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Formulation of electromagnetic potentials
Hertz vectors, or the Hertz vector potentials, are an alternative formulation of the electromagnetic potentials. They are most often introduced in electromagnetic
Hertz_vector
Theorem in optics that explains light propagation in a medium
\times {\boldsymbol {\pi }}_{\mathrm {m} }\right),} but the magnetic Hertz vector π m {\displaystyle {\boldsymbol {\pi }}_{\mathrm {m} }} is 0 since the
Ewald–Oseen extinction theorem
Ewald–Oseen_extinction_theorem
German physicist (1857–1894)
Heinrich Rudolf Hertz (/hɜːrts/ hurts; German: [hɛʁts] ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence
Heinrich_Hertz
Measure of directional electromagnetic energy flux
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or
Poynting_vector
Notation for quantum states
mathematical notation for linear algebra and linear operators on complex vector spaces together with their dual spaces both in the finite- and infinite-dimensional
Bra–ket_notation
Mathematical concept applicable to physics
in applied mathematics and vector calculus which has many applications in physics. For transport phenomena, flux is a vector quantity, describing the magnitude
Flux
Direction and rate of rotation
letter omega), also known as the angular frequency vector, is a three-dimensional Euclidean vector that uniquely identifies the plane, direction and angular
Angular_velocity
Property of space that quantifies the magnetic influence at a given location
mathematically by assigning a vector to each point of space, making it a vector field. There are two different, but closely related, vector fields which are called
Magnetic_field
Method to control electric motors
scalar control (volts-per-Hertz, V/f control). Technische Universität Darmstadt's K. Hasse and Siemens' F. Blaschke pioneered vector control of AC motors starting
Field-oriented_control
Quantity in electromagnetism
In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field
Magnetic_vector_potential
Property of a mass in motion
object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then
Momentum
Formulation in classical mechanics
consistent with the constraints. Hertz's principle is also a special case of Jacobi's formulation of the least-action principle. Hertz designed the principle to
Gauss's principle of least constraint
Gauss's_principle_of_least_constraint
and their notations. Note that bold text indicates that the quantity is a vector. List of letters used in mathematics and science Glossary of mathematical
List of common physics notations
List_of_common_physics_notations
4D analogue of electric current density
with the dimension of electric charge per time per area. Also known as vector current, it is used in the context of four-dimensional spacetime, rather
Four-current
Physical field surrounding an electric charge
and force is a vector (i.e. having both magnitude and direction), so it follows that an electric field may be described by a vector field. The electric
Electric_field
Dynamic display refresh rate that can continuously and seamlessly vary on the fly
rate usually supports a specific range of refresh rates (e.g. 30 Hertz through 144 Hertz). This is called the VRR range. The refresh rate can continuously
Variable_refresh_rate
Book on the history of mathematics by Michael J. Crowe
Heinrich Hertz' results with radio and the rush of German research using vectors. Joseph George Coffin of MIT and Clark University published his Vector Analysis
A_History_of_Vector_Analysis
Theorem in physics showing the conservation of energy for the electromagnetic field
energy flow out of the volume, given by the divergence of the Poynting vector S. J ⋅ E is the power density of the field doing work on charges (J is the
Poynting's_theorem
Formal and systematic written discourse on some subject
experiments, Maxwell's prediction was confirmed by Heinrich Hertz. In the process, Hertz generated and detected what are now called radio waves and built
Treatise
Relativistic vector field
relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential
Electromagnetic four-potential
Electromagnetic_four-potential
Electric and magnetic fields produced by moving charged objects
a pair of vector fields consisting of one vector for the electric field and one for the magnetic field at each point in space. The vectors may change
Electromagnetic_field
their transformation properties (i.e. whether the quantity is a scalar, vector, matrix or tensor), and whether the quantity is conserved. List of photometric
List_of_physical_quantities
Regularization method for artificial neural networks
is fixed), thus mean field theory can be applied. In the notation from Hertz et al. this would be written as ⟨ h i ⟩ {\displaystyle \left\langle h_{i}\right\rangle
Dropout_(neural_networks)
Amount of charge flowing through a unit cross-sectional area per unit time
a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the current density at a given point in space
Current_density
Physical model of propagating energy
wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually
Electromagnetic_radiation
Measure of radiant energy over surface area
irradiance of a frequency spectrum is measured in watts per square metre per hertz (W⋅m−2⋅Hz−1), while spectral irradiance of a wavelength spectrum is measured
Irradiance
Mathematical entity to describe the probability of each possible measurement on a system
represented as a vector in a Hilbert space. Mixed states are statistical mixtures of pure states and cannot be represented as vectors on that Hilbert space
Quantum_state
Flow of magnetic monopole charge
{M}}^{\text{i}}} is the impressed magnetic current (energy source). The electric vector potential, F, is computed from the magnetic current density, M i {\displaystyle
Magnetic_current
Branch of theoretical physics
two vectors. One is the cross product of the velocity and magnetic field vectors. Based on the properties of the cross product, this produces a vector that
Classical_electromagnetism
Process by which a quantum system takes on a definitive state
quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of several eigenstates—reduces
Wave_function_collapse
Josiah Willard Gibbs and Heinrich Hertz, grouped the twenty equations together into a set of only four, via vector notation. This group of four equations
History of Maxwell's equations
History_of_Maxwell's_equations
Line integral of the electric field
can be used. In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which
Electric_potential
Complex vector of electromagnetic fields
physics, in particular electromagnetism, the Riemann–Silberstein vector or Weber vector named after Bernhard Riemann, Heinrich Martin Weber and Ludwik Silberstein
Riemann–Silberstein_vector
Law of electrical current and voltage
also used to refer to various generalizations of the law; for example the vector form of the law used in electromagnetics and material science: J = σ E
Ohm's_law
Concept in the physics of electromagnetism
In electromagnetism, the magnetic moment or magnetic dipole moment is a vector quantity which characterizes the strength and orientation of a magnet or
Magnetic_moment
Indication of rate and sense of rotation
a. cycles) per second (hertz) or radian/second (where 1 cycle corresponds to 2π radians). Example: Mathematically, the vector ( cos ( t ) , sin (
Negative_frequency
Law of classical electromagnetism
for straightforward derivation of magnetic field B, while the fundamental vector here is H. The Biot–Savart law is used for computing the resultant magnetic
Biot–Savart_law
Measure of radiant energy over time
second (J/s), while that of spectral flux in frequency is the watt per hertz (W/Hz) and that of spectral flux in wavelength is the watt per metre (W/m)—commonly
Radiant_flux
Fundamental physical law of electromagnetism
{r_{12}=r_{1}-r_{2}} } is the displacement vector between the charges, r ^ 12 {\textstyle {\hat {\mathbf {r} }}_{12}} a unit vector pointing from q 2 {\textstyle q_{2}}
Coulomb's_law
Object movement along a circular path
2π seconds. The frequency is (2π)−1 hertz. The vector relationships are shown in Figure 1. The axis of rotation is shown as a vector ω perpendicular to the plane
Circular_motion
Surface integral of the magnetic field
magnetic interaction is described in terms of a vector field, where each point in space is associated with a vector that determines what force a moving charge
Magnetic_flux
Ways of writing certain laws of physics
covariant four-vector containing the electric potential (also called the scalar potential) ϕ and magnetic vector potential (or vector potential) A, as
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Equations describing classical electromagnetism
through a Gaussian surface is zero, and the magnetic field is a solenoidal vector field. The Maxwell–Faraday version of Faraday's law of induction describes
Maxwell's_equations
={\frac {1}{\mu _{0}}}\mathbf {E} \times \mathbf {B} } is the Poynting vector, σ i j = ϵ 0 E i E j + 1 μ 0 B i B j − 1 2 ( ϵ 0 E 2 + 1 μ 0 B 2 ) δ i j
Electromagnetic stress–energy tensor
Electromagnetic_stress–energy_tensor
Type of potential in electrodynamics
{J} } where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current
Retarded_potential
magnetic (TM) waves using the Borgnis functions, Debye potentials or Hertz vectors. Subsequent separation of the angular variables θ , φ {\displaystyle
Spacetime triangle diagram technique
Spacetime_triangle_diagram_technique
Spatial frequency of a wave
is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics
Wavenumber
Antenna consisting of two rod-shaped conductors
of dipole antennas of which they are one half. German physicist Heinrich Hertz first demonstrated the existence of radio waves in 1887 using what we now
Dipole_antenna
Topics referred to by the same term
Heinrich Hertz in 1894 from the Greek ὅλος meaning "whole", "entire" and νόμος meaning "law") may refer to: Holonomic basis, a set of basis vector fields
Holonomic
Fundamental interaction between charged particles
{v} \times \mathbf {B} \right)} Here, × is the vector cross product, and all quantities in bold are vectors. The Lorentz force can be used to define both
Electromagnetism
Electric charge per unit length, area or volume
dipole moment, n ^ {\displaystyle \mathbf {\hat {n}} } is the unit normal vector to the surface. Taking infinitesimals: d q b = d d | s | ⋅ n ^ {\displaystyle
Charge_density
Foundational law of classical magnetism
B has divergence equal to zero, in other words, that it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not
Gauss's_law_for_magnetism
Measure of electric field through surface
electric field is uniform, the electric flux passing through a surface of vector area A is Φ E = E ⋅ A = E A cos θ , {\displaystyle \Phi _{\text{E}}=\mathbf
Electric_flux
Ratio of magnetic moment to angular momentum
aligned with its magnetic moment, will precess at a frequency f (measured in hertz) that is proportional to the external field: f = γ 2 π B . {\displaystyle
Gyromagnetic_ratio
Mathematical object that describes the electromagnetic field in spacetime
=\mathbf {B} } ( A {\displaystyle \mathbf {A} } is a vector potential for the solenoidal vector field B {\displaystyle \mathbf {B} } ). The electric and
Electromagnetic_tensor
Technique for the generative modeling of a continuous probability distribution
Denoising Diffusion Probabilistic Models". arXiv:2201.09865v4 [cs.CV]. Hertz, Amir; Mokady, Ron; Tenenbaum, Jay; Aberman, Kfir; Pritch, Yael; Cohen-Or
Diffusion_model
Study of still or slow electric charges
{\mathbf {r-r_{i}} }{|\mathbf {r-r_{i}} |}}} is the unit vector of the displacement vector that indicates the direction of the field due to the source
Electrostatics
radiation developed by James Clerk Maxwell by 1873, which Hertz demonstrated experimentally. Hertz considered electromagnetic waves to be of little practical
Invention_of_radio
Electromagnetism in general relativity
electromagnetic potential is a covariant vector Aα, which is the undefined primitive of electromagnetism. Being a covariant vector, its components transform from
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
Formulations of electromagnetism
electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field. These vector fields each have a value defined at every
Mathematical descriptions of the electromagnetic field
Mathematical_descriptions_of_the_electromagnetic_field
Number of rotations per unit time
reciprocal seconds (s−1); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm). Rotational
Rotational_frequency
Force acting on charged particles in electric and magnetic fields
the magnetic term vanishes because a vector is always perpendicular to its cross product with another vector; the scalar triple product v ⋅ ( v × B
Lorentz_force
Relativistic quantum mechanical wave equation
phenomenological theory of spin. The wave functions in the Dirac theory are vectors of four complex numbers (known as Dirac spinors), two of which resemble
Dirac_equation
Measurement unit derived from basic metric value
has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their
SI_derived_unit
Mathematical description of quantum state
For example: Linear algebra explains how a vector space can be given a basis, and then any vector in the vector space can be expressed in this basis. This
Wave_function
Theorem in classical electromagnetism
the chosen reference. The complex vector multipliers of e j ω t {\displaystyle e^{j\omega t}} may be called vector phasors by analogy to the complex scalar
Reciprocity (electromagnetism)
Reciprocity_(electromagnetism)
Vector field related to displacement current and flux density
displacement field (denoted by D), also called electric flux density, is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic
Electric_displacement_field
Physical law
infinitesimal vectors associated with wire 1 and wire 2 respectively (usually measured in metres); see line integral for a detailed definition, The vector r ^ 21
Ampère's_force_law
Electromagnetic equations describing superconductors
can be combined into a single "London Equation" in terms of a specific vector potential A s {\displaystyle \mathbf {A} _{\rm {s}}} which has been gauge
London_equations
Phenomena related to electric charge
scientific curiosity into an essential tool for modern life. In 1887, Heinrich Hertz discovered that electrodes illuminated with ultraviolet light create electric
Electricity
94th 24 Hours of Le Mans endurance race
positions in each class are denoted in bold. Notes ^1 – The #38 Cadillac Hertz Team Jota set a time of 3:22.559, but it was later deleted after the completion
2026_24_Hours_of_Le_Mans
Recoil force on accelerating charged particle
radiation resistance appears. However, dipole antenna experiments by Heinrich Hertz made a bigger impact and gathered commentary by Poincaré on the amortissement
Abraham–Lorentz_force
Type of optimization problem
general are subject only to differential laws.] — Heinrich Hertz, Gesammelte Werke von Heinrich Hertz, vol. 3, Die Prinzipiender Mechanik (Leipzig: Metzger
Nonholonomic_system
Motor which works on direct current
known as Lorentz force. In a motor, the magnitude of this Lorentz force (a vector represented by the green arrow), and thus the output torque, is a function
DC_motor
Foundational law of electromagnetism relating electric field and charge distributions
electric field, dA is a vector representing an infinitesimal element of area of the surface, and · represents the dot product of two vectors. In a curved spacetime
Gauss's_law
Random process independent of past history
conditions the average outcomes of the Markov chain would converge to a fixed vector of values, so proving a weak law of large numbers without the independence
Markov_chain
Branch of physics
shaped antenna structure). Also calculating power flow direction (Poynting vector), a waveguide's normal modes, media-generated wave dispersion, and scattering
Computational electromagnetics
Computational_electromagnetics
Measure of the electric polarizability of a dielectric material
spectroscopy, covering nearly 21 orders of magnitude from 10−6 to 1015 hertz. Also, by using cryostats and ovens, the dielectric properties of a medium
Permittivity
Electromagnetic stress
{\displaystyle \mathbf {E} } and B {\displaystyle \mathbf {B} } . Using vector calculus and Maxwell's equations, symmetry is sought for in the terms containing
Maxwell_stress_tensor
Physical quantity in electromagnetism
\operatorname {\cdot } ~} is the vector dot product; d ℓ {\displaystyle \mathrm {d} {\boldsymbol {\ell }}} is an infinitesimal vector line element along the curve
Displacement_current_density
Method of encoding digital data on multiple carrier frequencies
f = k T U {\displaystyle \scriptstyle \Delta f\,=\,{\frac {k}{T_{U}}}} Hertz, where TU seconds is the useful symbol duration (the receiver-side window
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Statement on equilibrium in electromagnetism
does not require that all neighbouring force vectors point exactly toward the stable point; the force vectors could spiral in toward the stable point, for
Earnshaw's_theorem
Concept in classical electromagnetism
by the curve C, · is the vector dot product, dl is an infinitesimal element (a differential) of the curve C (i.e. a vector with magnitude equal to the
Ampère's_circuital_law
American scientist (1839–1903)
equations to problems in physical optics. As a mathematician, he created modern vector calculus (independently of the British scientist Oliver Heaviside, who carried
Josiah_Willard_Gibbs
Quantum mechanical operator related to rotational symmetry
orbital angular momentum operator. L (just like p and r) is a vector operator (a vector whose components are operators), i.e. L = ( L x , L y , L z )
Angular_momentum_operator
Expulsion of a magnetic field from a superconductor
dipole Magnetic field Magnetic flux Magnetic scalar potential Magnetic vector potential Magnetization Permeability Right-hand rule Electrodynamics Maxwell's
Meissner_effect
Basic law of electromagnetism
bounded by the closed loop ∂Σ and dl is an infinitesimal vector element along that loop. The vector area element dA is perpendicular to the surface and oriented
Faraday's_law_of_induction
Types of electrical circuits
dipole Magnetic field Magnetic flux Magnetic scalar potential Magnetic vector potential Magnetization Permeability Right-hand rule Electrodynamics Maxwell's
Series_and_parallel_circuits
Equations of electromagnetism
{\displaystyle \mathbf {r} } , and n {\displaystyle \mathbf {n} } is the unit vector pointing from the source toward the observer. Because electromagnetic disturbances
Jefimenko's_equations
British mathematician and electrical engineer (1850–1925)
equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today
Oliver_Heaviside
Vector field describing the density of electric dipole moments in a dielectric material
polarization density (or electric polarization, or simply polarization) is the vector field that expresses the volumetric density of permanent or induced electric
Polarization_density
Auto racing series
LMH. It partnered with Duqueine after a previous deal with Vector Sport fell through. Hertz Team Jota entered an additional Porsche 963 following LMP2's
2024 FIA World Endurance Championship
2024_FIA_World_Endurance_Championship
formulation of Maxwell's equations using matrices, complex numbers, and vector calculus. These representations are for a homogeneous medium, an approximation
Matrix representation of Maxwell's equations
Matrix_representation_of_Maxwell's_equations
92nd edition of the endurance race
PureRxcing's Klaus Bachler, Alex Malykhin and Joel Sturm. Porsche, the No. 12 Hertz Team Jota and the No. 91 Manthey EMA teams left Le Mans as the Hypercar
2024_24_Hours_of_Le_Mans
Measure of positive and negative charges
to use vector algebra, since a quantity with magnitude and direction, like the dipole moment of two point charges, can be expressed in vector form p =
Electric_dipole_moment
Technique in neural networks for learning joint representations of text and images
outputs a single vector representing its semantic content. The other model takes in an image and similarly outputs a single vector representing its visual
Contrastive Language–Image Pre-training
Contrastive_Language–Image_Pre-training
Physical quantity, density of magnetic moment per volume
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic
Magnetization
Electromagnetic property of matter
Buchwald, Jed Z. (2013). "Electrodynamics from Thomson and Maxwell to Hertz". In Buchwald, Jed Z.; Fox, Robert (eds.). The Oxford Handbook of the history
Electric_charge
proportional to frequency f (so called V/f control, V/Hz control, Constant Volts/Hertz, CVH). Advantage of the V/f variant is in keeping the magnetic flux inside
Scalar_control
Branch of physics about magnetism in systems with steady electric currents
from the magnetic potential. The magnetic field can be derived from the vector potential. Since the divergence of the magnetic flux density is always zero
Magnetostatics
HERTZ VECTOR
HERTZ VECTOR
Girl/Female
German
Of the earth.
Surname or Lastname
English and North German
English and North German : from a personal name or nickname meaning ‘stag’, Middle English hert, Middle Low German hërte, harte.German : variant spelling of Hardt 1 and 2.Jewish (Ashkenazic) : ornamental name or a nickname from German and Yiddish hart ‘hard’.Irish : Anglicized form of Gaelic Ó hAirt ‘descendant of Art’, a byname meaning ‘bear’, ‘hero’. The English name became established in Ireland in the 17th century.French : from an Old French word meaning ‘rope’, hence possibly a metonymic occupational name for a rope maker or a hangman.Dutch : nickname from Middle Dutch hart, hert ‘hard’, ‘strong’, ‘ruthless’, ‘unruly’.This name was brought independently to New England by many bearers from the 17th century onward. Stephen Hart was one of the founders of Hartford, CT, (coming from Cambridge, MA, with Thomas Hooker) in 1635.
Girl/Female
Australian, British, Danish, Dutch, English, Finnish, French, German, Swedish
Earth; Of the Earth; Strong; Bold
Surname or Lastname
Dutch
Dutch : patronymic from a reduced and altered form of the personal names Arnoud (see Arnold), Alaert, or Adriaan. Compare Artz.English : patronymic from Hart.Variant of German and Jewish Hartz.
Female
Russian
(Иоланта) Russian form of Greek Iolanthe, IOLANTA means "violet flower." This is the name of an opera by Pyotr Tchaikovsky, based on the Danish play "King René's Daughter," by Henrik Hertz. The first performance took place in St. Petersburg in 1892.
Female
Egyptian
, house above.
Surname or Lastname
English
English : nickname for a kindly person, from Middle English gode ‘good’ + herte ‘heart’.Probably also an Americanized form of German Gothard or Swiss Gutherz, a nickname for a charitable person, from Middle High German guot ‘good’ + herze ‘heart’.
Surname or Lastname
English
English : from the Old English personal name Heard or a Norman cognate Hard(on), also of Germanic origin. This was a byname meaning ‘hardy’, ‘brave’, ‘strong’, but it also seems to have been used as a short form of the various compound names containing this as a first element. Occasionally this may also be a variant of Hardy.English, German, Dutch, and Swedish (Hård) : nickname for a stern or severe man, from Middle English, Middle Low German hard, Middle Dutch hart, hert, Swedish hård ‘hard’, ‘inflexible’. The Swedish name was probably originally a soldier’s name.English : topographic name for someone who lived on a patch of particularly hard ground or one that was difficult to farm. Compare Hardacre.Dutch : occupational name from Middle Dutch harde, herde ‘herder’.
HERTZ VECTOR
HERTZ VECTOR
Girl/Female
Arabic
Safe; Mild
Girl/Female
Indian
Beautiful, A musical Raag
Female
Egyptian
, the great, or, the first.
Girl/Female
Muslim
Courage, Bravery
Girl/Female
Tamil
Goddess Durga, Red in color
Boy/Male
Australian, Chinese, Czech, Slovenia
War; Battle
Boy/Male
Arabic, Muslim
Earner; Aquirer
Male
English
Anglicized form of Hebrew Yehowshuwa, JOSHUA means "God is salvation." In the bible, this is the name of several characters, including the leader of the Israelites after Moses died. Jehoshua is another Anglicized form.
Boy/Male
Tamil
Devi Dyal | தேவீ தயாளÂ
Kind hearted Goddess
Boy/Male
Hindu
Boundless, Lord Vishnu
HERTZ VECTOR
HERTZ VECTOR
HERTZ VECTOR
HERTZ VECTOR
HERTZ VECTOR
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
A hart.
n.
Same as Radius vector.
n.
A spiral whose polar equation is r2/ = a; that is, a curve the square of whose radius vector varies inversely as the angle which the radius vector makes with a given line.
n.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.
n.
In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.
n.
A heart.
n.
The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.
n.
An ideal straight line joining the center of an attracting body with that of a body describing an orbit around it, as a line joining the sun and a planet or comet, or a planet and its satellite.
a.
Of or pertaining to an extensive forest in Germany, of which there are still portions in Swabia and the Hartz mountains.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.