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# Motions of the Inner and Outer Planets

I look up from Earth and try to see
The planets looking back at me.
I gaze at bright and distant stars
And search for Mercury, Venus, Mars.

-Carol Weston

## Overview

• Understand the apparent motion of the planets in the sky, and key positions.
• Understand the different observed behavior of inner and outer planets.
• Understand phases of the inner planets.

## Introduction

The word “planet” comes from the ancient Greek term asteres planetai meaning “wandering stars”. The Greeks observed that there were 5 objects that generally looked like the fixed stars, but they moved around compared to those stars. Their association of these objects with gods was adopted by the Romans, whose names for them are Mercury, Venus, Mars, Jupiter and Saturn. We now recognize these objects as physical planets of our solar system. What are the patterns of planetary motion in our sky? How do these patterns relate to the relative positions of the planets and the Earth in our solar system? We will see that the main difference in planetary motions is based on whether a planet's orbit is inside or outside of Earth's orbit, as shown in Figure 1. Thus, we distinguish between inner (inferior) and outer (superior) planets.

Figure 1: The orbits of Venus, Earth, and Mars. Venus’ orbit is inside Earth’s, so it is an inner planet; whereas Mars, having an orbit outside Earth’s, is an outer planet.

### Elongation

A planet's elongation is its angular distance from the Sun in the plane of the ecliptic, measured in degrees (Figure 2). Since it will appear to be east or west of the Sun, it is specified as either eastward or westward elongation. The solid lines in Figure 2 show a 16º eastward elongation if either planet is located on the upper solid line. At this position, the planet appears in the sky at an angular distance of 16º from the Sun, along the ecliptic. As seen in Figure 2, the inner planets have a maximum angular distance from the Sun, called the maximum eastward or maximum westward elongation.

Figure 2a: Top-down view of the ecliptic plane, showing elongation for the inner planets. The maximum elongations for Venus are shown with the dashed lines, and those for Mercury are shown with the dotted lines. Click the image for a larger view.

Figure 2b: View of inner planet orbits from Earth.

All of the planets can align with the Sun, or have an elongation of 0º. This is called conjunction. The outer planets can be on the opposite side of the Earth from the Sun, which is when we will see it in the opposite part of the sky from the Sun (Figure 3). When a planet's elongation is 180º, it is said to be at opposition. When a planet is at opposition, it will rise at sunset and be highest in the sky at midnight, making it easy to observe. Also, as you can see from Figure 3, this is basically when the planet is closest to Earth, which also makes it a good time to observe. Note that the inner planets can never be at opposition.

Figure 3: Conjunction and opposition.

Figure 3 also shows that the outer planets can only be at conjunction when they are on the opposite side of the Sun from the Earth, so the Sun is between us and the planet. The inner planets, however, can be at conjunction in two positions: either when they are on the opposite side of the Sun from the Earth, or when they are on the same side of the Sun as the Earth. When they are on the opposite side of the Sun, it is called superior conjunction, and if they are on the same side, it is called inferior conjunction. The inner planets are generally closest to us at inferior conjunction, but it is very hard to observe the planet because its angular distance is so close to the Sun. The planet will also be in the new phase, where our view of its illumination is close to zero (see below).

### Phases of the Inner Planets

The inner planets go through phases similar to the Moon. Just as with the Moon, it is the positioning between the planet, the Earth, and the Sun that determines how much of the illuminated portion we see, and hence, the phase. Figure 4 shows the phases of Venus.

Figure 4: The phases of Venus

One big difference between the phases of the inner planets and the phases of the Moon is that the angular size of the planet changes with the phase. As you can see from Figure 4, the full Venus appears much smaller than a crescent Venus because a crescent Venus is much closer to us. This means Venus is actually at its brightest when it is in a crescent phase.

Since the planets are rarely exactly on the ecliptic plane, they do not usually line up exactly with the Sun at conjunction. However, it does happen occasionally. If a planet passes directly behind the Sun at superior conjunction, it is called an occultation of the planet by the Sun. If an inner planet passes directly in front of the Sun, at inferior conjunction, it is called a transit of the planet. Transits are relatively rare events. Roughly 14 transits of Mercury occur every century. Transits of Venus, on the other hand, take place in pairs, with two transits occurring roughly 7.5 years apart, with either 105.5 or 120.5 years between pairs. The next transit of Venus will take place in 2012, and is the second in the current pair.

In addition to watching the positions of the planets relative to the Sun, we can watch their positions relative to the fixed stars. Since both the Earth and the planet are moving, this motion can be rather complicated. The planets normally move in one direction along the ecliptic. Occasionally, however, they will stop their "forward" motion and appear to reverse, which is called retrograde motion.