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You may have heard the terms arc-minute and arc-second mentioned on the TV, magazines or other websites. These are the units of measurement for angular size used in modern astronomy. Angular size is used to describe the dimensions of an object as it appears in the sky.
Introduction to Astronomy Series
  1. Introduction to Astronomy
  2. The Celestial Sphere - Right Ascension and Declination
  3. What is Angular Size?
  4. What is the Milky Way Galaxy?
  5. The Astronomical Magnitude Scale
  6. Sidereal Time, Civil Time and Solar Time
  7. Equinoxes and Solstices
  8. Parallax, Distance and Parsecs
  9. Luminosity and Flux of Stars
  10. Kepler's Laws of Planetary Motion
  11. What Are Lagrange Points?
  12. Glossary of Astronomy & Photographic Terms
  13. Astronomical Constants - Some Useful Constants for Astronomy

Angular Size is measured in arc-minutes and arc-seconds, which are used to represent angles on a sphere. An arcsecond is 1/3600th of one degree, and a radian is 180/π degrees, so one radian equals 3,600*180/π arcseconds, which is about 206,265 arcseconds.This is useful to astronomers when working out distances between objects or calculating magnifications required for observations. Angular Size is also used as a measure of optical instruments resolving power - basically how small an object can be seen.

Angular size refers to the object's apparent size as seen from an observer on Earth. For example, the Moon has an angular size of approximately 30 arcminutes.
Difference between Angular Size and Linear Size

Difference between Angular Size and Linear Size

The angular size of an object is determined by its actual size and its distance from the observer. For an object of fixed size, the larger the distance, the smaller the angular size. For objects at a fixed distance, the larger the actual size of an object, the larger its angular size.

Many deep sky objects such as galaxies and nebulas appear as non-circular and are thus typically given two measures of diameter: Major Diameter and Minor Diameter. For example, the Small Magellanic Cloud has a visual apparent diameter of 5° 20' x 3° 5'.

Experiment: Calculate the Angular Size of the Moon

Let's try and calculate the angular size of the Moon. All you need is a tape measure and a ruler.

Hold the ruler at arm's length and measure the diameter of the Moon, you may have to wait for a full moon to be able to accurately measure it. You should get a reading of between 5mm and 8mm depending on the season and the length of your arm. Note down your measured apparent size of the Moon.

Next, you need to measure the distance between your hand and your eye (you may need help with this one) and note this down as well. Both measurements need to be the same units, ideally millimetres.

Now, all we have to do is some simple maths.

Angular Size Calculation
Equation 12 - Angular Size Calculation

This will give you the angular size of the object in radians, where Sap is the apparent size measured and l is the between your hand and your eye. You can then use the formula to calculate its actual size:

Diameter given Angular size and Distance
Equation 13 - Diameter given Angular size and Distance

The Moons angular size can be converted from radians to arc-seconds by multiplying by 206,264. Arc-minutes can be found by dividing by 60.

Your answer should be between 30 and 35 arc-minutes in diameter.

Angular Size of the Sun

Do you think that the angular size of the Sun is greater or smaller than the angular size of the Moon

Do not look at the Sun! Blindness or visual impairment will be the result.

The Sun and the Moon appear to us the same size - almost exactly the same (hence Solar Eclipses), but we know that the Sun is many, many times bigger than the Moon. The Sun is 400 times bigger than the Moon, however, the Sun is also 400 times further away from us - so the result is that the Sun and the Moon have the same angular size.

2 thoughts on “What is Angular Size?
  • 18th July 2018 at 12:00 am

    If you haven't already solved your problem, the answer is simple - angular size in arcseconds = (d / D) x 206265, where d is the size of the object and D is the distance to the object, both in the same unit of measure (metres, Km, miles, etc.).
    For example, the Apollo LM is 4 metres in diameter (ignoring the legs), so 4/400000000*206265 = 0.002 arcseconds.
    This may be too late to help you, but may help others.

  • 20th October 2017 at 12:00 am

    Wow, really well explained, doesn't help me too much to solve My angular size problem because I have to find the angular size of the flag planted on the moon but definitely helpful  :) 


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