Alternative conceptions of orbital motion
A topic in science concepts and learners' conceptions and thinking
Science teaching involves teaching scientific concepts, yet these may be difficult to completely characterise, and may prove difficult for many learners to master (a very brief introduction to why this might be can be found at the foot of this page).
This page introduces some issues related to orbital motion, with links to examples discussed in more detail elsewhere on the site.
Orbital motion
We observe that celestial bodies often orbit over celestial bodies. So, in our solar system the planets move around the Sun, following predictable and fairly regular paths. (A good many comets also orbit the sun, although their paths may be less regular as they are more readily disturbed.)
The planets may have their own satellites. The Earth has its Moon. We now know that most of the other planets also have moons – and the moons tend to follow fairly regular and predictable orbits around the planets, as the planets do around the Sun. (Strictly we might say a planet and its moon(s) is the system which orbits the Sun.)
In recent years it has become clear that our solar system is not unique – many 'exoplanets' (planets outside out own solar system) have been detected around other stars. it is now thought such systems may be more the norm than the exception.
Science also has a robust model of why orbiting continues. Solar systems are bound by the gravitational force, which is always attractive. The Earth and Sun mutually attract (with a force determined by their masses and separation) and it is this force which is responsible for changing the earth's direction as it moves through space so that the earth follows a curved orbit.1 The gravitational force has just the right magnitude to provide the degree of centripetal acceleration (that is, acceleration towards the centre of a circle 2) required to curve the Earth's path just enough so it continues to move around the sun rather than spiral in or slowly recede into deep space. That is not a coincidence – once solar system has formed any bodies that were not in stable orbits would soon (in astronomical terms!) either collide with and be absorbed into the Sun or drift out of the solar system. 2
The planets (and their moons) orbit in ellipses, most of which are not far off being circular (they have low eccentricity). An ellipse has two foci, and the Sun is at one focus of the planet's orbit (and a planet is at one focus of a moon's orbit). If an obit is perfectly circular, the planetary body will move at a constant speed, subject to a constant centripetal acceleration. Because the orbital paths are not perfect circles the orbiting body will be slightly closer to the central body at some points in the path than others, so the centripetal force is slightly stronger when the two bodies are closer, and so the force acting on the orbiting body is slightly greater at these times 4, and so the shift in direction is also slightly greater – the orbiting body curve slightly more at these time – which is what is needed to maintain the elliptical path!
Historical conceptions
(This is a very complex topic, and this is only a brief outline sketch.)
Our modern scientific account of the solar system would have seemed very odd for much of human history. The 'ancients' had a range of ideas, but the model of the second century astronomer Claudius Ptolemy was largely accepted in Europe at least up until the seventeenth century.
In Ptolemy's system the fixed centre of the World (i.e., what we would think of as the Cosmos/Universe) was the Earth – which did not move (not even to rotate). There were eight concentric spheres surrounding the earth on which seven 'planets' and the outer sphere of fixed stars rotated around the earth. The seven planets (or wandering stars) were (from closest to the Earth out to the fixed stars):
- The Moon
- Mercury
- Venus
- The Sun
- Mars
- Jupiter
- Saturn
Clearly this reflects a different ontological commitment to the modern scientific account as the typology 'planet' excluded the Earth, but included the Sun and Moon. It was commonly thought that the material nature of the Earth was quite different from that of the celestial bodies. 5 This does not simply mean a different chemical composition, but that the 'sublunary' realm (beneath the moon) was comprised of different, mundane, basic matter than the heavens which were perfect and unchanging.
"The supralunary world, for its part, is animated by natural, circular movements, without beginning or end since they are enclosed on themselves, images of a perfect motion that there is no need to question."
Krivine, H. (2011/2015)
Because the heavens were perfect, the movement of heavenly bodies was based on the most perfect geometric shape, the circle. (Note, we might see this as an example of an non-scientific value or a metaphysical commitment that influences a theory regardless of any actual empiricism evidence.) However observations made it clear that the planets did not simply move on a simple circle centred on the earth. In order to 'save the phenomenon' a complex system was devised to explain the apparent motions of the planet in terms of combinations of perfect circles – such as having a planet move on a circle which itself moved on another circle.
"Astronomy, therefore, continued for ages a science of mere record, in which theory had no part, except in so far as it attempted to conciliate the inequalities of the celestial motions with that assumed law of uniform circular revolution which was alone considered consistent with the perfection of the heavenly mechanism. Hence arose an unwieldy, if not self-contradictory, mass of hypothetical motions of sun, moon, and planets, in circles, whose centres were carried round in other circles, and these again in others without end,–"cycle on epicycle, orb on orb,"–till at length, as observation grew more exact, and fresh epicycles were continually added, the absurdity of so cumbrous a mechanism became too palpable to be borne."
John Herschel, 1830
There may have been some exceptions – Freely (2011) suggests that Al-Biruni (973 – c. 1052) "seems to suggest that the heavens could have an elliptical motion without contradicting the laws of physics."
Movers
As there was no notion of universal gravity, the movement of the planets needed to be explained in other ways. One model had the concentric spheres as being crystalline solids in which the planets were embodied. (The planets then simply moved with ther spheres – but one now had to explain what moved the vastly more extensive sphere.) Some accounts referred to the planets having souls. However, in pre-modern thinking the concept of a soul was somewhat different from the common modern understanding: all animals were thought to have souls (allowing them to move), and indeed do did plants (making them alive), but these were not the premium level human souls that allowed rational thought. There were also suggestions of supernatural beings such as angels being charged with moving the planets trough the sky.
Alternative conceptions of orbital motion
Considering some of the once common ideas about the Cosmos that were treated as serious accounts by the wisest scholars of their day, it is hardly surprising that learners often struggle with orbital motion – even when an elementary treatment assumes circular motion as a suitably simplified treatment.
The modern account relies on the Newtonian concepts of inertia, centripetal force and universal gravitation.
Whilst learners usually understand that a force is needed to move a stationary object, the idea that a moving object will continue with constant motion unless a net force acts on it seems counter-intuitive to many people. (After all, in everyday experience moving objects seem to soon stop when we stop actively moving them.)
Read about common alternative conceptions related to Newton's first law
Even when learners can apply the principle of inertia to an object moving in a straight line, understanding it will keep on moving indefinitely, all others things being equal, they may not readily transfer this principle to circular motion. Perhaps like the ancients (see above), something about moving in a circle, so returning to the same point repeatedly, may seem to suggest a stable state. (Even Galileo appears to have held a notion of 'circular inertia'.)
Read about common alternative conceptions related to Newton's second law
Instead of understanding circular motion as constantly accelerated motion requiring a net force, learners commonly consider this a stable situation where any forces acting must be balanced and cancel each other out (as in the alternative conception figure below).
From Taber, K. S., & Brock, R. (2018). A study to explore the potential of designing teaching activities to scaffold learning: understanding circular motion.
In the nineteenth century, a leading astronomer wrote,
"…when we see a stone whirled round in a sling, describing a circular orbit round the hand, keeping the string stretched, and flying away the moment it breaks, we never hesitate to regard it as retained in its orbit by the tension of the string, that is, by a force directed to the centre; for we feel that we do really exert such a force. We have here the direct perception of the cause. When, therefore, we see a great body like the moon circulating round the earth and not flying off, we cannot help believing it to be prevented from so doing, not indeed by a material tie, but by that which operates in the other case through the intermedium of the string,–a force directed constantly to the centre."
John Herschell, 1830
Herschell had of course been educated to a high level in physics, and was very familiar with applying Newtonian ideas in astronomy. To him, this analogy seemed obvious. However, many learners do not spot this spontaneously (as Herschell suggests we should), and indeed find it a challenging and counterintuitive idea when they are taught it. This is not unreasonable, however, when we considered that for much of human history the greatest minds to ponder the nature of 'the heavens' also failed to spot this analogy, and indeed would also have found the idea of some invisible ('occult') force acting across the vastness of space without any material linkage not only ridiculous but quite inadmissible – in modern terms, unscientific!
Getting orbital motion wrong:
Students who present with alternative conceptions of orbital motion are not alone in finding this topic tricky.
An Oxford science professor wrote in a book:
"…in addition to the technical importance of Newton's mathematics, the concept of 'a balance of forces' keeping the moon circling the earth and the earth in orbit around the sun, quickly became a valuable metaphor…"
A book published by a chemicals company introducing the SI units included this:
"The story of the falling apple giving Newton the idea of a universal law of gravity embracing apples as well as stars had its root in this period. Why, he asked, doesn't the moon fall to earth in the same way? Of course, he reasoned, because centrifugal [sic] force keeps it in its orbital path."
Schwenk, 1994
(As the book has been translated, it is not clear it if was the author or the translator who confused centripetal {towards the centre} and centrifugal {away form the centre} forces.)
Read about 'centrifugal force' (a fictitious force)
Why is teaching and learning of science concepts so difficult: a brief overview
There are many possible ways of conceptualising natural phenomena and science topics. Arguably, we each have somewhat unique and idiosyncratic takes on scientific concepts, so there are always alternative conceptions which overlap and match to varying degrees.
Students often have intuitive ideas about the natural world, or have come across 'folk ideas', which are not consistent with scientific concepts. Some science teaching is regularly misunderstood so misconceptions circulate among students (and may even be found represented in text books).
Scientific theories may be sophisticated and nuanced, and so neither suitable for teaching novice learners nor (even with more advanced learners) for introducing in one step. Science curricula often have simplified and approximate representations of current scientific ideas ('curricula models') set out as target knowledge – so accounts at different levels are not entirely consistent.
Scientific ideas have developed over time, and have become more sophisticated and finely detailed. Many ideas once found useful in science have fallen into disuse either because it is now thought they were actually wrong, or they are no longer seen as helpful ways of thinking about a topic. Many of these ideas that are less developed, out of date, or now discredited, remain as 'conceptual fossils' that can be found in some science texts or more general literature and discourse.
Scientists develop models as thinking tools, often knowing the models are flawed: perhaps only giving approximate outcomes, or only being applicable in limited ranges of situations or they may be purely hypothetical (to be used to think through what would happen if…) without any expectation they reflect nature. Sometimes such models may appear in books to be of similar status to well founded principles laws and theories. Theories themselves vary in the extent to which they are considered to be likely correct, or just a provisional thinking tool.
Scientists, science communicators and journalists, and science teachers, use various techniques to help get a cross novel or abstract ideas: these can include analogies, similes, metaphors, narratives, and so forth. Sometimes these ideas get repeated and used so often they may seem to be part of the scientific idea, rather than just a linguistic tool. Indeed, sometimes terms originally used metaphorically become so widely adopted that they take on a new scientific meaning somewhat different form the original meaning.
Given all of that, it is not surprising that learning and teaching science can be quite challenging!
Work cited:
- Freely, J. (2011). Light from the East. How the science of medieval Islam helped to shape the Western World. I. B. Tauris & Co Ltd.
- Herschel, J. F. W. (1830/1840/2008). Preliminary Discourse on the Study of Natural Philosophy. Project Gutenberg EBook.
- Krivine, H. (2011/2015) The Earth. From myths to knowledge. Verso
- Schwenk, E. (1994). My name is Becquerel. The stories of the scientists whose names were given to the international units of measure (M. Beall, Trans.). Hoechst Aktiengesellschaft.
Notes:
1 This is taking a perspective from which the Sun is stationary. Actually the Sun itself is moving in an enormous orbit around the galaxy (although we do not notice this because of the vastness of space and so the incredible distance of the stars). Or rather the solar system is moving along this path. The attraction to the Sun is enough to make the earth move from just following this path for it to orbit the Sun as they both move through space (with the rests of the Solar system). Of course we can think about the moon as orbiting the Earth as if the earth is stationary, but actually the Moon has its orbit around the Earth, its orbit (with the Earth) around the Sun, and its movement (with the rest of the Solar system) through the Galaxy. For that mater the Galaxy is moving compared to other Galaxies…
However, as there is no centre to space or no fixed reference spot, it is quite reasonable for many purposes to take the Sun as if stationary (as long as we know this is a simplification).
2 Assuming a circular orbit for the moment, the acceleration is towards the central body. However the orbiting body already has movement (so a velocity) so the direction of the acceleration is towards the central body, and therefore the change in velocity is towards the central body, and the actual resulting velocity is the vector sum. The direction of travel shifts slightly, around the curved path.
3 The solar system is assumed to have formed by the gravitational collapse of a field of dust and other space debris (left over from the explosion of previous generation stars). If such a field of material started as a spherical, non-rotating, evenly distributed matter, its mutual gravity should bring it together as one body – a star. In in slightly off-centre and begin orbiting the central accumulating mass. Over time a relatively small amount of this material will form into bodies such as planets which have stable orbits.
4 Forces act between two bodies. So, when "the force acting on the orbiting body is slightly greater" that force acting on the central body will also be slightly greater. As the central body is usually MUCH more massive we tend to ignore that effect. Strictly, however, the central body is accelerated as well, but being much more massive, by a much smaller amount. (And, as pointed out in note 1, when we are only considering a solar system, we usually take the position of central body as the reference point, and treat it as if it is stationary.)
5 The matter of which the Earth and its immediate surroundings were made was widely considered to be comprised of various combinations of four basic elements: earth (the densest), water, air, and fire (the least dense). The heavens, however were made of a quintessence, a fifth element, known as ether or æther.
The book Student Thinking and Learning in Science: Perspectives on the Nature and Development of Learners' Ideas gives an account of the nature of learners' conceptions, and how they develop, and how teachers can plan teaching accordingly.
It includes many examples of student alternative conceptions in science topics.
