### When did people first measure that the Earth was closest to the Sun during January?

• When we talk about the reason for the seasons, we usually have to dispel the misconception that seasons are caused by being close and far away in the Earth's elliptical orbit.

And usually, we mention that the Earth is actually closest to the sun in January, in the dead of winter (for the Northern hemisphere).

But when did astronomers first have the Earth's orbit measured carefully enough that they knew the Earth was slightly closer during January? How was that measurement made? How accurate were the first measurements?

They didn't they measure the size of the disk of the sun very, very carefully, did they? Perhaps with a pin-hole camera? That seems like it would be very difficult to do.

I guess if we are talking about long enough ago, they would have thought it was the Sun's orbit that brought it closer because either because of an eccentric (the idea that the orbit of an ancient planet had a center that was offset) or because of epicycles bringing the Sun closer on the circle on a circle.

I just wonder what sort of observation they might have made.

If it was me with the tools available in ancient times, I'd probably use a rotatable camera obscura, and maybe a cone with markings to place at the center of the image of the sun, to exaggerate the effect of the size differences.

Based on JdeBP's answer I want to see if I have the correct concept. (I would put this in comments, but comments can't be nicely formatted.)

Doing a search for the dates and times of the solstices and equinoxes, and finding the time between those dates and times, I found the lengths of the upcoming seasons.

Summer 2020 is 93 days, 15 hours, 47 minutes

Fall 2020 is 89 days, 23 hours, 0 minutes

Winter 2020 is 88 days, 21 hours, 7 minutes

Spring 2021 is 92 days, 17 hours, 54 minutes

Summer 2021 is 93 days, 15 hours, 49 minutes

If we subtract from 1/4 of an astronomical year, we get about:
$$\begin{matrix}Spring & +1.4 \: days & & Summer & +2.4 \: days \\Fall & -1.4 \: days & & Winter & -2.4 \: days \end{matrix}$$
From there it seems like with a geocentric model with an eccentric, we could get a good approximation for the date of perihelion.

I'll have to think about the details of how to get there, though.

I don't want to make an answer, as I'm not well read on this, nor do I have a strong source that suggests he knew of the January perihelion, but Ptolomy's use of an equant implies a recognition that the Sun passed closer to and further from the Earth every year. He also used epicycles, so again, some uncertainty as the size and period of the epicycle could undo most of the variation from the equant. A 3% variation in size shouldn't be that hard to measure, even by ancient methods, so it may have been known as early as Ptolomy or even earlier.

@userLTK It was well-known that the Ptolemaic system wasn't good at predicting even relative distances; this was most obvious in regards to the Moon. From http://farside.ph.utexas.edu/Books/Syntaxis/Almagest/node3.html "Unfortunately, this model necessitates a monthly variation in the earth-moon distance by a factor of about two, which implies a similarly large variation in the moon's angular diameter. However, the observed variation in the moon's diameter is much smaller than this." That would discourage astronomers from generally trusting all such distance calculations.

2 years ago

# 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° Gemini. Astronomers in the 9th century in Baghdad applied the same calculations to their measurements and placed it at 20.45° 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.

When I first read this question I was really hoping it was going to be : before there was a month called, *January* ("Around 713 BC"), but it was about 600y after the fact : Hipparchus of Nicaea, c. 190~120 BC.