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European Journal of Applied Sciences – Vol. 12, No. 2
Publication Date: April 25, 2024
DOI:10.14738/aivp.122.16775
Lugo, L. M. (2024). About the Magnetic Field of the Earth and that of the Moon as a Gravitational Effect. European Journal of
Applied Sciences, Vol - 12(2). 294-308.
Services for Science and Education – United Kingdom
About the Magnetic Field of the Earth and that of the Moon as a
Gravitational Effect
Leandro Meléndez Lugo
Instituto Nacional de Investigaciones Nucleares, Centro Nuclear de México,
Departamento de Física, La Marquesa Ocoyoacac, Estado de México, México
ABSTRACT
The magnetic field is a concept in science that often lacks clarity and understanding.
It's crucial to emphasize the significance of the magnetic field, particularly for
human life. Life as we know it on Earth would not be possible without the existence
of the magnetic field. This discussion aims to clarify the sources of the magnetic field
in general. By considering the genesis of the field itself, we can explain not only the
magnetic field of the Moon but also that of other bodies in the Solar System, such as
Earth. The Dynamo Theory, traditionally used to explain the magnetic field of Solar
System bodies, is somewhat complex and leaves much to be desired. This work
proposes a plausible alternative: a phenomenological theory related to the force of
gravity. This theory provides an explanation for the magnetic field of numerous
Solar System bodies, particularly Earth, and addresses the absence of a magnetic
field on the Moon. Throughout the development of this theory, it is highlighted,
among other things, that tides significantly contribute to the magnetic field of both
orbiting bodies and the bodies they orbit. As will be demonstrated, the electric
dipole effect existing in common matter plays a crucial role in the genesis of the
magnetic field. Surprisingly, this effect is closely related to the force of gravity. In
conclusion, a fundamental point is presented regarding this electrical bipolarity,
intending to ultimately explain the authentic genesis of the force of gravity.
Keywords: magnetic field, electric dipole, tidal forces, satellite rotation, planets,
gravitational force
INTRODUCTION
Since the first Soviet spacecraft missions to the Moon in the 1960s, there has been evidence
suggesting that, if there were a magnetic field, it must be extremely small. Subsequent
measurements indicated that the Moon's magnetic field can be considered practically zero [1]-
[4]. However, some of the lunar rocks and dust brought back by astronauts showed signs of
magnetization [5]-[7]. Certain studies propose that when this material solidified billions of
years ago, a magnetic field of considerable importance might have existed, potentially more
intense than Earth's [5]-[7].
The Dynamo Theory, presented by Walter Maurice Elsasser in 1939 [8]-[13], suggests that in
sidereal bodies, a complex core of mobile and high-temperature parts, along with convective
displacements and the Coriolis force, generates electric currents producing the magnetic field
of planetary and satellite bodies [8]-[13]. This theory is intricate and challenging to accept.
While acknowledging the possibility of some part of the field being produced this way, a new
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Lugo, L. M. (2024). About the Magnetic Field of the Earth and that of the Moon as a Gravitational Effect. European Journal of Applied Sciences, Vol
- 12(2). 294-308.
URL: http://dx.doi.org/10.14738/aivp.122.16775
theory proposed here suggests that the genesis of the field might be even more intricate, though
perhaps more credible than the sole Dynamo Theory.
Certain bodies in the solar system, like Venus, lack their own magnetic field despite probable
complex nuclei [14]. For the Moon, researchers argue that its approximately 500 km diameter
core is insufficient to generate an intense magnetic field, justifying the magnetization of lunar
material through other means such as meteor impacts or ancient displacements of
incandescent material in the lunar crust [15].
The magnetization of lunar material would have a clear explanation if it could be proven that a
significant magnetic field existed on the Moon several billion years ago, which would include a
cause for its disappearance. Albert Einstein also attempted to explain the magnetic field of Solar
System bodies [16] [17], claiming success in explaining how migratory birds orient themselves
with the Earth's magnetic field [16] [17].
This work proposes an alternative theory to explain terrestrial magnetism, the duality of the
existence and/or absence of a magnetic field in Solar System bodies like the Moon. It is based
on three fundamental arguments:
1. A significant number of bodies in the Solar System, including Earth, have a magnetic
field. Some, like the Moon, lack a magnetic field, and the causality is proposed to be, to a
certain extent, the same. Examples include Venus, Mars, Pluto, and Charon [18]-[24].
2. All material bodies can manifest the Electric Dipole effect, except for particles like the
electron. Matter, consisting of positive (protons) and negative (electrons) charges, can
theoretically manifest some type of dipole effect. Every electric dipole that rotates
around an axis generates magnetic fields. Material bodies being dipoles, even without
the rigidity of the standard electric dipole, attract under certain orientations [25]-[28].
3. Tides, common in gravitationally bound systems, are likely to significantly contribute to
increasing the magnetic field of a body deformed by tidal forces when intense and under
specific conditions [29] [30].
This new theory about the magnetic fields of the Solar System, along with a transcendent
conjecture about the force of gravity, is developed using these key points. Among other results,
it provides a novel physical explanation for the magnetic fields of the Earth and the Moon in the
past, as well as the enigmatic absence of a field on our satellite at present. The following sections
elaborate further on these highlights and clarify the experimental fact of the magnetization of
lunar rocks despite the absence of a current magnetic field on the Moon.
MAGNETIC FIELD IN BODIES OF THE SOLAR SYSTEM
The magnetic field is a crucial component that, despite the solar wind, sustains the atmosphere
on planets, a vital factor for sustaining life as we know it. This section conducts an analysis of
various bodies in the Solar System, shedding light on their characteristics and positions. This
exploration contributes to explaining the Earth's magnetic field and the absence of a magnetic
field on the Moon today. Notably, the Sun, being a plasma or ionized gas at high temperatures,
possesses a magnetic field, a characteristic unique to it. Without a doubt the core of the Sun is
different from that of the planets.
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Among the four inner rocky planets, Earth stands alone with a significant magnetic field that
safeguards its atmosphere, supporting life [18]-[24]. In the upcoming theory, it will be argued
that the presence of a large satellite, such as the Moon, plays a crucial role in determining
whether a planet has a prominent magnetic field. Additionally, a body of substantial size in
orbit, like the Moon, is emphasized for its participation in a robust gravitational interaction.
Mercury, lacking moons, surprisingly exhibits a magnetic field, albeit around 150 times smaller
than Earth's. The peculiar synchronization of Mercury's orbit around the Sun (lasting 88 days)
and its rotation on its own axis (58 days) causes gradual changes in its face presented to the
Sun. This contrasts with the Moon's tidal coupling, where its rotation matches its translation
around the Earth, influencing the fate of its magnetic field.
Venus, devoid of satellites like our Moon, lacks its own magnetic field [21]-[24]. Despite its
retrograde rotation, Venus maintains a rotation period nearly identical to its translational
movement around the Sun. The absence of a magnetic field on Venus is compensated by its
dense atmosphere, potentially influenced by the Sun's magnetic field interacting with Venus'
outer atmosphere.
Mars, with a magnetic field thousands of times smaller than Earth's, shares similar dynamics.
Both Earth and Mars have comparable rotation periods, but the crucial difference lies in Earth
having a significant satellite, the Moon, while Mars has two smaller moons, Phobos and Deimos,
insufficient to generate substantial tidal forces.
Unlike Earth, the group of rocky planets lacks sizable satellites. Mars' moons, Phobos and
Deimos, are relatively small, around 20 and 12 km in diameter. The Moon, at 3476 km in
diameter with a density of 3.34 g/cm3, significantly impacts tidal forces. The outer planets,
except Pluto, all possess magnetic fields, rings, and multiple satellites. Pluto, currently
considered part of the Kuiper Belt, lacks a magnetic field and is in reciprocal tidal coupling with
its larger moon, Charon.
Notably, Jupiter, an outer gaseous planet, with its rapid rotation and strong gravitational
interaction with over 100 moons, exhibits a considerable magnetic field. This section
establishes a foundation for the new theory by emphasizing gravitational interaction, rotational
dynamics, tidal coupling (same face), and the presence of satellite bodies (moons). These
concepts will be crucial in explaining the magnetic fields of Solar System bodies and,
specifically, the present absence of a magnetic field on the Moon.
THE ELECTRIC DIPOLE AND THE MAGNETIC FIELD
This section establishes that, from a physics standpoint, the genesis of the magnetic field occurs
in two ways. According to Maxwell's laws, the time variation of the electric field generates
magnetic fields [25]-[28]. When electromagnetic waves are produced, inherent electric and
magnetic fields arise. Photons, being electromagnetic waves, exhibit mutually perpendicular
electric and magnetic fields that vary in phase [25]-[28]. While it is commonly stated that
electric currents generate magnetic fields in practice [14] [25]-[28], it will be demonstrated
that the magnetic fields in Solar System bodies are generated by electric currents, uniquely
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Lugo, L. M. (2024). About the Magnetic Field of the Earth and that of the Moon as a Gravitational Effect. European Journal of Applied Sciences, Vol
- 12(2). 294-308.
URL: http://dx.doi.org/10.14738/aivp.122.16775
defined by the dynamics of specific electric dipoles constituted by orbited and satellite bodies
[14].
An important arrangement of electric charges for this study is the Electric Dipole.
Conventionally, it comprises two equal and opposite electric charges, a positive charge q and a
negative charge −q, separated by a relatively small distance a̅. The electric dipole moment
vector is defined as the product [25]-[28]:
p̅ = q a̅ (1)
In conventional physics courses, it is generally assumed that the dipole moment remains
constant in magnitude, and the charges are equal and punctual, even when influenced by an
external electric field [25]-[28]. However, in this new theory, as will be seen, the dipole moment
may not always remain constant, as the displacement changes and/or the charges are not equal
or punctual.
A pivotal proposition made here, considered initially as a postulate and eventually as a premise
that can be demonstrated, is that all common matter is dipolar — it possesses positive and
negative charges not located in the same place. In the case of ordinary matter, the electric dipole
moment can vary, particularly depending on the value of the external electric field. Ordinary
matter deforms in the presence of an external electric field, altering its electric dipole moment
[25]-[28] (see Figure 1).
Figure 1: In theory, an atom or molecule can remain undeformed in the absence of an external
electric field. In the case of the atom, it is said that, on average, the position of the negative
charge practically surrounds the nucleus. When there is an external electric field, the negative
charge clearly separates from the positive charge, accentuating the electric dipole effect.
Common matter increases its electric dipole moment under the influence of an external electric
field, undergoing deformation. This external electric field can be produced by the electric dipole
moment of any other material body. If all macroscopic matter is dipolar, two material bodies
will be able to interact in the same way as two electric dipoles [25]-[28]. This premise can be
demonstrated by considering that two atoms interact in this way to form a molecule, and
molecules interact to form more complex material bodies, such as a gravitationally bound body
in the Solar System.
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On the other hand, by rotating an electric dipole about a perpendicular axis of rotation and
centered on the distance that separates the charges, the following configuration will be
obtained: two electric charges of opposite signs moving with the speed that reproduces the
angular velocity multiplied by the distance to the axis of rotation. The movements of these
charges, with a certain speed, generate a magnetic field [14]. An electric charge moving with
speed v̅produces a magnetic field around it given by the expression [25]:
B̅ = μ0/4π
(qv̅× u̅r/r
2
) (2)
See Figure 2.
Figure 2: An electric charge in motion q generates a magnetic field given by the expression in
(2). Magnetic field lines are circles perpendicular to the direction of motion.
In this part, it is highlighted that, if common matter is an electric dipole, then a planet or a
satellite turns out to be electric dipoles that, when they interact, attract each other, and when
their charges rotate, they produce magnetic fields in their surroundings (see Figure 3).
Figure 3: Electric Dipole that rotates. Moving charges generate magnetic fields. When an
electric dipole rotates around an axis of rotation, such as that perpendicular to the dipole
moment, it generates magnetic fields.
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Lugo, L. M. (2024). About the Magnetic Field of the Earth and that of the Moon as a Gravitational Effect. European Journal of Applied Sciences, Vol
- 12(2). 294-308.
URL: http://dx.doi.org/10.14738/aivp.122.16775
When a dipole rotates, each of the two charges generates a magnetic field, just as two electric
currents would do, flowing separately and in the same direction. The negative charge moving
in one direction generates an electric current in the opposite direction [14] [25] (see Figure 4).
Figure 4: Electric charges of opposite signs moving in the same direction each generate a
magnetic field given by the expression in (2), as shown here in the figure.
In the case of the rotating dipole, the displacements of the charges in Figure 4 are circular, i.e.,
the resulting electric currents form circles. Also, the resulting field would be the vector sum of
the two contributions [14] [25]. In this part, common matter such as a planet or a satellite, when
manifested as an electric dipole that rotates, can generate magnetic fields. In summary, the
presence of the Moon (dipole) generates gravitational interaction with the Earth, intensifying
the separation of positive and negative charges. This separation of charges in both bodies is
maintained along the line of interaction of both Earth and Moon. As the Earth rotates on its own
axis, an observer on the Earth's surface would determine that the induced charges rotate inside
the planet, probably close to the surface and the equator, in the opposite direction to the
planet's rotation (see Figure 5).
Figure 5: The separation of charges, in these dipoles of the Solar System, is maintained on the
line of interaction while the dipole bodies rotate on their own axis. In this way, an observer on
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the surface of one of them perceives electric currents that generate magnetic fields. The tides
and the rotation itself have the effect of moving the charges even further away from the center
of rotation. This results in an increase in field values.
This is how the electric currents are generated, which, in turn, generate the Earth's magnetic
field. The resulting magnetic field is complex and may have other sources in addition to these
electrical currents of bipolarity and spin. The currents generated in this way are not equal. The
electric field of the dipoles, in this case, is not constant on the other dipole. On both the Earth
and the Moon, the charges are not positioned symmetrically, but the resulting final attraction
means that the charges of one of the two positive or negative signs can give rise to a
preponderance of one of the two electric currents and the field, in the end, it tends to have only
two poles, when, in general, it can have a much more complex field.
The following sections will delve into this polarity configuration that rotates and generates
magnetic fields. In this section, concerning the magnetic field, the highlighted concepts include
an electric dipole that rotates, satellite bodies (moons), and moving charges, which are not
punctual, generating a magnetic field.
THE ORIGIN OF THE MOON AND THE TIDES
One way to explain the Moon's origin is to propose that it formed similarly to the majority of
bodies in the Solar System, possibly through the agglutination of smaller bodies [31] [32]. Lunar
material samples retrieved by astronauts suggest that the Moon likely originated from material
with a density not comparable to Earth's, but rather similar to that of Earth's crust [5]-[7]. The
Earth's crust has a lower density than the average density of the entire planet. This led to the
theory of a minor planet, possibly resembling Mars, colliding with the early Earth [31] [32]. Due
to the original angular momentum and that generated during this collision, a significant portion
of Earth's crust detached, giving rise to the current Moon [31] [32]. From this hypothetical
origin, the Moon has gradually moved away from the Earth; billions of years ago, it would have
been closer, following the rebound. Additionally, it was rotating on its own axis much faster
than it is today, likely a consequence of the collision. The Earth, too, spun on its axis much more
rapidly, resulting in significantly shorter days, lasting only a few hours.
Concerning tides or deformations of orbiting bodies, all gravitationally bound bodies undergo
some degree of deformation [29] [30]. This phenomenon is attributed to the fact that the law
of gravity was initially established for point masses [25]. In reality, bodies are not point-like;
they have dimensions. This causes different parts, especially those distant from the centers of
gravity, to attract one another, producing a deformation of the original structures, in addition
to the effects of centrifugal force. These forces are commonly known as tidal forces [29] [30].
The Moon induces a certain deformation on the Earth, and vice versa. The Moon exerts tidal
forces on the Earth, and reciprocally, the Earth exerts tidal forces on the Moon. Tidal forces
generally produce deformations that affect, among other things, the dipole moment and angular
momentum [25] [29] [30]. As charges separate further due to deformations, this can increase
the electric currents produced by the rotation of the dipoles, subsequently enhancing the
magnetic field.