Configurations of the Earth and the inner and outer planets. Positions of the inner planets are indicated by numbers: (1) inferior conjunction, (2) superior conjunction, (3 and 3') greatest elongation. Positions of the outer planets are indicated by letters: (A) opposition, (B) conjunction, (C) quadrature.
the morning. When it is east of the Sun, it rises and sets after the Sun, and is most easily visible in the evening.
We then look at planets that are farther from the Sun than the Earth. Let's start by looking at the planet when it is farthest from Earth, on the far side of the Sun. We say that the planet is simply at conjunction. At that point, it would be too close to the Sun in the sky to see. As it moves farther from that position it appears farther from the Sun on the sky. When it reaches a point where the Earth, Sun and planet make a right triangle, with the Earth at the right angle, we say that it is at quadrature. Notice that there is no limit on how far on the sky it can appear to get from the Sun. Eventually, it reaches the point where it is on the opposite side of the sky from the Sun. We call this point the opposition, and it is also the closest approach of the planet to Earth. When the planet is at opposition, it is up at night (since it is opposite to the Sun in the sky). Therefore, when a planet is favorably placed for observing, it is also closest to Earth and can be studied in the greatest detail.
When we talk about the orbital period of a planet, we mean the period with respect to a fixed reference frame, such as that provided by the stars. This period is called the sidereal period of the planet. However, we most easily measure the time it takes for the planet, Earth and Sun to come back to a particular configuration. This is called the synodic period. For example, the synodic period might be the time from one opposition to the next. How do we determine the sidereal period from the synodic period?
Suppose we have two planets, with planet 1 being closer to the Sun than planet 2. (For simplicity, we assume circular orbits.) The angular speed w1 of planet 1 is therefore greater than that of planet 2, «2. The relative angular speed is given by
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