Synodic Period

by Dominic Ford, Editor

Mars orbits the Sun once every 1.9 years, but only comes to opposition once every 2.1 years.

The synodic period of an astronomical body is the time interval between its successive conjunctions with the Sun.

It is also equal to the time period between the successive apparitions of that body, with the exception of Mercury and Venus, which have two apparitions within each synodic period.

## Differential rotation

The planets don't all orbit the Sun at the same speed. The inner planets feel a much stronger gravitational pull from the Sun than the outer planets, and have to move faster to remain in orbit.

This difference is compounded by the fact that the circumferences of the orbits of each of the planets get longer the further they are from the Sun, and means that it takes the inner planets much less time than the outer planets to complete each circuit around the Sun. This is called differential rotation.

Planets which are closer to the Sun move faster, and take much less time to complete each orbit, as compared to more distant planets.

## A celestial racetrack

Whether a planet is visible or not depends whether it is on the same side of the solar system as the Earth, or on the far side.

Planets such as Jupiter, which orbits further from the Sun than the Earth, are best seen when the lie on the same side of the solar system as the Earth – when it is at opposition. At this time, Jupiter, the Earth and the Sun lie in an almost straight line, with the Earth in the middle. Jupiter appears opposite to the Sun in the sky and is at its highest in the sky at midnight.

Jupiter passes solar conjunction when it is directly opposite to the Earth in the solar system.

The two exceptions to this rule are Mercury and Venus, which orbit closer to the Sun than the Earth.

They pass close to the Sun in the sky when they are on the same side of the solar system as the Earth – passing between the Sun and Earth – and when they are on the opposite side of the solar system – passing behind the Sun.

Between these two conjunctions, they alternately appear to the east of the Sun, and to its west, becoming either the morning star, or the evening star.

## Calculating a planet's synodic period

The time interval between successive oppositions or solar conjunctions of a planet depends not on how fast it goes around the Sun, but how often it overtakes the Earth in its orbit.

The outer gas giants move very slowly around their orbits. Each time the Earth completes an orbit, these planets have not moved very far from where they were a year earlier, and so the Earth overtakes them roughly once a year.

At the opposite extreme, Mercury circles the Sun once every 88 days, after which time the Earth has completed less than a quarter of a revolution. Mercury overtakes the Earth every 116 days, the additional 28 days being needed for it to catch up with the Earth's own orbital progress in the intervening time. This period – the time interval between any planet's closest approaches to the Earth – is its synodic period.

Those planets which are closest to the Earth – especially Venus and Mars – have very long synodic periods. This is because they orbit the Sun at speeds very similar to that of the Earth. If there were to be another planet that orbited the Sun at exactly the same distance as the Earth, it would orbit the Sun at exactly the same rate as the Earth and never overtake it – its synodic period would be infinitely long.

The equation for this is as follows: $\frac{1}{\text{Synodic Period}} = \left| \frac{1}{P_E} - \frac{1}{P_P} \right|$ where:

$$P_E$$ is the orbital period of the Earth (365.25 days), and

$$P_P$$ is the orbital period of the planet.

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