What Is Angular Diameter?

Angular diameter is the "apparent diameter" obtained by observing an object from a specific position when the angle is the unit of measurement.

Angular diameter

Angular diameter formula
Where is the angular diameter,
d is the actual diameter of the object, D
Is the distance to the object; is in radians
When D is much larger than d, the formula can be simplified to
For a spherical object with a diameter equal to the actual diameter, the angular diameter formula can be obtained % 5Cdelta% 3D1arcsin% 5Cleft (% 5Cfrac% 7Bd% 7D% 7B2D% 7D% 5Cright) </ math> </ p> <p> In practical applications, the small angle approximation is suitable when X is far less than 1: arcsin × arctan × </ p> <h2> For astronomy </ h2> <p> In <a> astronomy </a>, the size of <a> celestial body </a> is usually based on the size of the <a> Earth </a> > The angular diameters seen are given, not their actual dimensions. </ p> <p> Because these angular diameters are usually small, they are usually expressed as <a> arc seconds </a> (") </ p> <p> arc seconds are 1 <a> degrees </ a > (1 °) 1/3600, 1 radian is 180 / degrees, so 1 radian is equal to 3,600 * 180 / <math> {\ displaystyle \ pi} arcseconds, which is about 206,265 arc seconds
Therefore, the angular diameter of the object with physical diameter d at distance D is expressed in arc seconds and can be given by
= (206,265) d / D arcseconds
These objects have an angular diameter of 1 ":
  • Object with a diameter of 1 cm and a distance of 2.06 km
  • Object with a diameter of 725.27 km at a distance of 1 astronomical unit (AU)
  • Objects with a diameter of 45 866 916 km in 1 light-year
  • Objects with a diameter of 1 AU (149 597 871 km) and a distance of 1parsec (pc: second gap)
Therefore, from a distance of 1 pc, the angular diameter of the Earth's orbit around the sun is 2 ", because 1 AU is the average radius of the Earth's orbit.
From a distance of one light year, the angular diameter of the sun is 0.03 ", and the angular diameter of the earth is 0.0003".
Celestial body size seen from earth
Astral body Angular diameter
sun 31'27 "-32'32"
moon 29'20 "-34'6"
Venus 9.7 "-1'6"
Jupiter 29.8 "-50.1"
Saturn 14.5 "-20.1"
Mars
3.5 "-25.1"
Mercury 4.5 "-13.0"
Uranus 3.3 "-4.1"
Neptune 2.2 "-2.4"
Pluto 0.06 "-0.11"

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