A magnetorquer or magnetic torquer (also known as a torque rod) is a
satellite
A satellite or an artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication relay, weather forecasting, navigation ( GPS), broadcasting, scient ...
system for
attitude control
Spacecraft attitude control is the process of controlling the orientation of a spacecraft (vehicle or satellite) with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, ...
, detumbling, and stabilization built from
electromagnetic coil
An electromagnetic coil is an electrical Electrical conductivity, conductor such as a wire in the shape of a wiktionary:coil, coil (spiral or helix). Electromagnetic coils are used in electrical engineering, in applications where electric curre ...
s. The magnetorquer creates a magnetic dipole that interfaces with an ambient magnetic field, usually
Earth's, so that the counter-forces produced provide useful
torque
In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...
.
Functional principle
Magnetorquers are sets of electromagnets arranged to yield a rotationally asymmetric (
anisotropic
Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit ver ...
) magnetic field over an extended area. That field is controlled by switching
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (hydr ...
flow through the coils on or off, usually under computerized
feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handle ...
control
Control may refer to:
Basic meanings Economics and business
* Control (management), an element of management
* Control, an element of management accounting
* Comptroller (or controller), a senior financial officer in an organization
* Controlling ...
. The magnets themselves are mechanically anchored to the craft, so that any magnetic force they exert on the surrounding magnetic field will lead to a magnetic reverse force and result in mechanical torque about the vessel's
center of gravity
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For ...
. This makes it possible to freely pivot the craft around in a known local
gradient
In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase. The g ...
of the magnetic field by only using electrical energy.
The magnetic dipole generated by the magnetorquer is expressed by the formula
:
where ''n'' is the number of turns of the wire, ''I'' is the current provided, and A is the
vector area
In 3-dimensional geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an oriented area in three dimensions.
Every bounded surface in three dimensions can be associated with a ...
of the coil.
The dipole interacts with the magnetic field generating a torque
:
where m is the magnetic dipole vector, B the magnetic field vector (for a spacecraft it is the Earth magnetic field vector), and τ is the generated torque vector.
Construction
The construction of a magnetorquer is based on the realization of a coil with a defined area and number of turns according to the required performances. However, there are different ways to obtain the coil; thus, depending on the construction strategy, it is possible to find three types of magnetorquer, apparently very different from each other but based on the same concept:
; Air-core magnetorquer: This comprises the basic concept of magnetorquer, a conductive wire wrapped around a non-conductive support anchored to the satellite. This kind of magnetorquer can provide a consistent magnetic dipole with an acceptable mass and encumbrance.
; Embedded coil: This is constructed creating a spiral trace inside the
PCBs
Polychlorinated biphenyls (PCBs) are organochlorine compounds with the formula C12 H10−''x'' Cl''x''; they were once widely used in the manufacture of carbonless copy paper, as heat transfer fluids, and as dielectric and coolant fluids f ...
of solar panels which generates the effect of the coil. This solution is the one with the least impact on the satellite as it is entirely contained within the solar panels. However, due to the physical limit in the board thickness and the presence of other circuits and electronic components, it is not possible to reach a high value of the magnetic dipole.

;Torque rod: This is the most efficient solution. A conductive wire is wrapped around a ferromagnetic core which is magnetized when excited by the coil, thus generating a dipole considerably higher than the other solutions. However, the disadvantage is the presence of a residual magnetic dipole that remains even when the coil is turned off because of the
hysteresis
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
in the magnetization curve of the core. It is therefore necessary to demagnetize the core with a proper demagnetizing procedure. Normally, the presence of the core (generally consisting of heavy metal) increases the mass of the system.
Typically three coils are used, although reduced configurations of two or even one magnet can suffice where full attitude control is not needed or external forces like asymmetric
drag allow
underactuated control. The three coil assembly usually takes the form of three perpendicular coils, because this setup equalizes the
rotational symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape (geometry), shape has when it looks the same after some rotation (mathematics), rotation by a partial turn (angle), turn. An object's degree of rotational s ...
of the fields which can be generated; no matter how the external field and the craft are placed with respect to each other, approximately the same torque can always be generated simply by using different amounts of current on the three different coils.
As long as
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (hydr ...
is passing through the coils and the spacecraft has not yet been stabilized in a fixed orientation with respect to the external field, the craft's spinning will continue.
Very small satellites may use
permanent magnet
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, c ...
s instead of coils.
Advantages
Magnetorquers are lightweight, reliable, and energy-efficient. Unlike
thrusters, they do not require expendable
propellant
A propellant (or propellent) is a mass that is expelled or expanded in such a way as to create a thrust or another motive force in accordance with Newton's third law of motion, and "propel" a vehicle, projectile, or fluid payload. In vehicle ...
, so they could in theory work indefinitely as long as sufficient
power
Power may refer to:
Common meanings
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power, a type of energy
* Power (social and political), the ability to influence people or events
Math ...
is available to match the
resistive
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual paral ...
load of the coils. In Earth orbit, sunlight is one such practically inexhaustible energy source, using
solar panels
A solar panel is a device that converts sunlight into electricity by using photovoltaic (PV) cells. PV cells are made of materials that produce excited electrons when exposed to light. These electrons flow through a circuit and produce direct ...
.
Another advantage over
momentum wheel
A reaction wheel (RW) is an electric motor attached to a flywheel, which, when its rotation speed is changed, causes a counter-rotation proportionately through Angular momentum#Conservation of angular momentum, conservation of angular momentum. ...
s and
control moment gyroscope
A control moment gyroscope (CMG) is an attitude control device generally used in spacecraft attitude control systems. A CMG consists of a spinning rotor and one or more motorized gimbals that tilt the rotor’s angular momentum. As the rotor til ...
s is the absence of
moving parts
Machines include both fixed and moving parts. The moving parts have controlled and constrained motions.
Moving parts are machine components excluding any moving fluids, such as fuel, coolant or hydraulic fluid. Moving parts also do not include ...
, hence significantly higher reliability.
Disadvantages
The main disadvantage of magnetorquers is that very high
magnetic flux densities are needed if large craft have to be turned quickly. This either necessitates a very high
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (hydr ...
in the coils, or much higher ambient flux densities than are available in
Earth orbit Earth orbit may refer to:
* Earth's orbit, the orbit of the Earth around the Sun
* Low Earth orbit, an orbit around the Earth
* Geocentric orbit
A geocentric orbit, Earth-centered orbit, or Earth orbit involves any object orbiting Earth, such a ...
. Consequently, the torques provided are very limited and only serve to accelerate or decelerate the change in a spacecraft's attitude by small amounts. Over time, active control can produce fast spinning even on Earth, but for accurate attitude control and stabilization the torques provided are often insufficient. To overcome this, magnetorquer are often combined with
reaction wheels
A reaction wheel (RW) is an electric motor attached to a flywheel, which, when its rotation speed is changed, causes a counter-rotation proportionately through conservation of angular momentum. A reaction wheel can rotate only around its center ...
.
A broader disadvantage is the dependence on Earth's magnetic field strength, making this approach unsuitable for deep space missions, and also more suitable for
low Earth orbit
A low Earth orbit (LEO) is an geocentric orbit, orbit around Earth with a orbital period, period of 128 minutes or less (making at least 11.25 orbits per day) and an orbital eccentricity, eccentricity less than 0.25. Most of the artificial object ...
s as opposed to higher ones such as
geosynchronous
A geosynchronous orbit (sometimes abbreviated GSO) is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds (one sidereal day). The synchronization of rotation and orbital ...
. The dependence on the highly variable intensity of Earth's magnetic field is problematic because then the attitude control problem becomes highly
nonlinear
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...
. It is also impossible to control attitude in all three axes even if the full three coils are used, because the torque can be generated only perpendicular to the Earth's magnetic field vector.
Any spinning satellite made of a conductive material will lose rotational momentum in Earth's magnetic field due to generation of
eddy currents in its body and the corresponding braking force proportional to its spin rate.
Aerodynamic
Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...
losses can also play a part. This means that the magnetorquer will have to be continuously operated, and at a power level which is enough to counter the resistive forces present. This is not always possible within the energy constraints of the vessel.
The Michigan Exploration Laboratory (MXL) suspects that the
M-Cubed CubeSat
A CubeSat is a class of small satellite with a form factor of cubes. CubeSats have a mass of no more than per unit,, url=https://static1.squarespace.com/static/5418c831e4b0fa4ecac1bacd/t/5f24997b6deea10cc52bb016/1596234122437/CDS+REV14+2020-07-3 ...
, a joint project run by MXL and
JPL
The Jet Propulsion Laboratory (JPL) is a federally funded research and development center (FFRDC) in La Cañada Flintridge, California, Crescenta Valley, United States. Founded in 1936 by California Institute of Technology (Caltech) researche ...
, became magnetically conjoined to
Explorer-1 Prime, a second CubeSat released at the same time, via strong onboard magnets used for passive attitude control, after deploying on October 28, 2011.
This is the first non-destructive latching of two satellites.
See also
*
Gravity-gradient stabilization
Gravity-gradient stabilization or tidal stabilization is a passive method of stabilizing artificial satellites or space tethers in a fixed orientation using only the mass distribution of the orbited body and the gravitational field. The main adv ...
, a passive stabilization technique
References
{{Reflist, 2
Spacecraft attitude control
Spacecraft propulsion
Spacecraft components