When did people first measure that the Earth was closest to the Sun during January?
Hipparchus, not Kepler

Kepler got the conic sections right, and Newton gave us the mechanics.  But the question is about when people knew that the Earth was closer to Sol in one part of the year than others, and Hipparchus knew that, even though he wasn't too hot on the values of the orbital radii.  Hipparchus' version of the eccentric model had Sol's (purported) circular orbit around the Earth not centred upon the Earth, but 1/24th of an AU away.  Therefore Sol (purportedly) orbited at varying distances from Earth.  This was, after all, the whole point of the eccentric model, to explain non-uniform apparent motion through variation in distance.

Perigee and apogee were known in the times of Hipparchus and Ptolemy.  Hipparchus even worked out when the furthest point (apogee) was.  Ptolemy furthermore made an error based upon knowing that his placement of the apogee in Gemini was the same as that of Hipparchus 280 years beforehand, declaring that perigee and apogee were fixed.

They of course were not.  Hipparchus placed apogee at 5.30&deg; Gemini.  Astronomers in the 9th century in Baghdad applied the same calculations to their measurements and placed it at 20.45&deg; Gemini.  

As for how this was observed, it was not done by measuring the Sun's appearance at all (although Hipparchus did do that).  Ptolemy and Hipparchus had a geometric model of a true geocentric circular orbit versus the (purported)  eccentric circular orbit of Sol.  It incorporated the equinoxes and the solstices.  By observing the times of the equinoxes and solstices, the lengths of the periods between them, they were able to determine trigonometrically all of the other orbital parameters, which included placement of perigee and apogee.

That points of closest and furthest approach existed was known in the 2nd century BC, as was their angular locations relative to the solstices; they've been in the models from then onwards.  That they moved around took about 11 centuries after that to discover.  The correct conic sections and the idea of both bodies orbiting around a barycentre came somewhat later, but that wasn't the question.

Further reading


Hugh Thurston. (1994) "Appendix 2: Calculation of the Eccentric Quotient for the Sun, and the Longitude of its Apogee". Early Astronomy. New York NY: Springer.  DOI 10.1007/978-1-4612-4322-9_1
James Evans (1998). The History and Practice of Ancient Astronomy.  Oxford University Press. ISBN 978019509539.
Viggo M. Petersen and Olaf Schmidt (June 1968). "The Determination of the Longitude of the Apogee of the Orbit of the Sun according to Hipparchus and Ptolemy".  Centaurus.  Volume 12.  Issue 2.  Pages 73&ndash;96.  DOI 10.1111/j.1600-0498.1968.tb00080.x