<p>I have found 2 definitions of Eclipse Magnitude in total eclipse:</p>
<p>Solar eclipse for example, below we define <span class="math-container">$r_1$</span> as the radius of the Sun, <span class="math-container">$r_2$</span> as the radius of the Moon's Shadow, <span class="math-container">$d$</span> as the distance of Sun's center and Moon's center</p>
<p>if it is a partial eclipse, the Eclipse Magnitude have no objection:</p>
<p><span class="math-container">$$
\epsilon = \frac{r_1 + r_2 - d}{2r_1}
$$</span></p>
<h3>Definition 1:</h3>
<p>After the Sun is totally blocked, the Eclipse Magnitude jumps from <span class="math-container">$1$</span> to <span class="math-container">$r_2/r_1$</span>, which is the ratio of Moon and Sun's diameter</p>
<p><a href="http://www.jgiesen.de/eclipse/" rel="nofollow noreferrer">http://www.jgiesen.de/eclipse/</a></p>
<p><a href="https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100126148" rel="nofollow noreferrer">https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100126148</a></p>
<h3>Definition 2:</h3>
<p>After the Sun is totally blocked, the Eclipse Magnitude is still:</p>
<p><span class="math-container">$$
\epsilon = \frac{r_1 + r_2 - d}{2r_1} &gt; 1,\quad 0 \leq d \leq r_2 - r_1
$$</span></p>
<p>only if the Sun and Moon's center overlap, will <span class="math-container">$d = 0$</span>, and <span class="math-container">$\epsilon = \epsilon_{max} = \dfrac{r_1 + r_2}{2r_1}$</span>, but this will still be less than <span class="math-container">$r_2/r_1$</span></p>
<p>This provide a continuous definition of eclipse magnitude, on the other hand, in an annular solar eclipse, the Eclipse Magnitude is always <span class="math-container">$r_2/r_1$</span>, having nothing to do with <span class="math-container">$d$</span>, but this is continuous</p>
<p><a href="https://www.geogebra.org/m/SnZ7QGTJ" rel="nofollow noreferrer">https://www.geogebra.org/m/SnZ7QGTJ</a></p>
<h3>Which one is right? I didn't find any books or professional articles defines the calculation of Eclipse Magnitude, Thanks!</h3>
<hr />
<p>The core question I think is: a total eclipse, especially lunar total eclipse, while the earth's umbra is much larger than the moon.</p>
<p>Then the magnitude will be larger if the center of the Moon and the center of the Earth's umbra are closer together <code>See Bottom Figure</code></p>
<p>(comparing if the moon is close to the edge of the umbra <code>See Top Figure</code>) if using Definition II.</p>
<p>In Definition I, the magnitude will have nothing to do with center distance, as long as the moon is all in the earth's shadow.</p>
<p><a href="https://i.sstatic.net/oSVhdFA4.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/oSVhdFA4.png" alt="enter image description here" /></a></p>
<p><a href="https://i.sstatic.net/GLNOR2QE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/GLNOR2QE.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2024-11-05T19:05:39.207Z
Fred Espenak says "the eclipse magnitude is defined as the fraction of the Sun's diameter occulted by the Moon at the geographic location and instant of Greatest Eclipse". https://www.eclipsewise.com/solar/SEhelp/SEcatkey.html I think most modern writers would agree with Fred that this ratio of (angular) diameters is the most sensible measure of solar eclipse magnitude.
PM 2Ring
CC BY-SA 4.0
2024-11-05T22:54:12.397Z
I can't quote the equations easily, but the Explanatory Supplement gives equations similar to what PM 2Ring says above.  The equations in your question resemble those the ESAA gives for lunar eclipses.
Greg Miller
CC BY-SA 4.0
2024-11-06T03:28:02.803Z
@GregMiller where is the Explanatory Supplement?
Firestar-Reimu
CC BY-SA 4.0
2024-11-06T11:50:40.257Z
@Firestar-Reimu The Explanatory Supplement to the Astronomical Almanac, typically called the Explanatory Supplement for short. It's not a cheap book.
David Hammen
CC BY-SA 4.0
2024-11-06T17:12:45.310Z
The first edition (which has a slightly different title: The Explanatory Supplement to the Astronomical Ephemeris 1961) will probably be the most useful if you're interested in eclipses, as it has worked numerical examples.  It can usually be had for cheaper from used sources.
Greg Miller
CC BY-SA 4.0
2024-11-13T15:27:00.393Z
I can find only the 3rd edition, see edit
Firestar-Reimu
CC BY-SA 4.0
2024-11-13T17:52:20.753Z
The third edition is a step backwards IMHO in its handling of eclipses.
Greg Miller
CC BY-SA 4.0
2024-11-14T06:20:16.630Z
The core question I think is: a total eclipse, especially lunar total eclipse, while the earth's umbra is much larger than the moon. Then the magnitude will be larger if the center of the Moon and the center of the Earth's umbra are closer together (comparing if the moon is close to the edge of the umbra) if using Definition II. In Definition I, the magnitude will have nothing to do with center distance, as long as the moon is all in the earth's shadow.
Firestar-Reimu
<amateur-observing><solar-eclipse>
What is the definition of "Eclipse Magnitude" of total eclipse
Firestar-Reimu
# What is the definition of "Eclipse Magnitude" of total eclipse

(Asked by: username_0 on 2024-11-05)

I have found 2 definitions of Eclipse Magnitude in total eclipse:

Solar eclipse for example, below we define $r\_1$ as the radius of the Sun, $r\_2$ as the radius of the Moon's Shadow, $d$ as the distance of Sun's center and Moon's center

if it is a partial eclipse, the Eclipse Magnitude have no objection:

$$
\epsilon = \frac{r\_1 + r\_2 - d}{2r\_1}
$$

### Definition 1:

After the Sun is totally blocked, the Eclipse Magnitude jumps from $1$ to $r\_2/r\_1$, which is the ratio of Moon and Sun's diameter

<http://www.jgiesen.de/eclipse/>

<https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100126148>

### Definition 2:

After the Sun is totally blocked, the Eclipse Magnitude is still:

$$
\epsilon = \frac{r\_1 + r\_2 - d}{2r\_1} > 1,\quad 0 \leq d \leq r\_2 - r\_1
$$

only if the Sun and Moon's center overlap, will $d = 0$, and $\epsilon = \epsilon\_{max} = \dfrac{r\_1 + r\_2}{2r\_1}$, but this will still be less than $r\_2/r\_1$

This provide a continuous definition of eclipse magnitude, on the other hand, in an annular solar eclipse, the Eclipse Magnitude is always $r\_2/r\_1$, having nothing to do with $d$, but this is continuous

<https://www.geogebra.org/m/SnZ7QGTJ>

### Which one is right? I didn't find any books or professional articles defines the calculation of Eclipse Magnitude, Thanks!

---

The core question I think is: a total eclipse, especially lunar total eclipse, while the earth's umbra is much larger than the moon.

Then the magnitude will be larger if the center of the Moon and the center of the Earth's umbra are closer together `See Bottom Figure`

(comparing if the moon is close to the edge of the umbra `See Top Figure`) if using Definition II.

In Definition I, the magnitude will have nothing to do with center distance, as long as the moon is all in the earth's shadow.

[![enter image description here](https://i.sstatic.net/oSVhdFA4.png)](https://i.sstatic.net/oSVhdFA4.png)

[![enter image description here](https://i.sstatic.net/GLNOR2QE.png)](https://i.sstatic.net/GLNOR2QE.png)

**Tags:** amateur-observing, solar-eclipse

> **Comments:**
> **username_1**: Fred Espenak says "the eclipse magnitude is defined as the fraction of the Sun's diameter occulted by the Moon at the geographic location and instant of Greatest Eclipse". https://www.eclipsewise.com/solar/SEhelp/SEcatkey.html I think most modern writers would agree with Fred that this ratio of (angular) diameters is the most sensible measure of solar eclipse magnitude.  
> **username_2**: I can't quote the equations easily, but the Explanatory Supplement gives equations similar to what username_1 says above.  The equations in your question resemble those the ESAA gives for lunar eclipses.  
> **username_0**: @GregMiller where is the Explanatory Supplement?  
> **username_3**: @username_0 The Explanatory Supplement to the Astronomical Almanac, typically called the Explanatory Supplement for short. It's not a cheap book.  
> **username_2**: The first edition (which has a slightly different title: The Explanatory Supplement to the Astronomical Ephemeris 1961) will probably be the most useful if you're interested in eclipses, as it has worked numerical examples.  It can usually be had for cheaper from used sources.  
> **username_0**: I can find only the 3rd edition, see edit  
> **username_2**: The third edition is a step backwards IMHO in its handling of eclipses.  
> **username_0**: The core question I think is: a total eclipse, especially lunar total eclipse, while the earth's umbra is much larger than the moon. Then the magnitude will be larger if the center of the Moon and the center of the Earth's umbra are closer together (comparing if the moon is close to the edge of the umbra) if using Definition II. In Definition I, the magnitude will have nothing to do with center distance, as long as the moon is all in the earth's shadow.  

---

## 0 answers

