A new look at orbits

Many people assume that the orbits of the planets are far more elliptical than they actually are. However, the orbits of all the planets with the exception of Mercury and Mars are nearly perfect circles. If the orbits of the planets are modeled as 26 inch bicycle wheels, the deviation from a perfect circle is less than one millimeter. The Earth’s orbit around the Sun is normally depicted as being highly elliptical in order to teach students about Kepler’s laws. This has been identified as a possible source of the misconception that it is warmer in summer than winter because the Earth is closer to the Sun. A possible way forward is to first teach students that the orbit of the Earth is essentially circular, like a bicycle wheel, and that seasons are due to the tilt of the Earth’s axis of rotation, and then switch to exaggerated elliptical orbits to teach Kepler’s laws.

gee 405 000 km, perigee 362 000 km) the orbit of the Moon is close to circular due to the Earth being at a foci of the orbit.If the lunar orbit around the Earth were a 26 inch bike wheel, the deviation from a perfect circle would be only 1 mm.
A supplementary Excel file has been included with the above data and shows how the mm and % tolerances were calculated.
Table 1.Orbital characteristics of the Moon and eight planets.All values in the first five numerical columns are in millions of kilometres, f = focus, a = semi-major axis, b = semi-minor axis, e = eccentricity.The tolerance is based on the semi-major axis of the orbit being the rim of a 26 inch bicycle wheel.In the last column the tolerance is expressed as a percentage of 26 inches or 660.4 mm.

Introduction
Diagrams similar to figure 1 appear in almost all first-year university physics text books that teach students about planetary orbits and the first two laws of Kepler, (1) orbits are elliptical and, (2) a line joining the center of the Sun and the center of a planet sweeps out equal area in equal time.
In figure 1, the difference between the semimajor and semi-minor axes is greatly exaggerated, as is the distance of the Sun from the center of the ellipse.Similar diagrams are used to show the Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Earth at perihelion, aphelion, and at both ends of the semi-minor axis between these extremes.These diagrams are intended to show the circular orbit of the Earth at an oblique angle, but the perception is that the Earth's orbit is much more elliptical than it actually is.This leads to the impression that the Earth is much closer to the Sun at perihelion compared to aphelion, which is not the case.
Several papers in the education literature discuss the relation between teaching students about the elliptical orbits of the planets and the origin of the seasons (Aravind 1987, Lee 2010, Oostra 2014, 2015, De Paor et al 2017).A common theme discussed is the relation between how orbits are drawn and the very common misconception that it is warmer in summer because the Earth is closer to the Sun.

The orbit of the Earth around the Sun
A correctly scaled diagram of the Earth's orbit is shown in figure 2, which looks quite different from figure 1.The Earth's orbit around the Sun, and the other planets are far more circular than commonly supposed.
By definition, it is of course true that the semiminor axis (a) is smaller than the semi-major axis (b), and perihelion is smaller than aphelion, but due to the Sun being at the focus of an ellipse the ratio a/b is much closer to unity.
An analogy to the difference between figures 1 and 2 is that figure 1 is equivalent to exaggerated stage acting where emotions and movements are amplified so they can be seen by the audience seated out in the theatre.

The Moon and planets
Table 1 shows the orbital characteristics of the Moon and planets.The value in the 'f' column is the distance of the focus from the center of the ellipse in millions of km.The last column shows the tolerances of the orbits applied to a 26 inch bike wheel.For the tol.(mm) column, the semi-major axis is taken as exactly 26 inches (660.4 mm) for the Moon and eight planets.This value of 660.4 is then multiplied by the ratio of the semi-minor axis to the semi-major axes, i.e. b/a.In the case of mercury, b/a = 0.978 651 49 and when multiplied 660.4 gives 646.3 mm.The difference is 660.4 − 646.3 = 14.01 mm as seen in the table.
Bicycle wheels are considered to be 'true' if the variation is less than 1 mm.Using this criterion, table 1 shows that the orbits of all the planets, except Mercury and Mars are practically perfect circles.Venus and Neptune have the most circular orbits with respective 26-inch wheel equivalent tolerances of just 6 and 10 µm-much less than the thickness of the paint on most bicycles.Even the orbit of the Moon is close to a perfect circle.
The orbit of the Earth is equivalent to the rim of a 26 inch bike wheel with a diameter deviation less than 0.1 mm-about the same as the thickness of a thin coat of paint.Figure 3 shows a schematic comparison of the orbit of Mercury compared to the other seven planets.Mercury has by far the most elliptical orbit.However, even this is not far from circular.
Figure 4 shows a photo of a truing stand in the Uni Bike Shop (www.unibikeshop.com.au/) at the University of Queensland, St. Lucia Campus, which is used for making wheels more circular and the plane flatter, a process known as truing.The tolerance of the wheel on the stand was 2-3 mm, i.e. about the same as the orbit of Mars.

Using a bicycle wheel analogy to teach orbits
Studies have shown that it is extremely difficult to dislodge misconceptions about the orbit of the Earth, which has led some authors, for example De Paor et al (2017) to advocate teaching seasons before elliptical orbits.
The bike wheel analogy of planetary orbits is a good one to start with since even young children are familiar with bike wheels.The orbits of all the planets, with the exception of Mars and Mercury, are analogous to near perfect bicycle wheels.Mars is like a wheel slightly out of true and Mercury a wheel after it has had a major collision with a curb or rock-but you could probably still ride a bike with a wheel like this.
If students are initially taught that the orbit of the Earth is essentially circular, like a bike wheel, when they eventually come across diagrams like figure 1, they will realise that the shape of the orbit has been exaggeration for educational purposes, or they are viewing the circular orbit of the Earth Table 1.Orbital characteristics of the Moon and eight planets.All values in the first five numerical columns are in millions of kilometres, f = focus, a = semi-major axis, b = semi-minor axis, e = eccentricity.The tolerance is based on the semi-major axis of the orbit being the rim of a 26 inch bicycle wheel.In the last column the tolerance is expressed as a percentage of 26 inches or 660.4 mm.   at an oblique angle.The adage prevention is better than cure is relevant here.The Greeks believed that heavenly bodies travelled in perfect circles.Paradoxically the common idea of the Earth's orbit being highly elliptical is further from the truth.We have now come full circle if you will excuse the deliberate pun.

Figure 1 .
Figure 1.Generic diagram of the orbit of a planet around the Sun type that appears in most first year undergraduate text books.

Figure 2 .
Figure 2. A correctly scaled diagram of the Earth's orbit around the Sun.

Figure 3 .
Figure 3.Comparison of the circularity of the orbit of Mercury compared to the other seven planets.

Figure 4 .
Figure 4.A wheel on a truing stand.The callipers at the bottom left of the rim are used to gauge the radial and axial deviation of a wheel.