<p>The average angular diameter of the Moon, as seen from the Earth, is <a href="https://lcogt.net/spacebook/using-angles-describe-positions-and-apparent-sizes-objects" rel="noreferrer">about 31 arcminutes</a>.</p>

<p>The angular diameter depends on the distance between the two objects and the diameter of the object being viewed.  Specifically, <a href="http://en.wikipedia.org/wiki/Angular_diameter" rel="noreferrer">for small angles</a>, it is the diameter divided by the distance.  When the distance is the same, the angular size is proportional to the diameter.</p>

<p>The distance remains the same when viewing the Earth from the Moon, but the Earth is larger.  <a href="http://www.nasa.gov/pdf/180561main_ETM.Distance.Moon.pdf" rel="noreferrer">According to NASA</a>, the diameter of the Moon is 3,476 km, and the diameter of the Earth is 12,756 km.</p>

<p>So, because it's proportional, the angular diameter can be calculated as follows:</p>

<p>$a_{Earth} = a_{Moon} \times {d_{Earth}\over d_{Moon}}$</p>

<p>$ = 31 arcminutes \times {12,756 km \over 3,476 km}$</p>

<p>$ \approx 114 arcminutes$, or just under 2 degrees.</p>

<p>This is approximate, because not only is this valid only for small degrees, where the tangent of an angle can be approximated by the angle itself (in radians), the Earth-Moon distance varies because the Moon's orbit around the Earth is an ellipse.</p>

CC BY-SA 3.0
2014-10-21T16:33:15.073Z
2014-10-21T16:33:15.073Z
rgettman
<p>The Earth viewed from moon will appear larger, in proportion to how much larger the Earth's diameter is versus the moons diameter.</p>

<ul>
<li>Earth diameter 7900mi</li>
<li>Moon diameter 2100mi</li>
</ul>

<p>So the Earth-view from the moon would appear 3.75 times as large as the Moon appears in the sky on earth.</p>

<p>I looked up the moon's typical angular diameter, it is 0.5 degree.  So the Earth's typical angular diam would be 1.9 degree.</p>

CC BY-SA 3.0
2017-08-17T03:51:34.323Z
2017-08-17T06:15:47.283Z
2017-08-17T06:15:47.283Z
BrettB
<p>You 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. </p>

<p>The equatorial radius of the Earth is $r_E = 6378.1 \textrm{km}$, the diameter is therefore $D= 2 \times r_E = 12756.2$.</p>

<ul>
<li>The <a href="http://en.wikipedia.org/wiki/Moon" rel="noreferrer">mean distance to the Moon is $d=384399\textrm{km}$</a>. This gives a (mean) angular diameter of $a=1.90065$°.</li>
<li>At <a href="http://en.wikipedia.org/wiki/Moon" rel="noreferrer">Perigee the distance is $d=362600\textrm{km}$</a>. This gives an angular diameter of $a=2.01482$°</li>
<li>At <a href="http://en.wikipedia.org/wiki/Moon" rel="noreferrer">Apogee the distance is $d=405400\textrm{km}$</a>. This gives an angular diameter of $a=1.80226$°</li>
</ul>

<p>These Moon-Earth distances are as seen from the <strong>centre</strong> 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.</p>

<p>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: </p>

<ul>
<li>The mean distance to the Moon is $d=384399-1738 = 382661\textrm{km}$. This gives a (mean) angular diameter of $a=1.90928$°.</li>
<li>At <a href="http://en.wikipedia.org/wiki/Moon" rel="noreferrer">Perigee the distance is $d=362600-1738 = 360862\textrm{km}$</a>. This gives an angular diameter of $a=2.02452$°</li>
<li>At <a href="http://en.wikipedia.org/wiki/Moon" rel="noreferrer">Apogee the distance is $d=405400-1738 = 403662\textrm{km}$</a>. This gives an angular diameter of $a=1.81001$°</li>
</ul>

<p>The angular diameter of the Earth from the <strong>surface</strong> 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).</p>

<p>Or about 2 degrees.</p>

CC BY-SA 3.0
2014-10-21T16:32:34.283Z
2014-10-23T14:44:57.223Z
2014-10-23T14:44:57.223Z
Dieudonné
<p>...today I must have left my brain home. I know it's a simple calculation but I keep failing simplest calculations today.</p>

<p>What is the angular diameter of Earth as seen from the surface of the Moon?</p>

CC BY-SA 3.0
2014-10-21T14:56:48.217Z
https://www.google.com/search?btnG=1&pws=0&q=What+is+the+angular+diameter+of+Earth+as+seen+from+the+Moon%3F
LocalFluff
CC BY-SA 3.0
2014-10-21T14:59:14.120Z
@LocalFluff: Gives me a thousand results of angular size of the Moon as seen from Earth.
SF.
<the-moon><angular-diameter>
What is the angular diameter of Earth as seen from the Moon?
SF.
# What is the angular diameter of Earth as seen from the Moon?

(Asked by: username_0 on 2014-10-21)

...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?

**Tags:** the-moon, angular-diameter
> **Comments:**
> **username_1**: https://www.google.com/search?btnG=1&pws=0&q=What+is+the+angular+diameter+of+Earth+as+seen+from+the+Moon%3F  
> **username_0**: @LocalFluff: Gives me a thousand results of angular size of the Moon as seen from Earth.  

---

## 3 answers

### Answer by username_4 on 2014-10-21. Score: 12 | Accepted answer

You 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 $d=384399\textrm{km}$](http://en.wikipedia.org/wiki/Moon). This gives a (mean) angular diameter of $a=1.90065$°.
* At [Perigee the distance is $d=362600\textrm{km}$](http://en.wikipedia.org/wiki/Moon). This gives an angular diameter of $a=2.01482$°
* At [Apogee the distance is $d=405400\textrm{km}$](http://en.wikipedia.org/wiki/Moon). 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 $d=362600-1738 = 360862\textrm{km}$](http://en.wikipedia.org/wiki/Moon). This gives an angular diameter of $a=2.02452$°
* At [Apogee the distance is $d=405400-1738 = 403662\textrm{km}$](http://en.wikipedia.org/wiki/Moon). 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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### Answer by username_2 on 2014-10-21. Score: 6

The average angular diameter of the Moon, as seen from the Earth, is [about 31 arcminutes](https://lcogt.net/spacebook/using-angles-describe-positions-and-apparent-sizes-objects).

The angular diameter depends on the distance between the two objects and the diameter of the object being viewed. Specifically, [for small angles](http://en.wikipedia.org/wiki/Angular_diameter), it is the diameter divided by the distance. When the distance is the same, the angular size is proportional to the diameter.

The distance remains the same when viewing the Earth from the Moon, but the Earth is larger. [According to NASA](http://www.nasa.gov/pdf/180561main_ETM.Distance.Moon.pdf), the diameter of the Moon is 3,476 km, and the diameter of the Earth is 12,756 km.

So, because it's proportional, the angular diameter can be calculated as follows:

$a\_{Earth} = a\_{Moon} \times {d\_{Earth}\over d\_{Moon}}$

$ = 31 arcminutes \times {12,756 km \over 3,476 km}$

$ \approx 114 arcminutes$, or just under 2 degrees.

This is approximate, because not only is this valid only for small degrees, where the tangent of an angle can be approximated by the angle itself (in radians), the Earth-Moon distance varies because the Moon's orbit around the Earth is an ellipse.


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### Answer by username_3 on 2017-08-17. Score: 6

The Earth viewed from moon will appear larger, in proportion to how much larger the Earth's diameter is versus the moons diameter.

* Earth diameter 7900mi
* Moon diameter 2100mi

So the Earth-view from the moon would appear 3.75 times as large as the Moon appears in the sky on earth.

I looked up the moon's typical angular diameter, it is 0.5 degree. So the Earth's typical angular diam would be 1.9 degree.


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