The motion of the Earth around the Sun is a very important motion. Some early Greek philosophers initially decided that the earth was in orbit around the sun, but they could not solve the mathematics. Deciding that they could not make the arithmetic fit, they stated that the Sun revolved around the Earth. Simply because they could not make mathematics describe the motion of the Earth around the Sun, the Sun must be in orbit around the Earth. Because they could write a formula for the Sun's orbit around the Earth explaining the action of shadows, people were convinced for a long time that the Sun must be in orbit around the Earth.

The reason the arithmetic could not be solved is that the Earth is not rotating around the Sun. The Sun does not rotate around the Earth, and the Earth does not rotate around the sun. Neither theory was completely correct. Newton finally solved the problem around 1666. It required his understanding of gravity to realize that the Earth is not traveling around the Sun. The Earth and Sun act as a system. Imagine the Earth and Sun hooked together by a weightless strong rod. Where would it balance? Because the Sun is much heavier than the Earth, the system would balance near, but not at, the center of the Sun. The Earth and the Sun are traveling around a common center of mass, or the common center of gravity of the Earth-Sun system (Figure 7.22).

fig7.21

Fig 7.22 Center of the Earth-Sun system, around which the system revolves, is not at the center of mass of the Sun, although very close to it.

Some apparent irregularities occur because of the Earth-Sun connection. One irregularity would appear to some who thought the planet was going around the Sun. The irregularity is called the retrograde movement of the Sun, which occurs about every 176 years (Shirley, 1988). A shadow can actually reverse itself and can be seen if you are watching a sundial during that period of time. It does not really go backwards, but it elongates when it should be shortening. The way it occurs is explained clearly by this rotation around something other than the center of the Sun. Once, what Newton calls his "theory of gravity" was explained, the mathematics of planetary motion could be described. It describes the orbit of the Earth and the Sun with sufficient accuracy that travel from the Earth to the Moon and other planets by spacecraft can occur.

Gravity affects the orbit of the Earth by producing an orbit, which is not a circle. The orbit is slightly elongated into something more eccentric (termed an ellipse) than a perfect circle. At times the Earth is closer to the Sun that at others (Fig. 7.23). The orbital variation is not as extreme as depicted in this picture, but it is something other than a circle. This elliptical orbit actually has the Earth closer to the Sun during the Northern Hemisphere winter. The change is very small, amounting to a slight increase in radiation during the winter. This eccentricity changes over thousands of years, also. This is a cycle of about 100,000 years. The shifting center of mass for the solar system might make the Sun appear to wobble if viewed from some distinct point. Astronomers infer the existence of planets in other solar systems from observed wobbling of stars.

eccentricity

Fig 7.23 Eccentricity of the Earth's orbit causes the Earth to be slightly closer or farther from the sun during the year. Eccentricity varies over a 100,000 year cycle.