Physical unit
Unit name
Square degree
Unit symbol
d
e
G
2
{\ displaystyle \ mathrm {deg ^ {2}}}
, ,
s
q
.
d
e
G
.
{\ displaystyle \ mathrm {sq.deg.}}
(
∘
)
2
{\ displaystyle \ mathrm {(^ {\ circ}) ^ {2}}}
Physical quantity (s)
Solid angle
Formula symbol
Ω
{\ displaystyle \ Omega}
dimension
L.
2
L.
2
=
1
{\ displaystyle {\ mathsf {{\ frac {L ^ {2}} {L ^ {2}}} = 1}}}
In SI units
1
d
e
G
2
=
π
2
32
400
s
r
{\ displaystyle \ mathrm {1 \ deg ^ {2} = {\ frac {\ pi ^ {2}} {32 \, 400}} \; sr}}
Square degrees ( deg² , (°) ² ) ( English square degree or sq degree ) is a (non-legal) unit for the solid angle . It is mainly used in astronomy as a measure of the extent of an object in the sky .
The sub-units are called accordingly:
Square arc minute ( English square arcmin ) square degrees
=
1
3600
{\ displaystyle = {\ frac {1} {3600}}}
Square arcsecond ( English square arcsec ) square minute square degrees.
=
1
3600
{\ displaystyle = {\ frac {1} {3600}}}
=
1
12
960
000
{\ displaystyle = {\ frac {1} {12 \, 960 \, 000}}}
The full solid angle of the celestial sphere is sr =
4th
π
{\ displaystyle 4 \ pi}
(
360
d
e
G
)
2
π
≈
41
253
d
e
G
2
{\ displaystyle {\ frac {(360 \ \ mathrm {deg}) ^ {2}} {\ pi}} \ approx 41 \, 253 \ \ mathrm {deg ^ {2}}}
The size of a celestial object in square degrees results from the proportion of the celestial sphere that the object covers, multiplied by 41253.
The conversion of a square degree into steradian results in:
⇔
1
d
e
G
2
=
(
2
π
360
)
2
s
r
=
(
π
180
)
2
s
r
=
π
2
32
400
s
r
≈
3.046
1741
⋅
10
-
4th
s
r
≈
0.000
30461741
s
r
{\ displaystyle {\ begin {aligned} \ Leftrightarrow 1 \ \ mathrm {deg} ^ {2} & = \ left ({\ frac {2 \ pi} {360}} \ right) ^ {2} \ \ mathrm { sr} \\ & = \ left ({\ frac {\ pi} {180}} \ right) ^ {2} \ \ mathrm {sr} \\ & = {\ frac {\ pi ^ {2}} {32 \, 400}} \ \ mathrm {sr} \\ & \ approx 3 {,} 0461741 \ cdot 10 ^ {- 4} \ \ mathrm {sr} \\ & \ approx 0 {,} 00030461741 \ \ mathrm {sr } \ end {aligned}}}
or.
⇔
1
s
r
≈
3283
d
e
G
2
{\ displaystyle \ Leftrightarrow 1 \ \ mathrm {sr} \ approx 3283 \ \ mathrm {deg} ^ {2}}
For small angles , solid angles can be calculated approximately as with surfaces: an object whose extension measures 1 degree in one direction and 1 degree perpendicular to it, therefore covers a solid angle of around 1 square degree.
enlarged section of the function for opening angles 0–45 °
See also
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