Astrophysics (Index)About

solid angle

(Ω, angular area)
(three-dimensional analog of an angle)

A solid angle (or angular area) is a size measurement for a region of possible directions from a point, which is equivalent to regions on the surface of a sphere. The concept is applicable regardless of the shape of such a region on the sphere's surface (circle, rectangle-like, etc.). For example, a solid angle quantifies the size of a region of the celestial sphere. A unit of a solid angle is the steradian (for square radian, which is adopted as a SI unit): the area on the surface of a sphere of its radius squared. 4π (roughly 12.6) steradians cover a whole sphere. Another unit, the square degree (deg²) is similarly defined for a degree: a degree has a length along a circle of π/180 radii and a square degree is that value squared. A square-like shape on the surface of a sphere (four equal angles), where each edge is a degree in length following a great circle, is actually slightly more than a square degree in size because of the curvature of the surface, but the difference is small. 4π(180/π)² (roughly 41253) square degrees covers a whole sphere and (180/π)² (roughly 3283) square degrees covers a steradian. For example, the area of USA on the surface of the Earth is roughly 0.28 steradians or 922 square degrees. A square arcminute is 1/3600 square degree.

Solid angles are used in the definition of some electromagnetic radiation measurements, and equations modeling spherical objects such as stars. They are also cited to describe the apparent size of astronomical objects (galaxies or nebulae), fields of view, and the areas covered by surveys. Square degrees are often used for the latter, but steradians are as well.


(mathematics,measurement)
Further reading:
https://en.wikipedia.org/wiki/Solid_angle
https://en.wikipedia.org/wiki/Steradian
https://en.wikipedia.org/wiki/Square_degree
https://www.et.byu.edu/~vps/ME340/TABLES/12.0.pdf
https://mathworld.wolfram.com/SolidAngle.html
https://spie.org/publications/fg11_p02_solid_angle?SSO=1
http://www.physicsinsights.org/solid_angles_1.html
https://ui.adsabs.harvard.edu/abs/2020PhyEd..55e5003Q/abstract

Referenced by pages:
2dF Galaxy Redshift Survey (2dFGRS)
3D-HST
4MOST
Anglo-Australian Telescope (AAT)
APM Galaxy Survey (APMUKS)
Atacama Cosmology Telescope (ACT)
AtLAST
Baade's Window
BASS
black-body radiation
BlackGEM
Boötes Field
CFHTLS
cold spot
Cosmic Dawn Intensity Mapper (CDIM)
Cosmic Evolution Survey (COSMOS)
cross section
D56
Dark Energy Survey (DES)
deep field (DF)
Deep Lens Survey (DLS)
Deep Multicolor Survey (DMS)
deep survey
Dragonfly Telephoto Array
etendue (AΩ)
Euclid
Evryscope
Extended Groth Strip (EGS)
field of view (FOV)
FIRST
Fsky (fsky)
GAMA
GOODS
GOODS-North
GOODS-South
gravitational wave (GW)
Groth Strip
Hamburg/ESO Survey (HE)
Herschel Stripe 82 Survey (HerS)
High Energy Transient Explorer (HETE)
Hubble Deep Field (HDF)
Hubble Deep Field South (HDF-S)
intensity
inverse square law
jansky (Jy)
Kepler Telescope
Large Submillimeter Telescope (LST)
LaSilla-QUEST Variability Survey (LSQ)
Livermore Optical Transient Imaging System (LOTIS)
Lockman hole
magnitude
MeerKLASS
Millennium Galaxy Catalogue (MGC)
MORA
Multiwavelength Survey by Yale-Chile (MUSYC)
Munich Near-Infrared Cluster Survey (MUNICS)
NOAO Deep Wide-field Survey (NDWFS)
Outer Solar System Origins Survey (OSSOS)
Palomar 48 Inch Telescope (P48)
Pan-STARRS
Planck function
Pre-OmegaTranS (POTS)
PRIMUS
radiance
radio source (RS)
Rayleigh-Jeans law
SkyMapper
Spitzer HETDEX Exploratory Large Area Survey (SHELA)
STAR-X
STARE
stellar association
Subaru PFS
Subaru XMM-Newton Deep Survey (SXDS)
SuperWASP (SWASP)
surface brightness (SB)
ULTRASAT
VIMOS-VLT Deep Survey (VVDS)
VLT Survey Telescope (VST)
Wien approximation
XMM-Newton
Zwicky Transient Facility (ZTF)

Index