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As detailed on the solar measurements page, the difference between the altitude of the upper limb (edge) and the lower limb of the Sun is the angular diameter of the Sun, typically about 0.5 degrees. When my data for the solar diameter was plotted up I got this:
The horizontal axis is time, measured in days. MJD means 'Modified Julian Date' which is defined as a convenient offset from some reference start date. For my convenience I picked the reference start time for all my data collection as the midnight of January 1st, 2020 - New Year's midnight. This was Julian Date(JD) 2458849.5. True Julian dates for all my data can be obtained by adding 2458849.5 to all my MJD values. The full JD has so many digits that most spreadsheets can't retain the full accuracy when using single precision variables, so the large offset was subtracted to produce a MJD with many fewer digits which was then easily, and accurately, handled in the spreadsheet.
As a reference for the reader, the vernal equinox (March 20, 2021) was at JD 2459294.148 or MJD 444.648, near the center of the plot above.
The data is noisy, wiith a lot of scatter, but that was because the change in solar diameter is a small effect. The solar diameter is changing during the year because the Earth is moving closer, or further away, from the Sun due to the ellipticity of the Earth orbit. So this change in diameter, less than an arc minute, would not have been noticeable in Tycho's time. There were no telescopes in 1580, no optics of any kind.
Although the data was noisy, parabolic fits to the data gave a maximum diameter of 0.539 degrees and a minimum diameter of 0.525 degrees. These occurred at roughly MJD 365 and 557 which are at calendar dates of approximately December 31, 2020, and July 11, 2021, which starts to show that the closest approach to the Sun (perihelion) was not at the winter solstice (Dec 21, 2020) and the furthest distance (aphelion) was not at the summer solstice (June 21, 2021). Much more accurate estimates came from an analysis of the Sun's ecliptic longitude (on a later page). The changes in diameter should also yield an estimate of the eccentricity of the Earth's orbit.
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