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Angle between the orbital plane of a satellite and the vector to the sun
mechanics, the beta angle (𝜷) is the angle between a satellite's orbital plane around Earth and the geocentric position of the Sun. The beta angle determines
Beta_angle
Second letter of the Greek alphabet
of beta in physics and engineering include: In spaceflight, beta angle describes the angle between the orbit plane of a spacecraft or other body and the
Beta
\alpha \cos \beta -\sin \alpha \sin \beta \\\cos(\alpha -\beta )&=\cos \alpha \cos \beta +\sin \alpha \sin \beta \end{aligned}}} The angle difference identities
List of trigonometric identities
List_of_trigonometric_identities
Description of the orientation of a rigid body
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.
Euler_angles
Time period during which a rocket must launch to reach its target
Space Station were restricted by beta angle cutout. Beta angle ( β {\displaystyle \beta } ) is defined as the angle between the orbit plane and the vector
Launch_window
Simplification of the basic trigonometric functions
\alpha +\beta \cos \alpha ,\\\sin(\alpha -\beta )&\approx \sin \alpha -\beta \cos \alpha .\end{aligned}}} In astronomy, the angular size or angle subtended
Small-angle_approximation
Problem of finding unknown lengths and angles of a triangle
beta &=\arccos {\frac {a^{2}+c^{2}-b^{2}}{2ac}}.\end{aligned}}} Then angle γ = 180° − α − β. Some sources recommend to find angle β from the
Solution_of_triangles
Angle between a reference plane and the plane of an orbit
dictionary. Horizontal coordinate system Axial parallelism Axial tilt Azimuth Beta angle Kepler orbits Kozai mechanism Orbital inclination change Orbital pole
Orbital_inclination
Geometric theorem relating a given triangle and three angles to a point
{\displaystyle {\begin{aligned}\angle ZAB&=\angle YAC&=\alpha ,\\\angle XBC&=\angle ZBA&=\beta ,\\\angle YCA&=\angle XCB&=\gamma .\end{aligned}}} Then
Jacobi's_theorem_(geometry)
Hexahedron with parallelogram faces
= ∠ ( a , c ) {\displaystyle \beta =\angle (\mathbf {a} ,\mathbf {c} )} , γ = ∠ ( a , b ) {\displaystyle \gamma =\angle (\mathbf {a} ,\mathbf {b} )}
Parallelepiped
Relates tangents of two angles of a triangle and the lengths of the opposing sides
{\tfrac {1}{2}}(\alpha \pm \beta )={\frac {\sin \alpha \pm \sin \beta }{\cos \alpha +\cos \beta }}} (see tangent half-angle formula). The law of tangents
Law_of_tangents
Mechanism with bendable rotation axis
_{1}} the angle of rotation for axle 1 γ 2 {\displaystyle \gamma _{2}} the angle of rotation for axle 2 β {\displaystyle \beta } the bend angle of the joint
Universal_joint
Probability distribution
^{2}(2\beta -1)+\beta ^{2}(\beta +1)-2\alpha \beta (\beta +2)]}{\alpha \beta (\alpha +\beta +2)(\alpha +\beta +3)}}\\&={\frac {6[(\alpha -\beta )^{2}(\alpha
Beta_distribution
Group of eye diseases related to poor retinal and nerve perfusion
surgery may be required. Primary open-angle glaucoma: Prostaglandin agonists work by opening uveoscleral passageways. Beta-blockers, such as timolol, work by
Glaucoma
Matrix representing a Euclidean rotation
\beta &\cos \beta \sin \gamma &\cos \beta \cos \gamma \\\end{bmatrix}}\end{aligned}}} represents a rotation whose yaw, pitch, and roll angles are α, β and
Rotation_matrix
Technique in computer vision
{\displaystyle \alpha =\angle BPC} , β = ∠ A P C {\displaystyle \beta =\angle APC} , γ = ∠ A P B {\displaystyle \gamma =\angle APB} , p = 2 cos α {\displaystyle
Perspective-n-Point
Topics referred to by the same term
Steroidal antiandrogen, a type of antiandrogen medication Solar aspect angle or beta angle, in orbital spaceflight South Atlantic Anomaly, a magnetic anomaly
SAA
Parameters that define a specific orbit
Asteroid family, asteroids that share similar proper orbital elements Beta angle Ephemeris Geopotential model Orbital inclination Orbital state vectors
Orbital_elements
Type of diffraction grating
}+\sin {\beta }\right)=m\lambda } where: d {\displaystyle d} = line spacing, α {\displaystyle \alpha } = incidence angle, β {\displaystyle \beta } = diffraction
Blazed_grating
Wind experienced by a moving object
')=\cos(180^{\circ }-\alpha )=-\cos(\alpha )} . The angle of apparent wind ( β {\displaystyle \beta } ) can be calculated from the measured velocity of
Apparent_wind
Theory in soil mechanics
K_{a}={\frac {\cos \beta -\left(\cos ^{2}\beta -\cos ^{2}\phi \right)^{1/2}}{\cos \beta +\left(\cos ^{2}\beta -\cos ^{2}\phi \right)^{1/2}}}*cos\beta } K p = cos
Rankine's_theory
For angles in degrees, cos(20)*cos(40)*cos(80) equals 1/8
= ∠ D B F = 40 ∘ {\displaystyle \beta =\angle DBF=40^{\circ }} and α = ∠ C B D = 20 ∘ {\displaystyle \alpha =\angle CBD=20^{\circ }} (see graphic). Applying
Morrie's_law
Mathematical function
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function
Beta_function
2009 American crewed spaceflight to the ISS
Carrier Plate. Due to conflicts with the launch of the LRO, and due to a beta angle constraint, the next available launch opportunity was scheduled for July
STS-127
Trigonometric identity relating the sides and angles of a triangle
{\displaystyle \alpha =\angle BAD} , β = ∠ A B C {\displaystyle \beta =\angle ABC} , γ = ∠ B C D {\displaystyle \gamma =\angle BCD} , and δ = ∠ C D A {\displaystyle
Law_of_cotangents
Regression algorithm
data. The basic steps of the Least-angle regression algorithm are: Start with all coefficients β {\displaystyle \beta } equal to zero. Find the predictor
Least-angle_regression
Collection of proofs of equations involving trigonometric functions
O at an angle α {\displaystyle \alpha } above the horizontal line and a second line at an angle β {\displaystyle \beta } above that; the angle between
Proofs of trigonometric identities
Proofs_of_trigonometric_identities
Orbit about a small Solar System body
orbit Solar radiation pressure Orbital perturbation analysis (spacecraft) Beta angle Scheeres, D. J. (2007). Orbit Mechanics about Small Asteroids (PDF). 20th
Terminator_orbit
Protein structure
stagger of the strands in the beta-sheet. These two parameters (n and S) are related to the inclination angle of the beta strands relative to the axis
Beta_barrel
Trigonometric relation between sides and angles of a triangle
{\displaystyle \alpha ,} β , {\displaystyle \beta ,} and γ {\displaystyle \gamma } be the measures of the angles opposite those three sides respectively.
Mollweide's_formula
Correspondence between quaternions and 3D rotations
2D rotations. Specifically, quaternions encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have
Quaternions and spatial rotation
Quaternions_and_spatial_rotation
Excess energy at the surface of a material relative to its interior
way to measure surface energy is through contact angle experiments. In this method, the contact angle of the surface is measured with several liquids,
Surface_energy
Second brightest star in the southern constellation of Pictor
Beta Pictoris (abbreviated β Pictoris or β Pic) is the second brightest star in the constellation Pictor. It is located 63.4 light-years (19.4 pc) from
Beta_Pictoris
Unitary matrix containing information on the weak interaction
current families of quarks. In 1963, Nicola Cabibbo introduced the Cabibbo angle (θc) to preserve the universality of the weak interaction. Cabibbo was inspired
Cabibbo–Kobayashi–Maskawa matrix
Cabibbo–Kobayashi–Maskawa_matrix
3 intersections of any triangle's adjacent angle trisectors form an equilateral triangle
{\displaystyle (60^{\circ }+\beta )+(120^{\circ }+\gamma )+(60^{\circ }+\alpha )+\angle {XZY}=360^{\circ }} where equation (4) was used for angle A Z B {\displaystyle
Morley's_trisector_theorem
Event during which a spacecraft can be viewed from a specified ground location
Nighttime observation is possible under specific circumstances such as a high beta angle. A satellite flare occurs when sunlight is reflected by flat surfaces
Orbital_pass
Protein structural motif
The beta sheet (β-sheet, also β-pleated sheet) is a common motif of the regular protein secondary structure. Beta sheets consist of beta strands (β-strands)
Beta_sheet
Algebraic operation on coordinate vectors
square root of the scalar product of the vector by itself) and angles (the cosine of the angle between two vectors is the quotient of their scalar product
Dot_product
is based on measurements of the acetabular inclination angle (alpha), cartilage roof angle (beta), and infant age. The femoral head coverage can also be
Hip_pain
Cosines of the angles between a vector and the coordinate axes
=\arccos \left(\alpha _{u}\alpha _{v}+\beta _{u}\beta _{v}+\gamma _{u}\gamma _{v}\right).} Cartesian tensor Euler angles Kay, D. C. (1988). Tensor Calculus
Direction_cosine
Process of projecting a 3D object onto a 2D plane
\alpha :} angle between z ¯ {\displaystyle {\overline {z}}} -axis and x ¯ {\displaystyle {\overline {x}}} -axis β : {\displaystyle \beta :} angle between
Axonometry
Aerobatic maneuver
crosswind conditions. The sideslip angle, also called angle of sideslip (AOS, AoS, β {\displaystyle \beta } , Greek letter beta), is a term used in fluid dynamics
Slip_(aerodynamics)
Ratio of distance on a map to the corresponding distance on the ground
{\text{(b)}}\quad \tan \beta ={\frac {\delta x}{\delta y}}={\frac {a\,\delta \lambda }{\delta y}}.} The relationship between the angles β {\displaystyle \beta } and α
Scale_(map)
Equation in physics
{\displaystyle \alpha ,\beta ,\gamma } are the angles directly opposite to the vectors, thus satisfying α + β + γ = 360 o {\displaystyle \alpha +\beta +\gamma =360^{o}}
Lami's_theorem
5-sided star shaped polygon
)(1+\gamma )\\&=\beta +\alpha \beta +\beta \gamma +\alpha \beta \gamma =\beta +(1+\delta )+(1+\varepsilon )+\alpha (1+\varepsilon )\\&=2+\alpha +\beta +\delta
Pentagramma_mirificum
Phenomena that occur as a result of alternating current
magnitudes of 1. A ∠ θ = A ∠ δ − ( β ) {\displaystyle A\angle \theta =A\angle \delta -(\beta )} Lagging current can be formally defined with respect to
Leading_and_lagging_current
Pentagon with all sides equal but the angles may not be equal
green). We assume that we are given the adjacent angles α {\displaystyle \alpha } and β {\displaystyle \beta } . According to the law of sines the length
Equilateral_pentagon
Triple star system in the constellation Centaurus
although the position angle has changed six degrees since. Beta Centauri B is a B1 dwarf with an apparent magnitude of 4. In 1967, Beta Centauri's observed
Beta_Centauri
Geometric arrangements of points, foundational to Lie theory
\beta ,\alpha \rangle \langle \alpha ,\beta \rangle &=2{\frac {(\alpha ,\beta )}{(\alpha ,\alpha )}}\cdot 2{\frac {(\alpha ,\beta )}{(\beta ,\beta )}}\\&=4{\frac
Root_system
Performance metric in football and hockey
and shot angle a {\displaystyle a} (radians), and has illustrative coefficients: β 0 = − 1.50 , β d = − 0.08 , β a = 0.90. {\displaystyle \beta _{0}=-1
Expected_goals
Aircraft flight measures
oriented at angle ψ {\displaystyle \psi } (psi) with respect to inertial axes. The body is oriented at an angle β {\displaystyle \beta } (beta) with respect
Stability_derivatives
2021 film
"The Beta Test (2021)". The Numbers. Retrieved November 26, 2021. Rubin, Rebecca (June 24, 2020). "Vanishing Angle Sets Jim Cummings Thriller 'The Beta Test'
The_Beta_Test
Chemical compound
non-selective beta blocker. It is used topically in the form of eye drops to manage ocular hypertension (high pressure in the eye) and open-angle glaucoma
Levobunolol
(N.B., the symbol β {\displaystyle \beta } is also often used in the older literature to denote the collection angle instead of α {\displaystyle \alpha
Magic_angle_(EELS)
Shock wave that is inclined with respect to the incident upstream flow direction
flow deflection angle: M 2 = 1 sin ( β − θ ) χ M 1 2 sin 2 β + 1 γ M 1 2 sin 2 β − χ . {\displaystyle M_{2}={\frac {1}{\sin(\beta -\theta )}}{\sqrt
Oblique_shock
Method for calculating average values
{\displaystyle \varphi } and β {\displaystyle \beta } . A simple way to calculate the mean of a series of angles (in the interval [0°, 360°)) is to calculate
Circular_mean
Angle between diagonal and edge of a cube
}-1\right)\left(3\cos ^{2}\beta -1\right)\!,} where θ is the angle between the principal axis of the interaction and the magnetic field, θr is the angle of the axis
Magic_angle
Design rule for optical systems
variables ( α o , β o ) {\textstyle (\alpha _{\mathrm {o} },\beta _{\mathrm {o} })} are the angles (relative to the optic axis) of any two rays as they leave
Abbe_sine_condition
Mineral thought to be abundant in the Earth's mantle
violation of space group Imma, reducing the symmetry to monoclinic I2/m with beta angle up to 90.4º.[citation needed] Wadsleyite II is a separate spinelloid phase
Wadsleyite
Famous mathematical optimization problem
In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem posed by the 15th-century German mathematician Johannes
Regiomontanus' angle maximization problem
Regiomontanus'_angle_maximization_problem
}\cos {\alpha }+\gamma _{\theta \beta }\cos {\beta }+\gamma _{\alpha \beta }\ =0} where α, β, and θ are the angles shown and γij is the surface energy
Ideal_surface
Loss of one degree of freedom in a three-dimensional, three-gimbal mechanism
\beta } . It is possible to imagine an airplane rotated by the above-mentioned Euler angles using the X-Y-Z convention. In this case, the first angle -
Gimbal_lock
Method for visually representing three-dimensional objects
in which the three coordinate axes appear equally foreshortened and the angle between any two of them is 120 degrees. The term "isometric" comes from
Isometric_projection
Model of rotating physical systems
longitudinal angle α {\displaystyle \alpha \,} (commonly designated by φ {\displaystyle \varphi \,} ) and the colatitude angle β {\displaystyle \beta \,} (commonly
Rigid_rotor
Type of isosceles triangle
(isosceles) triangle. Since the angles of a triangle sum to π {\displaystyle \pi } radians, each of the base angles (CBX and CXB) is: β = π − π 5 2
Golden_triangle_(mathematics)
{\displaystyle \left({\begin{array}{cc}\cos(\beta +\beta _{0})&-\sin(\beta +\beta _{0})\\\sin(\beta +\beta _{0})&\cos(\beta +\beta _{0})\\\end{array}}\right)\left
K-Mirror_(optics)
{1}{2}}ca\sin \beta } Where a is the line BC, b is the line AC, c is the line AB, α is the interior angle at A, β is the interior angle at B, γ is the
Area_of_a_triangle
Binary star in the constellation of Delphinus
Beta Delphini is a binary star system in the constellation of Delphinus. It is the brightest star in Delphinus with a combined apparent visual magnitude
Beta_Delphini
Measure of the fluid slip in the impeller of a compressor or a turbine
exit angle and hence, gave the following equation. σ = 1 − 1.98 z ( 1 − ϕ 2 cot β 2 ) {\displaystyle \sigma =1-{\frac {1.98}{z(1-\phi _{2}\cot \beta _{2})}}}
Slip_factor
Class of chemical compounds
4353G. doi:10.1002/anie.201510612. ISSN 1433-7851. PMID 26924507 – via beta angle found in entry ICSD 430383. Nickelsen, Jasper; Edelmann, Arthur; Symeonidis
Borosulfate
The back angle of a bevel gear is the angle between an element of the back cone and a plane of rotation, and usually is equal to the pitch angle. The back
List_of_gear_nomenclature
vectors). This is multiplied by the sine of the angle of the base of the wedge ( β {\displaystyle \beta } ) to get the component parallel to the base:
Critical_taper
Angle between each wing or tail surface within a pair
\beta } meaning the change in rolling moment coefficient (the "Cl") per degree (or radian) of change in sideslip angle (the " β {\displaystyle \beta }
Dihedral_(aeronautics)
Fundamental topographical problem
two unknown angles is equal to the sum of β1 and β2, yielding the equation ϕ + ψ = β 1 + β 2 . {\displaystyle \phi +\psi =\beta _{1}+\beta _{2}.} A second
Hansen's_problem
Geometrical property of a bar's cross-section
property of a bar's cross-section. It is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous
Torsion_constant
{\displaystyle \angle _{U}(\alpha ,\beta ):=\varlimsup _{s,t\to 0}\arccos {\frac {d(\alpha (s),p)^{2}+d(\beta (t),p)^{2}-d(\alpha (s),\beta (t))^{2}}{2d(\alpha
Space_of_directions
Situation or phenomena, When light bounces off a material with a low index of refraction
electrons. The critical angle for total external reflection is defined by the scenario where, neglecting β ( ω ) {\displaystyle \beta (\omega )} , the refracted
Total_external_reflection
Study of the performance, stability, and control of flying vehicles
critical angles, the angle of attack of the wing ("alpha") and the angle of attack of the vertical tail, known as the sideslip angle ("beta"). A sideslip
Flight_dynamics
Far-field diffraction
{2A'}{\beta \sin \theta }}\sin \left({\frac {\beta a}{2}}\sin \theta \right)} Letting ψ ′ = β a sin θ = α r sin θ {\displaystyle \psi ^{'}=\beta a\sin
Fraunhofer_diffraction
Mathematical transformation in engineering
In electrical engineering, the alpha-beta ( α β γ {\displaystyle \alpha \beta \gamma } ) transformation (also known as the Clarke transformation) is a
Alpha–beta_transformation
Triple star system in the constellation Monoceros
Beta Monocerotis (Beta Mon, β Monocerotis, β Mon) is a triple star system in the constellation of Monoceros. To the naked eye, it appears as a single star
Beta_Monocerotis
Mammalian protein found in humans
glaucoma, drainage is reduced (open-angle glaucoma) or blocked completely (closed-angle glaucoma). In such cases, beta-2 stimulation with its consequent
Beta-2_adrenergic_receptor
Parameter used to characterize molecular geometry
\tau _{5}={\frac {\beta -\alpha }{60^{\circ }}}\approx -0.01667\alpha +0.01667\beta } where: β > α are the two greatest valence angles of the coordination
Geometry_index
Study of the 3D shapes of molecules
the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determine the position
Molecular_geometry
Theory of interwoven space and time by Albert Einstein
unprimed axes by an angle α = tan − 1 ( β ) , {\displaystyle \alpha =\tan ^{-1}(\beta ),} where β = v / c . {\displaystyle \beta =v/c.} The primed and
Special_relativity
Two-dimensional area measurement of a three-dimensional object projected onto a plane
A_{\text{projected}}=\int _{A}\cos {\beta }\,dA} where A is the original area, and β {\displaystyle \beta } is the angle between the normal to the local plane
Projected_area
Problem in trigonometry
(unknown) angles ∠CAP as x and ∠CBP as y gives: x + y = 2 π − α − β − C {\displaystyle x+y=2\pi -\alpha -\beta -C} by using the sum of the angles formula
Snellius–Pothenot_problem
Graph of space and time in special relativity
relative motion (see below). The angle α is given by tan α = v c = β . {\displaystyle \tan \alpha ={\frac {v}{c}}=\beta .} The corresponding boost from
Spacetime_diagram
Star in the constellation Taurus
Beta Tauri is the second-brightest star in the constellation of Taurus. It has the official name Elnath; Beta Tauri is the current Bayer designation,
Beta_Tauri
Flow behind a conical shock wave
{\displaystyle g'=U\chi } . In the small-angle approximation, the weak shock cone is given by z = β ρ {\displaystyle z=\beta \rho } . The trivial solution for
Taylor–Maccoll_flow
Measure of the "spread" of light in an optical system
optical system, which characterizes how "spread out" the light is in area and angle. The term étendue comes from French, where it means "extent". Other names
Etendue
Orientation of a geologic feature
horizontal line across the plane, and its dip is the angle of inclination (or depression angle) measured downward from horizontal. They are used together
Strike_and_dip
Inability to refrain from defecation
puborectalis. A weakened puborectalis leads to widening of the anorectal angle and impaired barrier to the stool in the rectum entering the anal canal
Fecal_incontinence
Super Jupiter orbiting Beta Pictoris
Beta Pictoris b (abbreviated as β Pic b) is an exoplanet orbiting the young debris disk, A-type main sequence star, Beta Pictoris located approximately
Beta_Pictoris_b
Triangle in hyperbolic geometry
consists of three line segments called sides or edges and three points called angles or vertices. Just as in the Euclidean case, three points of a hyperbolic
Hyperbolic_triangle
\beta _{1}} is the inlet flow angle on the airfoil β 2 {\displaystyle \beta _{2}} is the outlet flow angle on the airfoil β m {\displaystyle \beta _{m}}
Blade_solidity
Method of solution for certain mechanical problems
In classical mechanics, action-angle variables are a set of canonical coordinates that are useful in characterizing the nature of commuting flows in integrable
Action-angle_coordinates
Linear regression model with a single explanatory variable
function, β ^ = tan ( θ ) {\displaystyle {\widehat {\beta }}=\tan(\theta )} . Therefore, the angle θ {\displaystyle \theta } the graph of the function
Simple_linear_regression
Type of radioactive decay
In nuclear physics, double beta decay (ββ decay) is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons,
Double_beta_decay
Symbols for constants, special functions
II" error) the beta coefficient, the non-diversifiable risk, of an asset in mathematical finance the sideslip angle of an airplane a beta particle (e− or
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
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BETA ANGLE
BETA ANGLE
BETA ANGLE
BETA ANGLE
BETA ANGLE
BETA ANGLE
BETA ANGLE
BETA ANGLE
BETA ANGLE
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