Laws of Planetary Motion

sun, while others orbited in a more geocentric way. He could not himself decide that the earth was a moving thing.

The totality of Brahe’s contributions to astronomy were these:

• He made the most precise astronomical observations to date using his sextants.

• He provided input on the movement of planets that helped Kepler modify and create our current solar system depiction.

• He was able to carefully observe a supernova or exploding star but did not know what it was. It was thought at the time to be a “new star” rather than a “dying star”.

• He was able to carefully observe a 1577 comet and was able to measure the parallax effect for it. This proved it was further from the earth than the moon and not an atmospheric phenomenon.

• He determined there was no parallax with stars so he felt the earth was motionless or that the stars were too far away to measure their parallax. His final conclusion was that the earth didn’t move.

• He proposed a model for the universe that was a hybrid between the heliocentric and geocentric models.

LAWS OF PLANETARY MOTION

Johannes Kepler of the 1600s was a student of Tycho Brahe so he was able to use the data collected by the earlier astronomer in order to create his Laws of Planetary Motion. These were the laws every astronomer was missing because it proved the heliocentric theory but did not require the falsities of epicycles to explain what phenomena were being seen. He used the idea of elliptical orbits rather than that of circular orbits around the sun.

Kepler’s laws require a great deal of mathematical understanding. Orbital motions about the earth required several different key terms. The concept of the perihelion or the point where the earth or a planet is closest to the sun is offset by the aphelion, which is the

point where the Earth’s orbit is furthest from the sun. The aphelion does not necessarily happen in wintertime and the perihelion is not necessarily a summertime thing. In fact, it is the opposite of what you think. Figure 4 describes these states:

Figure 4.

Other terms to know are the apogee and the perigee. These relate to the lunar orbit. The perigee is when the moon is closest to the earth, while the apogee is the point when the moon is the furthest from the earth.

By the end of the 1600s, Johannes Kepler had determined the three laws of planetary motion. He used Brahe’s observations to make theses laws and was able to prove an entire heliocentric system. The laws themselves are still considered valid but his explanations have largely been discounted. The three laws briefly are these:

1. The planetary motions occur in an elliptical fashion around the sun. 2. An imaginary line from the sun’s center to the center of a planet will sweep the same area in the same amount of time spent in the movement. 3. The ratio of the squares of the periods of any two planets is the same as the cubic ratio of their average distances from the sun.

Let’s look at these laws in detail, which are described in figure 5:

Figure 5.

The Law of Ellipses is Kepler’s first law. It described an elliptical rather than circular orbit around the sun. There are two central foci that determine the ellipse’s shape. If they are close together, the ellipse will look more and more like a circle rather than an elongate ellipse. The sun is always one of these foci.

The Law of Equal Areas describes the speed at which a planet moves about the sun. This is not a static thing but always changes. The planet closest to the sun moves faster while the planet further from the sun moves slower. When you draw a line from the sun to any two points traveled over the same period of time, the area within this triangular area will always be the same.

The Law of Harmonies is Kepler’s third law. It looks at the orbital period around the sun and the radius of its orbit compared to the other planets in the solar system. It made a mathematical calculation that the ratios of the period squared to the average distances from the sun cubed are essentially the same for every planet around the sun. It was