The Sky Before the Telescope

  The stars we can see with the naked eye are the stars in our galaxy, the Milky Way. Other galaxies are visible, but look like clouds (nebula) because we cannot resolve individual stars. Our galaxy rotates around its center, and the stars change their relative positions. However,  all these motion  were not observable before the invention of the telescope in Holland  in the year 1600.  In this knol, we describe the sky as it appeared  before the telescope. These were the data which Newton used to explain the motion of the planets, as described in the knol "Newton's Laws."
 

Diurnal motion - longitude and time of the day

For a larger picture, credits, and explanation click on links "applet" beside these small picture-icons . You will need java enabled in your browser.


To actually see the rotation of the stars, one needs either a good deal of time and patience or time-lapse photography, as used here.

Are you able to tell from the arcs on the photo, how long the stationary camera was  taking repeated pictures of the sky?

To appreciate life  before the industrial revolution, imagine you are on a camping trip in an area far from city lights. You live in a tent, without electricity, your cell phone, GPS, or any other gadgets.  You do not even have a flashlight or a watch.

One thing you will notice at night is the moon and the stars. If you awaken at different times in the night, you will notice how the stars appear to rotate through the sky from rising positions to setting ones. You will look at the sky to know what time it is. When traveling, you will use the night sky to determine where you are. Most modern city dwellers have lost the ability to do this, a skill which was once crucial for ancient agricultural societies, as well as for explorers and merchant ships.

Near the equator stars rise "straight up", that is, in a plane nearly perpendicular to the horizon. as seen in this photo taken near the equator  in Kenya. Contrast these with the angle of about 63 degrees at the latitude of California, about 37 N in the White Mountains. Carefully observed differences such as these helped early travelers to navigate.

Images like these can be found using Google's image search with the search string "diurnal star motion" even though, literally speaking, the term nocturnal (nightly) would be more suitable than the term diurnal (daily).
Here is an  animation, taken from still another  location of Northern sky

and of the southern sky.

Time and the calendar

Ancient observations of the sky led to various methods for measuring time, to ways of subdividing years into month and days and days into hours and minutes.  Differing ways of subdividing the year competed for the dubious honor of promoting an accident of birth for our particular solar system into basic principles of the universe.

Setting the full circle of seasons, a year, to be 360 days, had the advantage having 12 new moons per year, and thus 12 months. In contrast, allotting 365 days to a year, disregarding the moon, lead to more accurate sun-based calendars. To this day, major religions use different calendars, some sun-based, some moon-based, and some mixing both.

Our ancestors had difficulties dealing with the fact that the time ratios of a year to a moon cycle to a day are not round numbers such as 360 and 30. They are not even integers.

The number of days in a year can be approximated as

360 = 12 * 30 = 60 * 6

or more exactly

365 = 13 * 7 * 4 = 13 *28

or by

365.242.. =365 +1/4 - 1/100 + 1/400 ...

This last is the current value leading to today's scheme of leap years.

The rate of rotation is 15 degrees per hour. This means every 24 hours there is one complete revolution of 360 degrees. This works out to 15 minutes per angular minute, or a quarter of a minute per second. That these are nice round numbers is not due to chance but reflects the subdivision of a day the by the numbers 12 and 60, numbers given their original significance by their use in subdividing the year

Navigation and the exploration of the globe

sextants used for ship navigation are pictured on this site featuring antique reproductions. 

The rate of rotation, as connected to time and space on the Earth, is reminiscent of the way in which the speed of light connects time and space in our vastly expanded universe.

On the Earth, if you know the longitude and latitude of two cities, you can estimate both the distance between them and the time difference. For example, we observe that San Francisco (CA) and New York (NY), which are at roughly the same latitude, have a difference in longitude of roughly 48 degrees (122 - 74). We can use this to quickly estimate the distance between them in meters, kilometers (km), or megameters (Mm), and to figure the time difference between the two locations. Here is how: We know that a 90 degree difference would cut an arc of 10 Mm (another round number due to the original way of defining a meter), one quarter of the 40Mm circumference of the Earth. This would mean 1/4 of a day, or a six hour time difference. Half of this, a 45 degree difference, leads to an estimated distance of 5Mm (5,000 kilometers) and a 3 hour time difference.

If you need a more exact calculation, taking differences in both latitude and longitude into account, the angle cut by the two cities is 37 degrees, giving a distance 4.147 Mm = 4147 km. Another way to say the same thing, is that each minute arc on the Earth is about 111 km. (Indeed, 4147 / 111 = 37) More precise calculations require the use of trigonometry and spherical geometry as explained here and here in more detail.

This kind of reasoning was used by both the ancient Greeks and by Columbus to estimate the circumference of the Earth. Such reasoning was also used in navigating. Two things were necessary: star charts and an accurate clock. A comparison of the observed positions of the stars with the ship's star charts gave the navigator his latitude. However, since the stars can appear in identical positions in different locations at the same latitude, depending on the time of night, one needed an accurate clock, set to one's home port time, to calculate longitude.

Incidentally, Columbus, in choosing the lowest of several estimates of the Earth's circumference, invented what today's grant writers would call "technological optimismus." As in his time, such optimism may actually facilitate discoveries.

Click for YouTube

Notice the emphasis on having a clock which was accurate. An inaccurate clock meant an inaccurate calculation of longitude, which could have catastrophic consequences, as recounted in this article. It took a challenge from the British government and the offer of a £20,000 prize to speed the invention of a mechanical nautical clock accurate enough to allow the calculation of a ship's longitude to within half a degree, that is about 111/2 ~ 55 km kilometers. This museum-quality video on YouTube re-creates that dramatic story.

Today, using artificial satellites, the GPS systems Navstar and Galileo can determine a position within meters. (Useful for finding your way in a foreign city, as well as for guiding intercontinental missiles to their targets.)

Annual parallax - latitude and the seasons

Click on this applet: Rotating Sky Explorer: Description and guide. The 2 frames of reference shown here, and the role of latitude in the rotation of the stars, are beautifully illustrated in this animation. View it before you read this more complex section of our knol.

Just as longitude and the time of day are reflected in the positions of the stars, so latitude and the seasons of the year determine how high the sun will rise on the sky or, stated in astronomical terms, the angle between horizon and ecliptic.

The stars do not move as if attached to rigid crystal spheres, as the ancients surmised. When viewed against the background of more distant stars, relatively closer stars describe small ellipses during the year. Objects which are even closer, such as the planets in our solar system, follow bigger oval paths in the heavens.

This phenomenon, called annual parallax, is a special case of parallax, the apparent displacement of an image when an object is observed from different points of view. This is shown in the illustration below on the right and explained here in more detail.

Parallax for objects decreases with the distance. It is large for the sun, and becomes smaller and smaller for more remote outer planets. This parallax motion is added to the object's diurnal motion, but it can be detected by looking at the position of the object at the same hour every day throughout the year, a strategy which eliminates the factor of diurnal motion.

The image of an object recorded in this way, usually achieved now with photographs, will be a curve on the background of the stars. For remote outer planets, that curve is a small ellipse, For the sun, it looks like a figure 8 and has a special name, the analemma.

The analemma and the seasons

The path of the sun in our sky during the year, the analemma, is shown at the right. This image was obtained by taking one picture per day, always at the same time of the day, with a fixed camera.
More on the analemma

Two views of a system - two frames of reference

Early in history, people realized that the rotating sky might be an illusion caused by the rotation of the Earth. Philosophers argued about which motion was only "apparent" and which was "real." Both pictures, the Earth observed from the system attached to the stars (or firmament) or the sky observed from the Earth, describe the same reality, the same seasons and motions of the planets, sun, and stars. Each has some advantages.

The question Newton's Laws was not resolved at that time, but a related question, "Is the Earth moving with respect to stars?" could be decided. How?  By using the parallax. It was Tycho de Brahe, and his assistant Johannes Kepler, who did this.

The year 1600, when the telescope was invented, was also a year when Brahe was offered a position as Imperial Mathematician in Prague, then the capitol of the Holy Roman Empire.   Holy Roman Emperor Rudolf II invited astrologers and artists from all over Europe to his court. Rudolf's Imperial Mathematician, which actually meant his astrologer, was Tycho de Brahe [1]. Brahe decided to do some science in his free time, when he was not casting horoscopes. He decided to measure the parallax of heavenly bodies, the planets and stars, to settle the question of whether the Earth is moving or not.

Brahe himself believed in a mixed, helio-geocentric system, in which the Earth was still the center of universe, and was orbited by the sun. The sun, in turn, was orbited by Venus and Mercury.

It had long been observed that Venus, alias the Morning Star, alias the Evening star, never moves far away from the sun. In 1577, even before arriving in Prague, Brahe had mentioned in his writings that some people believed that Mercury and Venus encircle the sun. On the other hand, the possibility of Earth itself orbiting sun was rejected, since Earth was huge and massive. How could it move so fast? Whenever Brahe criticized the physical reality of the heliocentric system, he repeatedly said that it violated physics and Holy Scripture -- always in that order.

Tycho de Brahe was a master instrument builder, who was able to determine using pre-telescope instruments, the positions of the planets, with unprecedented accuracy of half to 2 arc minutes, as well as their parallaxes. Brahe improved the accuracy of measurement 30 times, to an accuracy of half of one degree. His measurements of the parallax of the planets allowed calculation of their distances from the Earth.

His fame, or rather his data, attracted another mathematician-astrologer, Johannes Kepler , to Prague. Kepler wrote to his teacher, Michael Maestlin, "Tycho has the world's finest observations, but he only lacks an architect to construct an edifice out of them."

After Brahe's death in 1601 Kepler, until then just one of Brahe's assistants, got hold of his data. He published some the next year in the "Astronomia nova". A complete compendium (the Rudolfine Tables) appeared in 1625.

Kepler, younger and more radical than Brahe, believed in a heliocentric system. He calculated the parallax of the stars and planets using Brahe's data. He was disappointed when he looked at the star data. Either the Earth was not moving with respect to the stars, or the stars were so incredibly far away that parallax was too small to be measurable, even using Brahe's instruments.

However, the planet data was extremely useful. It allowed him to determine their distances and, connecting the dots, to determine the shape of their orbits. To his surprise, these were not circles but ellipses. This was groundbreaking information.

Wandering stars (planets, sun and moon)

We look again at how planetary motion looked from the Earth. This applet shows that indeed Venus, like Mercury, is always near the sun. The outer planets have both Earth and the sun inside their orbits. They move against the background of distant stars.

The view from Earth was quite confusing. A second applet, giving both an Earth-centered view and a sun-centered view, shows the retrograde motion during which some planets move "backwards" for a while, from West to East.

However, when Kepler charted the data in a system attached to the stars, the motion looked simple, but not quite as expected. Galileo had believed that the sun was at the center of circular planetary orbits. Brahe's data, more accurate then ever before, tabulated by Kepler, showed the orbits were not circles. Now it could be determined that they were moving in ellipses with the sun in one focus. Kepler deduced this elliptical shape first for Mars, where it is most apparent.

Interestingly, the motivation for collection all the data in the first place, to observe the parallax of stars, and so to show that the Earth is moving with respect to the stars, was not achieved. The parallax of nearby stars is visible only with a telescope. Kepler did not expect the stars to be so far away, and their parallax to be so small. However, what Brahe and Kepler together did discover was even more valuable. The so-called "Keplerian orbits"and the laws Kepler deduced about the movement of the planets set the stage for Newton to realize his monumental theories.

There are many applets which show these Keplerian orbits. We list some of them in order of their increasing complexity:

Monument to Brahe and Kepler in Prague

Planetaria