<p>I will take a stab at it.  Assuming </p>

<ul>
<li>the last eclipse happens when the moon is at perigee and the earth is at aphelion.</li>
<li>the moon's perigee is increasing by 4 cm per year,</li>
<li>the earth's aphelion does not change with time,</li>
<li>the sun and the moon are perfect spheres,</li>
<li>the radius of the sun and moon don't change, and</li>
<li>a total eclipse occurs when <span class="math-container">$r_{\mathrm{sun}}/d_{\mathrm{sun}} &lt; r_{\mathrm{moon}}/d_{\mathrm{moon}}$</span> where <span class="math-container">$r$</span> is radius and <span class="math-container">$d$</span> is distance,</li>
</ul>

<p>I get the following results:</p>

<ul>
<li>The last total eclipse at sea level will occur in 721,587,917 years at sea
level  (obviously too many significant digits).</li>
<li>The last total eclipse at mount Everest will occur in 721,807,917 years.</li>
<li>The difference is 220,000 years = (height_of_Everest) * 25000 years/km.</li>
</ul>

<p>Mathematica Source Code:</p>

<pre><code>dSun = 152097000; rSun = 695508; dMoonNow = 357347; rMoon = 1737; 
rEarth = 6371; hEverest = 8 + 8/10;
sol2 = Solve[ rMoon/(d + t 4/100/1000) == rSun/(dSun - rEarth), t][[1]];
Print[ t /. sol2 /. d -&gt; dMoonNow - rEarth  // Round];
Print[ t /. sol2 /. d -&gt; dMoonNow - rEarth - hEverest // Round];
</code></pre>

CC BY-SA 4.0
2019-01-19T19:08:47.820Z
Over that time scale and to that level of precision, will the Sun's diameter change as it evolves?
Steve Linton
CC BY-SA 4.0
2019-01-19T19:32:09.933Z
I think so!   (I added the assumption that it stays constant.)
irchans
CC BY-SA 4.0
2019-01-20T09:13:57.547Z
The Sun will get larger by  2-3% on that timescale. So this answer would be an upper limit.
ProfRob
CC BY-SA 4.0
2019-01-20T09:17:47.090Z
But since the apparent size of the Moon shrinks by 8% in the same time, I would guestimate that the overestimate of the time is only by about 25%.
ProfRob
CC BY-SA 4.0
2020-07-19T20:34:01.277Z
There are several things wrong with this answer. (1) "The moon's perigee is increasing by 4 cm per year." That is the current rate, and it is abnormally high, thanks to the Americas, Afro-eurasia, both of which block equatorial tidal flow, and due to the shape of the North Atlantic, whose shape resonates with the M2 tide. A better figure is less than 2 cm per year. (2) "The earth's aphelion does not change with time." It most certainly does. The key reason we are not seeing an ice stage starting now is because the Earth's eccentricity is very low. (Continued)
David Hammen
CC BY-SA 4.0
2020-07-19T20:39:50.117Z
(3) "The radius of the sun and moon don't change." The Sun's radius increases as it ages. When one takes all of these into consideration, the correct answer is somewhere between a few hundred million years to over two billion years.
David Hammen
CC BY-SA 4.0
2020-07-25T07:47:59.487Z
@a_donda - No, it is not. A constant rate is ludicrous. Tidal friction suggests the recession rate falls extremely rapidly with distance. (Tidal heating of a moon is proportional to $r^{-15/2}$). This is in fact an argument used by young earth creationists. (Know thine enemy.) The problem with these YEC arguments is that the current lunar rate is known to be anomalously high. Tidal rhythmites show that the lunar recession rate was less than half the current rate half for almost all of the last 2.5 billion years. (Continued)
David Hammen
CC BY-SA 4.0
2020-07-25T07:52:21.753Z
Why 2.5 billion years? It's hard to find rock that show signs of tides that are older than 2.5 billion years. This raises a question: Despite the current distance between the Earth and Moon being larger than it was in the past, why is the current lunar recession rate so large? The answer lies in the shape of the continents and the shape of the oceans, particularly the North Atlantic.
David Hammen
CC BY-SA 4.0
2020-07-25T08:07:23.337Z
Projecting the current value of 4 cm/year (better: 3.8 cm/yr) forward is equally incorrect, for two reasons. One is that the recession rate should naturally drop as the Moon recedes, even if the North Atlantic holds its shape. A constant rate is inconsistent with physics. The other is that plate tectonics will eventually reshape the North Atlantic so that it is not nearly as good a damped resonator with regard to the M2 tidal constituent as it is now. The lunar recession rate will drop precipitously somewhere in the next 721 million years.
David Hammen
CC BY-SA 4.0
2019-01-19T18:00:09.370Z
2019-01-21T01:22:50.733Z
2019-01-21T01:22:50.733Z
irchans
<p>Because the moon distance from earth grows, how long will it take, that it is no longer possible to see a total eclipse but only circular eclipses? And does it make a difference if you are on the mount everest or on sea level?</p>

CC BY-SA 4.0
2019-01-19T12:50:24.260Z
About 600 million years.
PM 2Ring
CC BY-SA 4.0
2019-01-20T02:20:29.747Z
@PM2Ring is that back of the envelope or is there a source available? Since it matches the [posted answer](https://astronomy.stackexchange.com/a/29246/7982) nicely, it would be cool to know.
uhoh
CC BY-SA 4.0
2019-01-20T13:15:42.887Z
@uhoh That info comes from Richard Vondrak of NASA's GSFC. I found it at https://www.google.com.au/amp/s/amp.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html
PM 2Ring
CC BY-SA 4.0
2019-01-20T13:24:56.173Z
@PM2Ring thanks! btw I'm curious, what is google.com/amp/...?
uhoh
CC BY-SA 4.0
2019-01-20T13:32:16.410Z
@PM2Ring okay I see, thanks!  (https://www.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html)
uhoh
CC BY-SA 4.0
2019-01-23T10:00:02.757Z
**This is not a duplicate.** That whole thing is about the definition of transits, and the answer is 10 Tyr  or 1E+13 years. The answer her 8E+08 years, a factor of 10,000 longer. @PM2Ring has also independently mentioned 6E+08 years. That answer does not answer this question, not even close!
uhoh
CC BY-SA 4.0
2019-01-23T10:01:19.153Z
@CarlWitthoft these are very different questions. By closing, you send people to the wrong answer to this question.
uhoh
CC BY-SA 4.0
2019-01-23T15:03:59.737Z
@uhoh I think the questions are similar in principle. Grimaldi made a reasonable but arbitrary decision about what the angular diameter of the Moon needs to be so that its transit of the Sun doesn't qualify as an eclipse. But the 10 trillion years he calculates isn't really valid. The Sun will be a white dwarf *long* before then, and the Earth-Moon system will have suffered major disruption during the Sun's red giant phase, and will most likely get swallowed at some stage.
PM 2Ring
CC BY-SA 4.0
2019-01-23T15:06:03.760Z
@Carl If there's any dupe-closing to be done, I'm inclined to go in the other direction, closing coblr's old question as a dupe of this new one.
PM 2Ring
CC BY-SA 4.0
2019-03-15T17:20:19.777Z
You have an answer to this question here: https://www.skyandtelescope.com/astronomy-resources/astronomy-questions-answers/when-will-the-last-total-solar-eclipse-occur and here: https://www.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html.
User123
<the-moon><solar-eclipse>
When will the last total solar eclipse occur?
Luky
# When will the last total solar eclipse occur?

(Asked by: username_0 on 2019-01-19)

Because the moon distance from earth grows, how long will it take, that it is no longer possible to see a total eclipse but only circular eclipses? And does it make a difference if you are on the mount everest or on sea level?

**Tags:** the-moon, solar-eclipse
> **Comments:**
> **username_1**: About 600 million years.  
> **username_2**: @PM2Ring is that back of the envelope or is there a source available? Since it matches the [posted answer](https://astronomy.stackexchange.com/a/29246/7982) nicely, it would be cool to know.  
> **username_1**: @uhoh That info comes from Richard Vondrak of NASA's GSFC. I found it at https://www.google.com.au/amp/s/amp.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html  
> **username_2**: @PM2Ring thanks! btw I'm curious, what is google.com/amp/...?  
> **username_2**: @PM2Ring okay I see, thanks!  (https://www.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html)  
> **username_2**: **This is not a duplicate.** That whole thing is about the definition of transits, and the answer is 10 Tyr  or 1E+13 years. The answer her 8E+08 years, a factor of 10,000 longer. @PM2Ring has also independently mentioned 6E+08 years. That answer does not answer this question, not even close!  
> **username_2**: @CarlWitthoft these are very different questions. By closing, you send people to the wrong answer to this question.  
> **username_1**: @uhoh I think the questions are similar in principle. Grimaldi made a reasonable but arbitrary decision about what the angular diameter of the Moon needs to be so that its transit of the Sun doesn't qualify as an eclipse. But the 10 trillion years he calculates isn't really valid. The Sun will be a white dwarf *long* before then, and the Earth-Moon system will have suffered major disruption during the Sun's red giant phase, and will most likely get swallowed at some stage.  
> **username_1**: @Carl If there's any dupe-closing to be done, I'm inclined to go in the other direction, closing coblr's old question as a dupe of this new one.  
> **username_3**: You have an answer to this question here: https://www.skyandtelescope.com/astronomy-resources/astronomy-questions-answers/when-will-the-last-total-solar-eclipse-occur and here: https://www.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html.  

---

## 1 answers

### Answer by username_4 on 2019-01-19. Score: 9

I will take a stab at it.  Assuming 

the last eclipse happens when the moon is at perigee and the earth is at aphelion.
the moon's perigee is increasing by 4 cm per year,
the earth's aphelion does not change with time,
the sun and the moon are perfect spheres,
the radius of the sun and moon don't change, and
a total eclipse occurs when $r_{\mathrm{sun}}/d_{\mathrm{sun}} < r_{\mathrm{moon}}/d_{\mathrm{moon}}$ where $r$ is radius and $d$ is distance,

I get the following results:

The last total eclipse at sea level will occur in 721,587,917 years at sea
level  (obviously too many significant digits).
The last total eclipse at mount Everest will occur in 721,807,917 years.
The difference is 220,000 years = (height_of_Everest) * 25000 years/km.

Mathematica Source Code:
dSun = 152097000; rSun = 695508; dMoonNow = 357347; rMoon = 1737; 
rEarth = 6371; hEverest = 8 + 8/10;
sol2 = Solve[ rMoon/(d + t 4/100/1000) == rSun/(dSun - rEarth), t][[1]];
Print[ t /. sol2 /. d -> dMoonNow - rEarth  // Round];
Print[ t /. sol2 /. d -> dMoonNow - rEarth - hEverest // Round];

> **Comments:**
> **username_5**: Over that time scale and to that level of precision, will the Sun's diameter change as it evolves?  
> **username_4**: I think so!   (I added the assumption that it stays constant.)  
> **username_6**: The Sun will get larger by  2-3% on that timescale. So this answer would be an upper limit.  
> **username_6**: But since the apparent size of the Moon shrinks by 8% in the same time, I would guestimate that the overestimate of the time is only by about 25%.  
> **username_7**: There are several things wrong with this answer. (1) "The moon's perigee is increasing by 4 cm per year." That is the current rate, and it is abnormally high, thanks to the Americas, Afro-eurasia, both of which block equatorial tidal flow, and due to the shape of the North Atlantic, whose shape resonates with the M2 tide. A better figure is less than 2 cm per year. (2) "The earth's aphelion does not change with time." It most certainly does. The key reason we are not seeing an ice stage starting now is because the Earth's eccentricity is very low. (Continued)  
> **username_7**: (3) "The radius of the sun and moon don't change." The Sun's radius increases as it ages. When one takes all of these into consideration, the correct answer is somewhere between a few hundred million years to over two billion years.  
> **username_7**: @a_donda - No, it is not. A constant rate is ludicrous. Tidal friction suggests the recession rate falls extremely rapidly with distance. (Tidal heating of a moon is proportional to $r^{-15/2}$). This is in fact an argument used by young earth creationists. (Know thine enemy.) The problem with these YEC arguments is that the current lunar rate is known to be anomalously high. Tidal rhythmites show that the lunar recession rate was less than half the current rate half for almost all of the last 2.5 billion years. (Continued)  
> **username_7**: Why 2.5 billion years? It's hard to find rock that show signs of tides that are older than 2.5 billion years. This raises a question: Despite the current distance between the Earth and Moon being larger than it was in the past, why is the current lunar recession rate so large? The answer lies in the shape of the continents and the shape of the oceans, particularly the North Atlantic.  
> **username_7**: Projecting the current value of 4 cm/year (better: 3.8 cm/yr) forward is equally incorrect, for two reasons. One is that the recession rate should naturally drop as the Moon recedes, even if the North Atlantic holds its shape. A constant rate is inconsistent with physics. The other is that plate tectonics will eventually reshape the North Atlantic so that it is not nearly as good a damped resonator with regard to the M2 tidal constituent as it is now. The lunar recession rate will drop precipitously somewhere in the next 721 million years.  

---

