### What is the angular diameter of Earth as seen from the Moon?

...today I must have left my brain home. I know it's a simple calculation but I keep failing simplest calculations today.

What is the angular diameter of Earth as seen from the surface of the Moon?

@LocalFluff: Gives me a thousand results of angular size of the Moon as seen from Earth.

Dieudonné Correct answer

8 years agoYou can calculate the angular diameter of the Earth using the equation:

$$a = \arctan \frac{D}{d}$$

where $a$ is the angular diameter, $D$ is the physical diameter of the Earth, and $d$ is the distance from the Moon to the Earth.The equatorial radius of the Earth is $r_E = 6378.1 \textrm{km}$, the diameter is therefore $D= 2 \times r_E = 12756.2$.

- The mean distance to the Moon is $d=384399\textrm{km}$. This gives a (mean) angular diameter of $a=1.90065$°.
- At Perigee the distance is $d=362600\textrm{km}$. This gives an angular diameter of $a=2.01482$°
- At Apogee the distance is $d=405400\textrm{km}$. This gives an angular diameter of $a=1.80226$°

These Moon-Earth distances are as seen from the

**centre**of the Moon. To calculate the diameter from the surface of the Moon, you'll have to subtract the position of the observer along the Moon-Earth axis.If the observer is on the Moon's equator and the Earth is at zero hour angle (i.e. on the local meridian), the distance to the Earth needs to be subtracted by $r_M=1738.14\textrm{km}$. This gives the following values:

- The mean distance to the Moon is $d=384399-1738 = 382661\textrm{km}$. This gives a (mean) angular diameter of $a=1.90928$°.
- At Perigee the distance is $d=362600-1738 = 360862\textrm{km}$. This gives an angular diameter of $a=2.02452$°
- At Apogee the distance is $d=405400-1738 = 403662\textrm{km}$. This gives an angular diameter of $a=1.81001$°

The angular diameter of the Earth from the

**surface**of the Moon is, therefore, between $a=1.80226$° (at apogee and the Earth is near the horizon) and $a=2.02452$° (at perigee and for an observer at the equator and when the Earth is at maximum altitude on the meridian).Or about 2 degrees.

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Content dated before 7/24/2021 11:53 AM

LocalFluff 8 years ago

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