Monetae cudendae ratio is a paper on coinage by which Renaissance- and Reformation-era mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe?
Nicolaus Copernicus Nicolaus Copernicus ( ; Polish: "Mikołaj Kopernik" ; German: "Nikolaus Kopernikus; Niklas Koppernigk" ; 19 February 1473 – 24 May 1543) was a Renaissance- and Reformation-era mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe, likely independently of Aristarchus of Samos, who had formulated such a model some eighteen centuries earlier.
Helioseismology Helioseismology is the process of inferring the internal structure and kinematics of the Sun from the propagation of seismic waves, particularly acoustic waves (p waves) and surface gravity waves (f waves). It was developed by analogy to geoseismology (originally called simply seismology), and subsequently there emerged asteroseismology, in which seismic waves are analysed to constrain the internal structures of other stars. Because the Sun is fluid, to a first approximation it cannot support shear waves (s-waves), unlike the seismic waves on Earth. An exception is the magneto-acoustic waves which appear to be important only in the atmosphere. The helioseismic waves are generated by the turbulence in the convection zone immediately beneath the Sun's surface. Certain frequencies are amplified by constructive interference, leading to resonance. In other words, the turbulence "rings" the sun like a bell. The resonant waves are reflected near the photosphere, the visible surface of the sun, where they can be observed. The oscillations are detectable in almost any time series of solar images, but are best observed by measuring the Doppler shift of atmospheric absorption lines. Details of the propagation of the seismic waves through the Sun, inferred from the resonant frequencies, reveal the Sun's inner structure, allowing astrophysicists to develop an extremely detailed representation of the hydrostatic stratification and the internal angular velocity. That has permitted the evaluation of the quadrupole moment, formula_1, and higher-order moments of the Sun's external gravitational potential. It is a more accurate and more robust procedure than trying to infer it from the oblateness of the visible disc. Together with measurements of the orbits of Mercury and of spacecraft, the result is consistent with General Relativity.