Dance of the Planets: Tracking the Wanderers

This article was originally published in 2007, and is reused occasionally by changing the conjunction and finder chart that is used in the introduction.

Summer Conjunctions

An interesting planetary conjunction will be coming up in the next few weeks.

On July 10, 2008 Saturn will be very close to Mars, and will be attractive in the field of view of a pair of binoculars. Unfortunately, their closest approach will be at about 10:30 PM, and they will have already set in the West by then. However, they should be visible close together low in the Western sky just before sunset. And, at the same time, a beautiful quarter-moon will be visible low in the Southwest.

Conjunctions are pretty, and provide great opportunities for easy astrophotography. Any good camera on a tripod can capture the two bright objects in the sky, in the context of the larger star field. (Note: regular camera astrophotos are usually more attractive if you include some foreground objects – trees, horizon, etc., in the view to establish context.)

Conjunctions are also a good excuse to do some Sidewalk Astronomy, especially if you can manage 3 scopes side-by-side (one wide field view showing both objects, and one magnified view of each separate object).

What’s Going On?

For your own enjoyment of these beautiful events, and especially for discussion points if you do Sidewalk Astronomy, it’s worth thinking for a moment about what’s going on up there.

“Why are the Moon and Venus so close together tonight, when they weren’t a week ago? Is it just that the Moon caught up with Venus, which is always in this spot? But wasn’t Venus in a different spot a while ago too? It must have been, because it wasn’t near Saturn, and I don’t see Saturn moving. No, Saturn was in a different spot a year ago (I remember because it was easier to find last year). What’s going on?”

Questions like these fascinated early Astronomers as they tried to understand how the sky worked. So, rather than just giving the answer, let’s briefly trace how the early theories about the motion of the sky evolved to our present understanding.

What They Observed

Without telescopes, ancient astronomers relied on naked-eye observation of the sky. They saw that the stars remained in fixed positions (relative to each other) but rotated around the Earth approximately once a day, slightly changing their positions each night with the changing seasons.
5 bright stars, however, moved differently. They moved at different speeds from the stars and each other, following their own paths through the sky. Two moved around the sky quite quickly (with a noticeably different position every few days) while others moved rather slowly – taking months or a year to appreciably change position. Sometimes these unusual stars even moved backward in the sky for a few days before resuming their forward wandering. The backward movement is called retrograde motion.

These wandering stars were named planets (from the greek word for “wanderer”). (The moon was sometimes considered a planet too, as it clearly also wandered). The irregular motion of these 5 planets, Mercury, Venus, Mars, Jupiter, and Saturn was a great puzzle for ancient scientists.

Why didn’t everything in the sky behave the same way like it was supposed to (ancient texts called the heavens “unchanging”)? The stars were unchanging, but the moon moved at a different speed and showed phases, and the other 5 planets were hard to explain – especially when they moved backward.

Early Thoughts

Early scientists sought an explanation of the arrangement of the sky that matched both their observations and some assumptions they thought obvious, namely:

  • The Earth is at the centre and does not move; and
  • Everything revolves around the earth; and
  • Everything that moves in the sky moves in circles because the heavens are perfect and circles are perfect (Aristotle argued this, 322 BC – 384 BC).

Two Models

The two basic models for the arrangement of the sky were each identified about 2500 years ago.

Greek astronomer Eudoxus of Cnidus, who lived from about 347 BC – 400 BC is credited with proposing the Geocentric model of the universe (Pythagoras may have suggested something similar a hundred years earlier):

  • The Earth is at the centre of the universe; and
  • Other objects in the sky (sun, moon, planets, and stars) are arranged on a series of crystalline spheres, centred on the earth, and turning around the Earth at different distances and speeds.

An alternate model was proposed, on philosophical grounds, around 300 BC (possibly by Heraclides and probably by Aristarchus). Since the Sun was clearly placed in the sky to provide light and warmth for us, wouldn’t it make sense to think it would be in the centre? You’d put a lamp intended to light an entire room in the centre of the room. This was called the Heliocentric model.

The Heliocentric idea was rejected, however, because, while philosophically interesting, it was thought obviously wrong. If the Sun were stationary, then the Earth must have been moving, and it was obvious that it was not. We didn’t feel the motion; unfastened objects didn’t fly away backward; and the stars didn’t change position from opposite sides of the Earth’s orbit, which they should have. (In fact they do, but the ancients vastly underestimated how far away they are, and the parallax motion is too small to be detected without telescopes.)

Improving the Model

Even though the Geocentric model was believed correct, there was one problem with it: it didn’t work. It could not easily account for the irregular motion of the planets, and could not account for retrograde motion at all. It also did not explain the phases of the moon, why the moon’s diameter appeared to change slightly, or why the planets appeared to change brightness.

In about 200 AD, Ptolemy (the librarian of Alexandria) developed a modified version of the Geocentric model – making it more complex in order to produce the varying and retrograde motion of the planets, while preserving the essential characteristic of having the Earth in the centre and unmoving. His system proposed:

  • Each planet orbits the earth in its own circular orbit.
  • While the Earth is roughly at the centre of the system of planets, it is not precisely in the centre of each planet’s orbit. All the planets orbits are slightly offset from being centred directly on the Earth, by different amounts.
  • Also, each planet does not travel on the circular path of its orbit. Instead, it follows a small circular path and the centre of that little circle is what is orbiting the Earth. These little orbiting circles were called Epicycles.

By experimenting with different numbers, sizes, and speeds of circles, offsets, and epicycles, Ptolemy was able to develop a model that quite accurately reproduced what could be observed visually. The model was a departure from the “pure Geocentric” model, since the circular orbits were not centred on the earth, and the Epicycles were not called for by the basic model. It was controversial, but it seemed to work.

A few weaknesses remained in this model, but were ignored because no better explanation could be found that preserved the predetermined answers of Earth in the centre and circular motion.

  • There were still small differences between observations and the predictions of the model;
  • It still did not explain why the moon appeared to change size;
  • It did not explain why Mercury and Venus were never more than a certain distance from the Sun (about 28 and 47 degrees, respectively) while Mars, Jupiter, and Saturn showed no such constraints.

Cracks in the Theory

Ptolemy’s model, then, ruled (with gradual modifications but no revolutionary changes) for about 1500 years. Gradually, however, in the 1500s, cracks that were difficult to ignore began to appear in the underlying assumptions that made it the preferred model. These cracks were discovered by a series of brilliant scientists.

Tycho Brahe

Tycho Brahe was a Danish astronomer who lived from 1546 to 1601. He made several important contributions to Science, of which we will mention two here.
A superb technician, he collected a large volume of the most precise measurements yet made of the positions of the stars and planets, although he did little analysis on his collected data. We’ll come back to his data in a moment.

Tycho also observed a supernova in the year 1573, taking extensive notes on his observations, and he noted that this “new star” temporarily appearing in the heavens was clearly evidence against the belief that “the heavens are unchanging”. He was the first modern astronomer to clearly state that observational data are more important than philosophical arguments.

Nicolas Copernicus

Polish mathematician Copernicus realized, in about 1507, that a model with the Sun, not the Earth, at the centre of the solar system, and with planets moving at different speeds, could also explain retrograde motion and the other things we observe.

He was aware, however, that this model would be very controversial, and fearing accusations of heresy, he delayed the publication of his work for 36 years. He sent it to the publisher in 1543 and history records that he received the first printed copy back from the publisher on the last day of his life, May 24, 1543.

It’s important to understand that, with the limited measurement abilities of the day, his model was not more accurate than the Ptolemaic model which, for naked-eye visual observation, was adequate. Copernicus’s model still assumed circular orbits and had other weaknesses. It was simply a suggestion that a Heliocentric model was an interesting alternative.


About 20 years after Copernicus’ death, Galileo Galilei was born in Italy, and grew to become a scientist of great repute, making many contributions to mathematics, physics, and astronomy.

While serving as a professor of astronomy in 1609, he heard of the recent invention of the telescope, studied this new concept, and began to make his own instruments. His first telescope magnified 3 times, his second 10 times, and his third 30 times. With this 30-power instrument he made a number of startling discoveries in the sky:

On Jan 7, 1610, he saw the disk of Jupiter, with pinpoints of nearby light that might have been stars. But on the next night, one of the “stars” had changed position, to the other side of Jupiter. After observing for some weeks, he realized that the points of light were satellites of some kind orbiting Jupiter, and that this was evidence that it was not true that everything in the heavens orbited the Earth.

He observed Venus and discovered that it passes through a complete set of phases, like the moon. The Ptolemaic model made a different prediction than this. The Copernican model, on the other hand, was compatible with these observations. (To show a complete set of phases, an object must be between the observer and the light source – i.e. between the Earth and the Sun.)

Galileo eventually became convinced of the superiority of the Copernican model, and published his data and arguments in a lengthy work. And, unlike the tradition of publishing scholarly works in Latin, he published his in Italian, and in a conversational style that enabled the majority of the population to read and follow his arguments. The trouble this brought him with the Church, and the fact that he was eventually forced to renounce his work under threat of heresy, is the subject of another story.

Development of the Modern Model

Meanwhile, Tycho’s observational data was being put to good use. After Tycho’s death, his former lab assistant Johannes Kepler, a gifted mathematician, began to analyze the collected data in detail.

Analyzing Tycho’s observations of Mars, he realized that the position could be better explained with the assumption that the plane of Mars’ orbit was tilted slightly from the Earth’s equator. With this new revelation and further analysis he gradually developed three laws of motion that correctly described the motion of the planets, using Copernicus’ Heliocentric model. The resulting model was both more accurate and simpler than that of Ptolemy, and gradually won acceptance as correctly representing reality.

The essence of Kepler’s laws are:

  • Planets orbit the sun in Ellipses, not Circles. The sun is at one focus of the ellipse. (Note: for most planets the ellipses are not very elongated, and, to his credit, Ptolemy’s “offset circles” were a good approximation.)
  • Planets speed up as their orbit approaches the sun, and slow as they move farther away from it.
  • The speed and distance are all related by a simple formula involving a constant. All the planets use the same formula and constant. Orbits around a different object (e.g. the Moon’s orbit around the Earth) use the same formula but a different constant; so the constant seems to be related to some property of the central object.

His laws correctly and precisely predicted the next retrograde period of Mars’ orbit, and this was considered a strong verification.

Kepler’s laws only describe the orbit of an object, they do not offer an explanation as to why it is happening. Kepler knew some kind of attractive force had to be involved, and suggested (incorrectly) it might be magnetism.


English physicist, mathematician, and astronomer Isaac Newton made the next step in developing a mathematical model consistent with observational data and Kepler’s laws. Whether or not there was a falling apple involved (as legend relates) he realized that the same attractive force that makes objects fall on Earth could reach much farther and, for example, prevent the moon from flying off into space. This line of reasoning led to the development of three laws of motion that explained, simply and accurately, all the motions we could observe, from the fall of a rock to the orbit of planets.

One very exciting property of Newton’s laws was that they could be rearranged algebraically in a way that gave Kepler’s laws. Kepler had simply discovered a simpler case of the same laws (the simplification being that the Sun was so massive compared to the planets that the mass of the planets did not need to be taken into account). When a new scientific discovery incorporates previous theories in a compatible way and then adds new predictive capability for new cases, this is taken as very powerful support for the theory.

Newton showed that the attractive forces between objects such as the Earth and Moon, or a planet and the sun, is a simple function involving only their masses, the distance between them, and a universal constant. This simple function was compatible with everything observed to date, and generated testable predictions: the planet Neptune was found by analyzing small irregularities noted in the orbit of Uranus, and calculating where another planet would have to be in order to have that effect. Neptune was found where Newton’s formulae predicted it would be.

Newton’s laws, and Newton’s generalization of Kepler’s laws, seemed to be the final correct answer to describe the motion of not only the planets but everything that moves.

Except. . .


As measuring technique became more accurate, one small nagging problem remained. The planet Mercury wasn’t quite obeying the rules – its orbit was changing at a slightly different rate than Newton/Kepler predicted.

In 1915 Albert Einstein published his General Theory of Relativity, which was a yet more complete theory of gravitation. It was related to Newton’s formula in the same way Newton’s was related to Kepler’s: it gave exactly the same predictions as Newton’s formula in a large number of cases but differed under special circumstances, namely when objects are moving at very high speed (close to the speed of light), or are moving in a region of very intense gravity.

Mercury, being so close to the Sun, is moving in the Sun’s intense gravity field. General Relativity predicted motion for Mercury that precisely matched available observations, while continuing to correctly explain the motion of all the other planets. Since then, General Relativity has been confirmed in many other precise experiments as well.

So What’s Going On Up There?

Which brings us to today. Our current model for the motion of the objects we see in the sky (verified to great accuracy by multiple experiments) is as follows.

The stars are in fixed positions. (In fact they are moving quite quickly but they are so far away that, for purposes of discussing nearby events in our solar system, their relative motion is insignificant.)

All the planets, asteroids, and comets, are orbiting the sun. All the orbits are elliptical, with the Sun at one of the foci of the ellipses. However, the elliptical orbits of the planets are not very “stretched” – they are almost circular. (The orbits of comets, by comparison, are quite elliptical.) The planes of the orbits of the planets are all roughly, but not precisely, aligned – some tip “up” a bit, some tip “down”.

The orbits are elliptical, but are “stretched” so little that they appear circular. Jupiter is much farther out than the first 4 planets, and the outer 3 planets are so far out they can’t be shown on this scale.

The closer an object is to the Sun, the faster it moves, so Mercury and Venus orbit faster than the Earth, while Mars, Jupiter, Saturn, Uranus, and Neptune, orbit slower. This is why, from our point of view, Mercury and Venus change position in the sky quite quickly, while Jupiter and Saturn move through about one constellation per year.

The Outer Planets. The orbits of Mars, Earth, and Jupiter are shown again to establish the scale.

Since the outer planets move more slowly than the Earth, we catch up and pass them in our orbit. While we are passing an outer planet, it appears to move backward from our point of view; this is the retrograde motion that puzzled the ancient observers.

Gibbous Mars
Gibbous Phase of Mars
Hubble Imaage courtesy NASA.

In theory, all planets show phases like the phases of the moon. However, only an object between the Earth and the Sun can have a crescent phase (where it is less than 50% illuminated), so only Mercury, Venus, and the Moon ever show crescent phases. While the outer planets can, in theory, show gibbous phases (in which there is less than 50% of the disk in shadow), the maximum amount of shadowed area is a function of distance and, in practice, only Mars ever shows a gibbous phase that is detectable to a visual observer on Earth.


Beginning observers should make a point of knowing the location of the easily visible bright planets (Venus, Mars, Jupiter, and Saturn) through the year. Enjoy the dance of these wanders as they move around the sky, and remember that they were also responsible for promoting much of the early thought and debate in Astronomy that lead us to our current understanding of the universe.

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