Journal of Latin American Sciences and Culture, 4(5)

¹ Agencia Bolivariana para Actividades Espaciales (Bolivarian Venezuelan Space

Agency)

* Correspondence: arojas@abae.gob.ve; arturo.jose.rm@gmail.com

Abstract: A very preliminary proposal to make up a system that

cancels the magnetic eld of Earth for executing satellite magnetic

tests in Venezuela is made. Firstly, it is reviewed general satellite

magnetic status considering electrical currents in it and possible

magnetic domains in the structure and equipment is reviewed. After

checking some magnetic cancellation systems, it is concluded that an

optimal option to be selected is a Merri 4-coil system because it oers

good uniformity of magnetic eld in a large relative volume. After

some considerations and taking into account the usual size of a small

satellite, the size of the coils should be around 32 meters. Finally, some

considerations about the movement of the Earth’s magnetic poles are

taken into account.

Keywords: Merri coils, magnetic eld, magnetic moment, vertical

component, horizontal component.

1. Introduction

The objective of this work is to establish which items would be

taken into account to build a satellite magnetic test facility in Vene-

zuela. Firstly, it is considered a general magnetic status of a satellite,

specically referred to small satellites, and then it is proposed a system

of coils to cancel the Earth’s magnetic eld. Some basic calculations are

executed to estimate the characteristics of these coils and then a system

is proposed.

2. Materials and Methods

In a satellite, electrical currents circulate through equipment and

cables. An electrical current generates a magnetic eld perpendicular

to the direction of the ow of the electrical current.

A framework of trajectories of electrical currents inside equipment

and cables generates a satellite magnetic eld, which is associated with

dierent modes of operation of the satellite, creating a dipolar mag-

netic momentum of the satellite. Besides that, materials that make up a

satellite can have a residual and permanent dipole magnetic momen-

tum. Based on that, the satellites could be regarded as heterogeneous

domains of magnetic dipoles. These magnetic dipoles can be added as

independent vectors, generating a total dipolar magnetic momentum

characteristic of the satellite under study. In the following gure this

idea is presented:

Review article

Preliminary proposal to build a magnetic cancella-

tion system for satellite magnetic tests in Venezuela

Arturo Rojas ¹

Citation: Rojas, A. (2022).

Preliminary proposal to

build a magnetic cancellation

system for satellite magnetic

tests in Venezuela. Journal of

Latin American Sciences and

Culture, 4(5), 65-72. hps://doi.

org/10.52428/27888991.v4i5.195

Received: November 17, 2021

Accepted: January 18, 2022

Published: June 29, 2022

Publisher’s Note: JLASC stays

neutral with regard to jurisdic-

tional claims in published maps

and institutional aliations.

authors. Submied for open

access publication under the

terms and conditions of the

Creative Commons Aribution

(CC BY) license (hps://

creativecommons.org/licenses/

by/4.0/).

JLASC

Journal of Latin American

Sciences and Culture

Journal of Latin American Sciences and Culture, 4(5)

Figure 1. A very rst approximation of the magnetic status of satellites.

In orbit, the Earth’s magnetic eld will exert a torque on the sat-

ellite because its total dipole magnetic moment has not been compen-

sated or reduced. This torque will generate perturbations in the ai-

tude of the satellite (its movement around its center of mass). So, in the

process of development of the satellite, it is measured its total dipole

magnetic moment and then it is compensated by installing small mag-

nets on strategic places on the satellite. Consequently, it is necessary to

measure the total magnetic moment of the satellite in a clean electro-

magnetic environment, which implies cancelling the Earth’s magnetic

eld in the region in which the test is executed.

Based on this argument, the objective is to reduce the total dipole

magnetic moment of the satellite. One way to achieve it is to submit

the satellite to an oscillatory magnetic eld at a high frequency. Thus,

the magnetic dipoles get aligned from the dierent magnetic domains

in opposite directions, such that the vector summations of the dipolar

magnetic moments cancel each other. Then, the satellite magnetic mo-

ment should be made smaller.

Journal of Latin American Sciences and Culture, 4(5)

(a)

(b)

(c)

Figure 2. In (a), (b), (c) it is shown the sequence to reduce the total magnetic dipole moment

of the satellite. It is assumed that the magnetic dipole moments change its direction when an

external magnetic eld is applied.

A graphical representation of this idea is presented: at the instant

t1, the satellite is submied to an external magnetic eld in the X-direc-

tion; the dipolar magnetic moments from dierent magnetic domains

would try to get alienated to the direction of the external magnetic

eld. Then, the direction of the external magnetic eld is inverted and

then the dipole moments of the satellite would try to get aligned again.

The oscillatory magnetic eld is executed at high frequency such that

at the instant tn, after several cycles, the magnetic domains would be

distributed approximately equally in +X and –X-directions. This oper-

ation is repeated in Y and Z.

As this study is concerning building a satellite magnetic test facil-

ity, it is necessary to consider that the magnetic environment near the

equator diers from the magnetic environment in the north and south

hemispheres. Thus, it wonders about the possible design of coils in

order to remove the vertical and horizontal magnetic component of the

Earth’s magnetic eld in a specied volume, in Venezuela.

Journal of Latin American Sciences and Culture, 4(5)

3. Results

3.1. Propositions to cancel the Earth’s magnetic eld

It is proposed to build a magnetic test facility for small satellites

at about 8 degrees latitude north. So, the vertical component of the

Earth’s magnetic eld should be greater than the value on the equator.

In the beginning, it was considered three kinds of arrangement of

coils to cancel the horizontal component of the Earth’s magnetic eld.

These include Helmhol coils, square coils, Merri coils systems, and

Ruben coils systems. From (Abbo, 2015; Herceg, Juhas, & Milutinov,

2009; Kirschvink, 1992; Magdaleno, Olivares, Campero, Escalera, &

Blanco, 2010; Merri, Purcell, & Stroink, 1983; Pourtau & Terral, 2005),

and as we are interested in obtaining uniformity in the distribution of

the magnetic ux density generated inside these coils, the Helmhol

coil and the square coils are not taken account. The Ruben coils system

oers a good solution with respect to the uniformity of the magnetic

ux density at the centre of the system. However, there are some re-

sults that discuss it and imply higher costs for building this system.

Therefore, it is analyzed in this paper implementation of the Merri

coil system.

3.2. Values of Earth’s magnetic eld in Venezuela

Values of vertical component Hv and horizontal component Hh

of the Earth’s magnetic eld in the probable facility location in Venezu-

ela according to (“ IGRF Model (13th Generation)”, 2019) are:

According to these values, the magnitude of the vertical compo-

nent of the Earth’s magnetic eld is not zero, nor is its value much

smaller than the horizontal component. Therefore, it implies that the

system of cancellation of the Earth’s magnetic eld as the vertical as

the horizontal component should be similar.

3.3. Coil systems proposed

Previously, it was considered two kinds of system of coils: one for

the cancellation of the vertical component and another for the cancel-

lation of the horizontal one. However, as it has to achieve a uniformity

of the magnetic ux density in a specic volume (in this volume is the

satellite for executing the test) then, it has decided to choose the same

kind of system of coils for the vertical component and the horizontal

component.

According to (Herceg et al., 2009; Merri et al., 1983), a Merri

Journal of Latin American Sciences and Culture, 4(5)

4-coil system provides a good uniformity of magnetic ux density, and

it is a very well-known system in the scientic community. This sys-

tem achieves a good uniformity in the magnetic ux density when the

number of turns in the inner coil is 0.423514 times the number of turns

in the outer coil. Also, the separations between inner coils and outer

coils follow the next expressions:

And the relationship between a, b and d is illustrated in the fol-

lowing gure:

Figure 3. Illustration of arrangement of coils for cancellation the horizontal component of

the Earth’s magnetic eld.

In the beginning, implementing a square coil system of three coils

was considered. In that way, the uniformity of the magnetic ux den-

sity does not sacrice, and costs would be reduced compared with

an implementation of a four-coil system. However, uniformity in the

magnetic ux density is a characteristic that must be assured.

Also, according to (Magdaleno et al., 2010), a Merri 4-coil sys-

tem, which d has a value of 89.75 cm and volume V of 730882.65 cm

according to their calculation, it is obtained a volume of 50 cm

of the

uniform magnetic ux density inside this system. This is a ratio of just

6.84x10

-5

. Taking into account this architecture, if the size of the coil is

adjusted to 32 m, then it is obtained:

So, if d has a value of 32 m, then just a volume V of 2.26 m

should

provide a uniform magnetic ux density. However, the dimensions of

small satellites are very near to 1.31 m. Therefore, for this initial pro-

posal, this value is used. Also, it has to be mentioned that according

Journal of Latin American Sciences and Culture, 4(5)

to (Herceg et al., 2009; Kirschvink, 1992), the volume V associated with

the uniformity of the magnetic ux density looks to be larger.

Taking into account the following equation to calculate the mag-

netic ux density B at the center of the system (Magdaleno et al., 2010):

It may be speculated that the value of the electrical current

through one turn of the inner (I’) and outer (I) coils could be adjusted

to 1.5 amperes, and d is 32 m. Then, the values for N, the number of

turns for the outer coil, and consequently N’ the numbers of turns for

the inner coil are related by (Herceg et al., 2009; Kirschvink, 1992):

If the direction of the axis in gure 3 is parallel to the direction of

the Earth’s magnetic eld according to the direction of a compass, this

work proposes an arrangement of coils oriented vertically to cancel the

vertical component of the Earth’s magnetic eld. The following gure

illustrates this idea. It is noted that the value of d should be the same

for the horizontal and vertical orientations.

Figure 4. Illustration of arrangement of coils for cancellation the horizontal component of

the Earth’s magnetic eld.

Journal of Latin American Sciences and Culture, 4(5)

3.4. Other considerations

Until this moment, just two sets of Merri 4-coils have been con-

sidered: one set to cancel the vertical component of the Earth’s mag-

netic eld and another one to cancel the horizontal component of the

Earth’s magnetic eld because the arrangement of the coils would be

built such as these are aligned to the direction of the north magnetic

pole. This supposition does not take into account a scenario in which

the Earth’s magnetic poles move (Wie, 2019).

Based on that, it is suggested to add a third set of Merri 4-coils

to be used to compensate for changes in the direction of the horizontal

component of the Earth’s magnetic eld. However, at this moment, it

cannot be assured what kind of coils could be utilized and its charac-

teristics such that accomplish uniformity in a generated magnetic ux

density.

Also, additional reviews must be done related to power consump-

tion, electrical resistances of coils, inductances, and other parameters

related to magnetic dipole moment (Abbo, 2015; Lackey, 1968; Me-

hlem, 1978).

4. Discussions

After considering dierent kinds of coil systems, the Merri 4-coil

system is suitable to cancel the Earth’s magnetic eld. We could have

considered Merri’s 3-coils system to cancel the vertical component

of the Earth’s magnetic eld to reduce costs. However, it would im-

ply reducing the uniformity of magnetic ux density generated inside

coils, which could conduct non-suitable magnetic measurements on

satellites under study. Additional studies related to what kind of ma-

terials could be used to build the system, the generation system for the

electrical current, vibrations of the coils, and other issues have to be

executed.

Funding: This research received no external funding.

Acknowledgments: the author of this work acknowledges to the man-

agers of ABAE to authorize to publish this article.

Conicts of Interest: The author declares no conict of interest.

Journal of Latin American Sciences and Culture, 4(5)

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