presented not as an arithmetical exercise, but as a emblem of universal law, order, and Deity 3. Through geometry, natural laws on earth demonstrate the unchanging principles governing the heavens, providing a symbolic means to contemplate the Great Geometer of the Universe 3. Astronomical symbolism also pervades the Craft, defining lodge orientation by the cardinal points according to the ecliptic, structuring lodge governance after the movements of the sun and moon, and establishing the measurement of time 2. Geometry serves in the Middle Chamber as the method by which the astronomer fixes the duration of cycles and seasons 2.

In the Scottish Rite, Albert Pike notes that the letter G suspended in lodges signifies geometry, though he argues that trigonometry and the broader science of numbers better express the calculations needed to determine astronomical laws and distant star positions 4.

The supplied sources do not contain material on how Geometry and Astronomy relate specifically to the Holy Royal Arch.