Loops in the sky

Introduction
An earlier article by Paul Abel outlined the motions of the planets. This tutorial goes into the subject a little more deeply and considers some of the apparent gyrations made by planets which orbit further from the Sun than the Earth does. These planets are often referred to as the Superior Planets. Also explained are some of the terms often encountered, for example in the BAA Sky Notes, when describing the motions of the planets.

Loops
In this article we will concentrate on the movements of the planet Mars against the background of stars as seen from Earth. The same effects apply to all the outer planets and asteroids though for objects more distant than Mars the loops are smaller and less obvious.

Figure 1 shows the path of Mars for part of 2018. Starting at the right hand side of the image the planet moves eastward, gradually slowing down until on June 28th it stops at S1 where it reverses direction. It then tracks westward for a while before slowing down once more, stopping on August 28th at S2 and resuming its normal eastward motion.

The motion towards the East is the normal apparent motion of an outer planet and is known as direct or sometimes prograde motion. The motion towards the West is referred to as retrograde and the points where it is stationary are unimaginatively known as the stationary points! Notice that opposition on July 27th occurs in the middle of the retrograde motion.

What is the cause of this? As the Earth moves around the Sun in its orbit, it catches up the slower moving planets further out. As it passes them on the inside – so to speak – they appear to be moving backwards. Figure 2 shows how this happens.

The Earth, on the ‘inside track’, catches up with Mars. From positions 1 to 3 the observed motion is direct. Position 3 is the first stationary point. From there the motion is retrograde through to point 7 with opposition occurring at position 5. Following point 7, the planet resumes its direct motion once more.

A helpful analogy to consider is overtaking a slower car on a dual carriageway. While you are still some distance behind it seems to be passing objects on the horizon in the same direction as you are. As you get closer the speed that this happens slows down. When passing it, with respect to you, it appears to be moving backwards. Once you are well ahead it again seems to be moving forwards with respect to the horizon.

This is all well and good but why do planets appear to create loops rather than straight lines? After all, when you overtake a car on the motorway it does not seem to rise up into the sky and then fall back down again!

The answer lies in the fact that the orbits of the planets are tilted with respect to one another and generally when the Earth overtakes one it does so from ‘above’ or ‘below’. This means that as the Earth’s distance from the planet changes so does the angle at which we see it. The greater the distance the shallower the angle and vice-versa. This changing angle combined with both planets’ motions creates the effect of a loop.

There is an exception to the loops that does occur from time to time. Figure 3 shows the path of Mars during part of 2020. Here the planet describes not a loop but rather a distorted ‘Z’ shape. What is happening here is that as the Earth overtakes Mars, Mars itself is moving from below to above the Earth. The plane of the Earth’s orbit, the ecliptic, is the yellow line. Note how the path of Mars moves from South to North across the ecliptic, from ‘below’ to ‘above’ the Earth’s orbital plane. Contrast this situation with that in Figure 1 where Mars remains entirely south of the ecliptic and hence describes a loop rather than a ‘Z’.

Acknowledgements
The charts in Figures 1 and 3 were adapted from the dynamically generated maps available at in-the-sky.org a website offering much valuable information on what happens in the sky.