Moon is a planet by "Clearing the neighborhood" condition?

Question

Whether the Moon (Earth's natural satellite) is a planet is an old debate in planetary science.
Though I do not agree that Moon is a planet, I found something difficult to clearly understand.

According to the 2006 IAU definition of planet, a planet must satisfy Clearing the neighbourhood condition. And some criteria for the condition are introduced in the Wikipedia article about Clearing the neighbourhood.

• Stern–Levison's $\Lambda$

$$\Lambda = \frac {m^2}{a^{\frac 3 2}} k$$

• Margot's $\Pi$

$$\Pi=\frac {m}{m^{\frac 5 2}a^{\frac 9 8}} k $$

In the above equations, $m$ is the mass of the body, $a$ is the body's semi-major axis, and other factors are described in the Wikipedia article. Both criteria are said to be satisfied if the calculated value is greater than 1.

My calculations are simple. Let $m_{Moon} = 0.0123 \times m_{Earth}$ and Moon's other factors (such as $a$, $k$ and $M$) have the same values as Earth's. Then I can get...

$$\Lambda_{Moon} = 0.0123^2 \times \Lambda_{Earth} = 23.147$$

$$\Pi_{Moon} = 0.0123 \times \Pi_{Earth} = 9.963$$

Both $\Lambda_{Moon}$ and $\Pi_{Moon}$ thus satisfy the Clearing the neighbourhood condition. Though I do not calculate the Soter's $\mu$, it will not change my results.

What is wrong with my calculations and results? Do I miss something about the condition and the criteria? Or is there something wrong with the Clearing the neighbourhood condition?

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Edit in response to comments:

This question can be related to the idea that the Clearing the neighborhood condition is inadequate and ambiguous for the planet definition. More deeply, this question can be related to the idea that 2006 IAU definition of planet is logically ambiguous and clumsy.
For example, the 2006 definition of planet defines the Moon as a satellite and not a planet. If one celestial body can be defined as a planet or not without rules and conditions, why other conditions are needed? All we need is just a planet list, not other planet conditions.

And...

Frankly speaking, the Clearing the neighborhood condition is like comedy. The condition says "Planet must sweep out other bodies" ... Then says "Except satellites" ... Then again says "Except bodies having no significant size" ... Then again "Except bodies having resonant orbit" ... Then again "It may take billions of years" ... Then again "Sweep-out process and time are influenced by other planets and bodies, actually" .......

It is obvious that sometimes the Clearing the neighborhood theory is useful. But it is inappropriate for the rule and definition requiring strictness.

Answer 1

According to the 2006 IAU definition of a planet, a celestial body must meet all 3 criteria to be considered a planet. The Moon fails the first criteria "1. Is in orbit around the Sun". The Moon orbits Earth, not the Sun, and thus it doesn't have a legitimate "neighbourhood" (solar orbit) to clear in that context.

Also to note, according to the Clearing the neighbourhood article, this criteria is contentious as it is vaguely written and Earth, Mars, Jupiter and Neptune have not "cleared the neighbourhood" of their respective solar orbits.

Answer 2

What you have shown is that the Moon is large enough so that it would be a planet by the IAU definition if the Earth were not present. But, because the Moon does orbit the Earth, it is not a planet by the IAU definition. If the "clearing the neighborhood" criterion were sufficient by itself to define a planet, then the other criteria would not be part of the definition.

Answer 3

(Please excuse my English)

Above question arose during my investigation on the double planet/dwarf planet system. As we know, the definition of satellite and the definition of double planet/dwarf planet system are closely related. And currently there is no clear definition of the satellite, and so is the double planet/dwarf planet system.
I thought a simple and obvious criterion is better. However, the simple size criterion is not sufficient for complex combinations of celestial bodies. In other hand, the position of barycenter is often said to be a criterion for satellite, but it can not be an appropriate criterion as described here.
What I thought as a criterion is : If two celestial bodies bound by gravity are classified as same class, we should classify the two bodies as a double body system. For example, if two stars are bound by gravity, we classify it as double star system. And if two black holes are bound, we classify it as a double black hole system.
So if two planet/dwarf planet bodies are bound, it is natural to classify it as a double planet/dwarf planet system.

For test, I applied the criterion to Pluto-Charon system. Pluto is classified as a dwarf planet by 2006 IAU definition. If we consider Charon as a seperated body, Charon also satisfies the conditions for dwarf planet. So we can classify Pluto-Charon system as a double dwarf planet system.

Next, I applied the criterion to Earth-Moon system. As I mentioned in above question, I do not agree that Moon is a planet and Earth-Moon system is a double planet system. I thought Earth and Moon should be classified to different classes, because there are too many differences between two bodies.
However, Moon as a seperated body satisfies IAU planet conditions(especially Clearing the neighborhood condition) as I described in above question. I was embarrassed. So I asked my calculation is correct.

I have thought for a long time that there are many problems with the Clearing the neighborhood condition for the planet definition. Above situation increased my distrust of the Clearing the neighborhood condition. Thus, as I replied the comments and answers, I became over-expressing my opinion on the condition.

Answer 4

At present, the Moon is defined as a satellite of the Earth, but over time the Earth-Moon barycenter will drift outwards (see tidal acceleration) and could eventually become situated outside of both bodies.²⁵ This development would then upgrade the Moon to planetary status at that time, according to the definition. The time taken for this to occur, however, would be billions of years, long after many astronomers expect the Sun to expand into a red giant and destroy both Earth and Moon.²⁶

²⁵ _{Robert Roy Britt (2006). Moon Mechanics: What Really Makes Our World Go 'Round'}

²⁶ _{Robert Roy Britt (2006). Earth's moon could become a planet}

$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ — Wikipedia : Criticism of the IAU definition of 'planet'