#### DavidB66

##### Active Member

This post may be unpopular, but I think it falls within the stated goal of Metabunk 'to find and expose bunk.'

The BBC TV series

In the last episode, Cox makes a general comment about the motion of moons and other objects in orbit around a planet. On checking the recording on the BBC iPlayer I transcribed his comment as follows:

The episode is available here for those who have access to the iPlayer:

https://www.bbc.co.uk/iplayer/episode/p06qj389/the-planets-series-1-5-into-the-darkness-ice-worlds

The passage is about 11 minutes into the final episode. If anyone thinks I have misheard or misunderstood it, please say.

The only natural meaning of the comment, as far as I can see, is that the orbital velocity of a moon, etc, is negatively related to its distance from the planet: the nearer, the slower, and the further, the faster. This is surely wrong. For example, if we take the major moons of Jupiter, the distances and orbital velocities are approximately as follows:

Io......422,000 km............17.3 km/s

Europa......671,000 km................13.7 km/s

Ganymede.....1,070,000.............10.9 km/s

Callisto......1,883,000...........8.2 km/s.

[Source: Wikipedia]

Evidently, the greater the distance, the slower the orbital movement. The orbits of planets around the sun follow the same inverse relationship; for example the orbital velocity of Mars is lower than that of Earth.

Then there is Kepler. According to Kepler's 3rd law of planetary motion, the square of the period of an orbit is directly proportional to the cube of the semi-major axis of the orbit. (That is, half the longest diameter of an elliptical orbit. In the special case of a circular orbit, this reduces to the radius of the circle.) [Added: Here is a link to a Wikipedia article on Kepler's Laws, as requested by a moderator.

https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion ]

Sticking to the simple case of a circular orbit, if we put P for the orbital period, r for the radius, and ¬ for 'is proportional to', this can be expressed as P² ¬ r³, or P ¬ r^3/2. This does not directly give us the orbital velocity, but in a circular orbit the average velocity, V, is given by the circumference of the circle divided by the period. Since the circumference is proportional to r, we have V ¬ r/P ¬ r/[r^3/2] = r^-1/2, or 1 over the square root of r. This gets smaller with increasing r, confirming that the orbital velocity of planets should be lower the further they are from the sun.

Newton showed that under an inverse square law of gravity, Kepler's laws for the planets apply to orbital motions generally, whether circular or elliptical. If instead orbital motion followed 'Cox's Law', with velocity increasing with distance from the centre, orbits would not be stable. Any slight increase or decrease in velocity, from an initial position of equilibrium, would send the body spiralling outward or inward indefinitely.

Cox's remark would be true of a solid ring rotating around a planet, as the outer parts of the ring would be moving faster than the inner parts. But the rings of the Sun's outer planets (Jupiter, Saturn, Uranus and Neptune all have rings) are not solid. If they were, they would quickly be torn apart.

If I've got any of this wrong, please correct me. Incidentally, when I first noticed the point I did send a message to Brian Cox on Twitter, but got no reply.

Assuming I am right, does it matter? In the specific context of the episode, perhaps not. In his discussion of the stability of the rings of Uranus, Cox seems to assume (correctly) that a 'shepherd moon' on the inside of a ring is moving faster than one on the outside. It would be charitable to suppose that his general remark was just a casual slip of the tongue, or a 'brain fart', as he excused a previous goof about the phases of the moon. But that was an unprepared response to a question in a live radio broadcast.

The BBC TV series

*, presented by Professor Brian Cox, was recently shown in the UK, and will presumably be shown world-wide in due course. The series gives an overview of current scientific knowledge about the planets of the Solar System. It has been well-received, with praise for its breathtaking visuals and CGI. It is co-produced by the Open University, and might reasonably be relied on for factual and scientific accuracy. It therefore gives me no pleasure to draw attention to an apparent blunder. Still, someone has to do it!***The Planets**In the last episode, Cox makes a general comment about the motion of moons and other objects in orbit around a planet. On checking the recording on the BBC iPlayer I transcribed his comment as follows:

*The thing you need to know about orbits: a moon or a ring particle that is orbiting closer to a planet is moving more slowly than a moon or ring particle that's orbiting further away.*

The episode is available here for those who have access to the iPlayer:

https://www.bbc.co.uk/iplayer/episode/p06qj389/the-planets-series-1-5-into-the-darkness-ice-worlds

The passage is about 11 minutes into the final episode. If anyone thinks I have misheard or misunderstood it, please say.

The only natural meaning of the comment, as far as I can see, is that the orbital velocity of a moon, etc, is negatively related to its distance from the planet: the nearer, the slower, and the further, the faster. This is surely wrong. For example, if we take the major moons of Jupiter, the distances and orbital velocities are approximately as follows:

Io......422,000 km............17.3 km/s

Europa......671,000 km................13.7 km/s

Ganymede.....1,070,000.............10.9 km/s

Callisto......1,883,000...........8.2 km/s.

[Source: Wikipedia]

Evidently, the greater the distance, the slower the orbital movement. The orbits of planets around the sun follow the same inverse relationship; for example the orbital velocity of Mars is lower than that of Earth.

Then there is Kepler. According to Kepler's 3rd law of planetary motion, the square of the period of an orbit is directly proportional to the cube of the semi-major axis of the orbit. (That is, half the longest diameter of an elliptical orbit. In the special case of a circular orbit, this reduces to the radius of the circle.) [Added: Here is a link to a Wikipedia article on Kepler's Laws, as requested by a moderator.

https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion ]

Sticking to the simple case of a circular orbit, if we put P for the orbital period, r for the radius, and ¬ for 'is proportional to', this can be expressed as P² ¬ r³, or P ¬ r^3/2. This does not directly give us the orbital velocity, but in a circular orbit the average velocity, V, is given by the circumference of the circle divided by the period. Since the circumference is proportional to r, we have V ¬ r/P ¬ r/[r^3/2] = r^-1/2, or 1 over the square root of r. This gets smaller with increasing r, confirming that the orbital velocity of planets should be lower the further they are from the sun.

Newton showed that under an inverse square law of gravity, Kepler's laws for the planets apply to orbital motions generally, whether circular or elliptical. If instead orbital motion followed 'Cox's Law', with velocity increasing with distance from the centre, orbits would not be stable. Any slight increase or decrease in velocity, from an initial position of equilibrium, would send the body spiralling outward or inward indefinitely.

Cox's remark would be true of a solid ring rotating around a planet, as the outer parts of the ring would be moving faster than the inner parts. But the rings of the Sun's outer planets (Jupiter, Saturn, Uranus and Neptune all have rings) are not solid. If they were, they would quickly be torn apart.

If I've got any of this wrong, please correct me. Incidentally, when I first noticed the point I did send a message to Brian Cox on Twitter, but got no reply.

Assuming I am right, does it matter? In the specific context of the episode, perhaps not. In his discussion of the stability of the rings of Uranus, Cox seems to assume (correctly) that a 'shepherd moon' on the inside of a ring is moving faster than one on the outside. It would be charitable to suppose that his general remark was just a casual slip of the tongue, or a 'brain fart', as he excused a previous goof about the phases of the moon. But that was an unprepared response to a question in a live radio broadcast.

*, by contrast, is a lavishly produced, scripted, and carefully edited major TV production. Dozens of people must have seen the passage in question before the broadcast. I am not sure which would be more disturbing: that nobody noticed or queried the error, or that they did, but did not think it worth correcting. It would be nice to think that if it is pointed out now, some correction or footnote might still be inserted.***The Planets**
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