Skip to main contentMotion of the Planets
The ancients knew that in addition to the Sun and Moon, there were five other bright objects that slowly moved among the stars. Those other objects are the planets. In fact, the name “planet” comes from the Greek word for “wanderer”. Over the course of weeks and months, the planets appear to move forward, then stop in their tracks, move backward, then resume course again. The strange, looping paths that the planets charted across the sky must have been a great source of curiosity and puzzlement to ancient observers.
The path of Mars through the constellations of the Zodiac over the course of a year.This is just one example year; the planets’ paths are different every year.
The Geocentric Model
Contrary to popular belief, the ancient Greeks knew that the Earth was round. They knew this because of the way ships appeared mast-first over the horizon, and because of the round shape of the Earth’s shadow on the Moon during a total lunar eclipse. The Greeks also believed that the Earth was at the center of the universe.
Around 400 B.C., Plato claimed that heaven is perfect, and that the circle is the most perfect form. Thus, the heavens are in uniform circular motion with the Earth at its center. This was the beginning of the geocentric model. This simple geocentric model cannot explain the retrograde motion of the planets, however. Around 140 A.D., Ptolemy proposed a refined geocentric model. (He proposed many refinements; we’ll only discuss the simplest one.)
Ptolemy’s geocentric universe.
In the Ptolemaic universe, a planet moves in a small circle called an epicycle, and the center of the epicycle moves along a larger circle around the Earth. Since Mercury and Venus never appear very far from the Sun, the centers of the epicycles of Mercury and Venus must lie on a line joining the Earth and the Sun. Stars are fixed to an outermost sphere.
This model gives predictions of the positions of the planets that are accurate to within a few degrees of their actual positions. The Ptolemaic model was generally accepted, and dominated the western world for about 1500 years.
The Heliocentric Model
Nicolaus Copernicus (1473-1543) proposed the heliocentric model. In this model, the center of the universe is the Sun, not the Earth. The Earth is just another planet orbiting around the Sun, and it no longer has a special place in the universe.
Nicholas Copernicus (left); the heliocentric universe (right).
This model is simple and elegant, and it explains the retrograde motion of planets. Even though the accuracy of this model was as good as Ptolemy’s, the Copernican model was not commonly accepted in its time.
The heliocentric model neatly explains the retrograde motion of Mars.
Galileo and the Telescope
Galileo Galilei (1564-1642) was a great defender of the heliocentric model. He did not actually invent the telescope; in fact, no one’s sure who invented it. But Galileo was the first person to observe the sky with a telescope, in 1609. When he did so, Galileo made four major discoveries:
- The Moon’s surface is covered with craters and mountainous terrain.
- There are dark spots on the Sun.
- Four satellites orbit around Jupiter.
- Venus goes through a full set of phases, just like the Moon.
The first two discoveries proved that the heavens were not perfect. The discovery of satellites orbiting Jupiter showed that there are other “centers” in the universe; in fact, those four satellites are now called the Galilean satellites. The phases of Venus proved that Venus must orbit the Sun, not the center of an epicycle.
Galileo’s observation of the phases of Venus proved that Venus must orbit the Sun, not the center of an epicycle.
Galileo was condemned for “doing science.” Galileo searched for the truth by observing and performing experiments - but the Vatican believed the truth could only be found in faith. The Inquisition sentenced Galileo to life imprisonment, and he was confined to his villa for the last ten years of his life.
But in the end, Galileo was right.
Kepler’s Three Laws
In the late 16th century, the wealthy Danish astronomer Tycho Brahe (1546-1601) undertook a program to measure the positions of the planets with unprecedented accuracy almost every night. The large amount of data he accumulated allowed his assistant and successor, Johannes Kepler (1571-1630), to discover the three laws of planetary motion.
Kepler’s first law states that the orbits of the planets around the Sun ellipses (not circles) with the Sun at one focus. One way to draw an ellipse is to pin down the ends of a string, then use a pencil to stretch out the string. The positions of the two pins are the foci, and curve drawn around them is an ellipse.
Kepler’s second law states that a line from a planet to the Sun sweeps over an equal area in an equal interval of time. This means that when the planet is closer to the Sun, it moves faster.
How to draw an ellipse (left); Kepler’s second law (right).
Kepler’s third law states that the square of a planet’s orbital period (P) is proportional to the cube of its average distance from the Sun (a).
These three laws could explain Brahe’s data to the limit of his observational accuracy, and finally proved that the heliocentric model was correct.
A demonstration of Kepler’s third law (left); Kepler and Brahe (right).
Newton and Universal Gravitation
Kepler did not know the reasons behind his three laws; he had just deduced them from observational data. He knew that they were true, but he did not know why they were true. Sir Issac Newton (1642-1727) provided the theoretical basis for Kepler’s three laws - and much more - from even more basic assumptions.
Newton realized that four basic principles could explain the motion of (essentially) anything in the universe. The first three principles are known as Newton’s Three Laws of Motion. The fourth is the Law of Universal Gravitation. Newton’s laws are as follows:
1 - Every object stays at rest, or in uniform motion in a straight line, unless another force acts on it. This is inertia.
2 - If a force acts on an object, the objects accelerates in the direction the force was applied, at a rate that is directly proportional to the force, and inversely proportional to the object’s mass. In other words, F = M a.
3 - Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first.
4 - There is an attractive force between any two objects, equal to a constant (G) times the product of the objects’ masses (M1 and M2), divided by the square of the distance between them: F = G M1 M2 / r2
An apple, for example, falls to the ground because the apple and the Earth attract each other. Now, it is not difficult to understand why the Moon orbits around the Earth. If the Earth were not there, the Moon would fly away in a straight line (inertia). The Earth and the Moon attract each other (gravity), so the Moon falls toward the Earth, just like an apple. This falling keeps the Moon in its orbit. Similarly, the Earth and other planets are constantly “falling” around the Sun.
Inertia and Newton’s Law of Universal Gravitation (left) explain why the Moon orbits the Earth (right).
Newton’s gravitational theory also predicts that, in general, an object’s orbit can be any one of the four conic sections: a circle, an ellipse, a parabola, or a hyperbola. Conic sections get their names because they take the shapes of the cross sections of a cone. We have found some comets in parabolic or hyperbolic orbits.
Newton’s laws predicted that all orbits must take the shape of a conic section.
The story that an apple hitting Newton’s head was the inspiration for his law of gravitation might not be true. But Newton did make the realization that the same forces which affect objects on Earth also explain their motion in the heavens. Newton was the founder of modern physics.