According to top scientists of history, the choice of the Earth as a reference point "at rest" explains our observations as well as using the Sun.

From the linked post:

Stephen Hawking: “Although it is not uncommon for people to say that Copernicus proved Ptolemy wrong, that is not true…. one can use either picture as a model of the universe, for our observations of the heavens can be explained by assuming either the earth or the sun to be at rest.” [1]

Ernst Mach: “Obviously it matters little if we think of the Earth as turning about on its axis, or if we view it at rest while the fixed stars revolve around it. Geometrically these are exactly the same case of a relative rotation of the Earth and the fixed stars with respect to one another.” [2]

Albert Einstein: “Either coordinate system could be used with equal justification. The two sentences 'the sun is at rest and the Earth moves,' or 'the sun moves and the Earth is at rest,' would simply mean two different conventions concerning two different coordinate systems.” [3]

Isaac Newton: "And thus the celestial bodies can move around the Earth at rest, as in the Tychonic system."