# 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 May 16 '20 at 16:25
• @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 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. – PM 2Ring May 17 '20 at 5:02

# 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. – Mazura May 18 '20 at 10:05

This answer was wrong the answer from @JdeBP below convincingly shows that this was know thousands of years earlier than Kepler. I'll leave this answer here in case the information in it is considered a useful part of the story, but this was very far from being the first realisation of this.

Looks like this was Kepler in the early 1600s.

The source says:

In contrast to the orbit of Mars, Kepler found the earth's orbit to be essentially a perfect circle. (It is actually off by about one part in 10,000.) However, the center of the circle is about 1.5 million miles away from the sun, and the speed of the earth in its orbit varies, being greatest at the closest approach to the sun. At the furthest point, the earth is 94.5 million miles from the sun, and it is moving around its orbit at a speed of 18.2 miles per second. At the point of closest approach to the sun, the earth is 91.4 million miles from the sun, and moving around at a speed of 18.8 miles per second. Kepler noticed that there was an interesting relationship among these numbers. The ratio of the speeds, 18.8/18.2 = 1.03, is the inverse of the ratio of the corresponding distances, 91.4/94.5 = 1/1.03.

while that source doesn't expressly mention that Kepler determined when in the year it was closest and when furthest, it is inconceivable that he could have got the ratio of the distances and speeds without knowing that. A little earlier the same article describes his main method:

Kepler realized that to get the kind of precision he needed in analyzing the orbit of Mars, he first needed to have a very accurate picture of the earth's orbit,

But how could he pin down the earth's position in space accurately? This is rather like being in a boat some distance from shore. If you can see only one landmark, such as a lighthouse, and you have both a compass and a map, that is not enough to really fix your position, because you cannot tell very accurately just how far away the lighthouse is. On the other hand, if you can see two landmarks, in different directions, and measure with your compass the exact directions they lie in from your boat, that is enough to fix your position exactly without any guessing about distances. You just take out your map, draw lines through the two landmarks on the map in the direction your boat lies in from each of them in turn, and the point where the two lines intersect on the map is your location.

The idea is to use this same technique repeatedly to find the location of the earth, and thereby to map out its orbit. The catch is, we need two fixed lighthouses to form the baseline, and we only have one, the sun. The fixed stars won't do, they are infinitely far away for all practical purposes, and just play the role of the compass, giving a fixed direction. Kepler solved the problem of the second fixed lighthouse by a very clever trick. He used Mars. Of course, Mars is moving all the time, and the orbit of Mars is what we are trying to find, so this doesn't seem a promising approach. But one thing we do know is that if Mars is in a certain location at a certain time, it will be in exactly that same place 687.1 days later. Kepler was able to use Tycho's mountains of data to find the exact direction of Mars from the earth at a whole series of times at 687.1 day intervals. By finding the direction of Mars and that of the sun at those times, he had a steady Mars--sun baseline to use in constructing the earth's orbit.

• The "...off by about one part in 10,000" line in the quote could use a footnote; I think it's really about 1.7 percent if it's referring to Earth's orbit's deviation from a circle, but maybe I'm misunderstanding? – uhoh May 16 '20 at 12:26
• @uhoh Earth's orbit is very nearly a circle, but with the Sun shifted a bit to one side of the centre. That shift is the 1.7% while the deviation in shape from a circle is the 1 in 10000. – Steve Linton May 16 '20 at 12:46
• Yep that sounds about right! According to this answer the polar equation for an ellipse from its focus is $$r=\frac{a\!\left(1-e^2\right)}{1+e\cos(\theta)}\tag7$$ and from its center is $$r^2=\frac{\overbrace{a^2\!\left(1-e^2\right)}^{b^2}}{1-e^2\cos^2(\theta)}\tag3$$ so it's more like 1 part in 7,000 roughly, but close enough for government work! – uhoh May 16 '20 at 15:24
• @uhoh: The major and minor axes differ by 0.014% (1 in 7000), but the ellipse is within 0.007% of a circle (1 in 14000). – robjohn May 16 '20 at 16:21
• @userLTK: Thanks for that, I wasn't aware of Cassini's contribution. But his estimate was 87 million miles, whereas the estimate obtained from the Venus observations was 93,726,900 miles. The true average distance is 92,955,000 miles, so it depends how you interpret my "reasonably precise". – TonyK May 17 '20 at 9:08

Johannes Kepler in 1605 may have been the first person to know that Earth is closest to the Sun in January, and the very last slight lingering doubts about that (and many much more important facts) should have been ended by the discovery of stellar parallax by 1840.

Early astronomers naturally assumed that the planets in the solar system, (including the Sun and the Moon) orbited around the Earth. And they were one seventh or 14.28 percent correct, since the Moon does orbit the Earth.

Early astronomers believed that outer space or the heavens was heavenly perfect and unearthly and therefore everything traveled in orbits that were perfect circles, which are perfect shapes.

But that is not actually the case, and so complications in the apparent motions of the planets kept being discovered.

So early astronomers had to modify the idea of having planets travel in perfect circular orbits by having the planets travel in smaller perfect circles around points in space which traveled in larger perfect circles. And they made the planets orbit in perfect circles which were not centered on the object they orbited around - the object that they orbited around was not at the center of those perfect circular orbits but offset.

In the 2nd century AD, the geocentric (Earth as the center of the universe) model was more or less perfected by Claudius Ptoleomaeus in Roman Egypt, which was the standard concept of the universe for over a thousand years. Ptolemy had to use an elaborate system with many epicycles, eccentric deferents, and equants to explain how the planets appeared to move as seen from Earth.

And I suppose that for over a millennium astronomers could have used the Ptolemaic system to calculate when a particular planet would be closer or farther from Earth, or from another "planet" such as the Sun, though since the geocentric model of the universe was inaccurate such calculations would be inaccurate.

And the heliocentric theory of Copernicus simplified the problem a bit but the planetary orbits were still complicated.

And of course, if a planet orbits in a small circle around a point that orbits in a much larger circle, that planet will sometimes be closer to it's primary, whether that primary is the Sun or the Earth, at some times than it is at other times. So it is possible that some followers of Copernicus did discover that Earth was closest to the Sun in January before Kepler.

Johannes Kepler worked on the problem of the planetary orbits using the data of Tycho Brahe who measured the directions to planets at specific times with a greater accuracy than anyone before. And Kepler tried every way he could to make perfect circular orbits fit with the date.

And eventually Kepler gave up and tried using elliptical orbits, and found that he could make planetary motions fit the the available data. And Kepler came up with his three laws of planetary motion.

So Kepler found that elliptical orbits for Earth and Mars around the Sun enabled him to make the planetary motions fit the observation data. In 1605, 415 years ago.

The perihelion of a planet is when it is closest to the Sun,and the aphelion of a planet was when it was farthest from the Sun. And Kepler had to know when Earth and Mars were at their perihelions and aphelions to make his calculations work.

So I would say that be the end of 1605, when Kepler had completed his work on the Astronomia Nova he knew how the distance between Earth and the varied at different dates, and thus when the perihelion of Earth occured.

Of course, the sizes of the Earth and the Moon, and distance between the Earth and the Moon, had been measured with fair accuracy in ancient times, but distances beyond the orbit of the moon were still a mystery. Copernicus had worked out the relative distances between various planets and the Sun according to the Copernican system, but nobody knew the absolute distances, but nobody knew how many millions, or billions, or trillions of miles those relative distances equaled.

The first close to accurate measurement of an interplanetary distance, and thus of the scale of the solar system, was in 1672.

So as astronomers accepted the heliocentric model of the solar system, and Kepler's laws of planetary motion, they came to accept that the Earth is closest to the Sun in January. When Newton's Principia Mathematica was published in 1687, scientists who accepted Newton's laws of physics now had a theoretical explanation for why planets would orbit the Sun, and for why they would have elliptical orbits.

So as Newtonian physics became accepted, scientists became more and more certain that the Earth is closest to the Sun in January.

However, if the Earth orbits the Sun, when a star was viewed at different times of the year it would be from different points on the earth's orbit, and thus the direction to the star would vary slightly. The star would show a parallax. Since astronomers could not measure any stellar parallaxes, it was argued that the Earth could not orbit the Sun.

So astronomers who supported the heliocentric theory often attempted to measure the parallaxes of stars. And finally, in the late 1830s, Friedrich Wilhelm Bessel measured the parallax, and thus distance of 61 Cygni, Thomas Henderson measured that of Alpha Centauri, and Struve measured that of Vega.

Therefore, Kepler in 1605 may have been the first person who could demonstrate, among other things, that earth is closest to the Sun in January, and the last lingering doubts about the heliocentric theory, Kepler's Laws, Newton's Laws, and the fact that the Earth is closest to the Sun in January, should have be closed no later than by the time of the discovery of stellar parallax by 1840.

• If you wrote this from memory, you've seen either the original Cosmos or The Mechanical Universe and Beyond too many times, +1 – Mazura May 16 '20 at 22:48