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Does a solar eclipse have an impact on global temperature?

Wired theory :

When I jump, does the Earth recoil? Yes, the Earth has to move in some way for momentum to be conserved. However, since the mass of the Earth is 1023 times the mass of me, its recoil velocity would just be 10-23 times my velocity. Even if I jumped with a speed of 10 m/s, the Earth’s recoil speed would be unmeasurably small.

If you said the Earth doesn’t really recoil when I jump—you could be correct, from a certain point of view. You could also say that the Earth theoretically recoils, but you can’t measure it. So, this is my first answer to the solar eclipse question. Yes, there is less energy hitting the Earth, so it wouldn’t be as hot.

Normal day :

As per wikepedia :

The Sun produces electromagnetic radiation that carries energy. At the distance of the Earth, the solar intensity is about 1,000 Watts per square meter. If we assume all of this light is absorbed by the Earth over a 24 hour period, we can get the solar energy in one day (of course, not all the light is absorbed, but this is a good place to start). In order to calculate this energy, I will need the cross sectional area of the Earth—which would be a circle with the same radius as the Earth (6.37 x 106 m). Even though different parts of the Sun get light, I can still calculate the total energy over that day.

For instance :

enter image description here

Eventhough the sunlight is not for 24 hours the above picture was an approximate stuff

Now for the total energy on a day with a solar eclipse. This will be the exact same energy as before, except for the part of the Sun’s light that is blocked by moon. So, there are two things—how much sunlight is blocked and for how long.

Since the Sun isn’t a point light source, from different parts of the Earth’s surface you might get a partial eclipse. In these locations, you would still get some solar energy—but just not as much. Of course, you could find the total area of the partial shadow and do a surface integral to find the total amount of light blocked—but there’s no point. Instead, let’s look at the moon. Any shadow on the surface of the Earth is due to the cross sectional area of the moon. Who cares if a location is partially or fully blocked—it’s all about the moon.

Now what about the time? An eclipse doesn’t last all day. The total time it takes the shadow to pass the Earth varies,for instance consider this eclipse which will last for 4.5 hour

if we calculate the amount of blocked sunlight energy.

enter image description here

That’s about 1 percent of the energy on a normal day. So, an eclipse day would get 99 percent the normal energy. Is that significant?

based on the above facts Does a solar eclipse have impact on global temperature?If yes,is this undetectable change?

Image & question credits : Wired

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    $\begingroup$ You could reach the 99% by simply saying "The Sun shines for half a day per day. A Solar eclipse lasts roughly 7 minutes. That's 1% of half a day." $\endgroup$ – pela Mar 9 '16 at 12:28
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    $\begingroup$ @pela that's a slightly different calculation - the flux at a point in the path of the solar eclipse, rather than the average over the whole earth. And it ignores the several hours partial eclipse either side of totality, which average 50% illuminance. $\endgroup$ – PhillS Mar 9 '16 at 13:31
  • $\begingroup$ @PhillS: Yes, you're right. I forgot that the shadow is much smaller than the cross section of Earth. My bad. $\endgroup$ – pela Mar 9 '16 at 13:48
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That estimate seems reasonable to me.Then the question is how much that affects temperature.

Lets ignore the contribution to the earth's temperature from nuclear decay and tidal friction, and work out the case where it is purely a balance between the earth's radiative cooling and the sun's radiative heating. Without worrying about the details we can say that the earth is initially at temperature $T_0$.

In the case that the sun's output drops by $1\%$ permanently, the temperature of the earth will drop to $T$. Since the power radiated by the earth is $\propto T^4$ then $\left(\frac{T}{T_0}\right)^{4}=0.99$, so $T\approx T_{0}*(0.99)^{0.25}$.

With $T_0\approx 280K$ as a ballpark figure, then T$\approx 279.3K$, a drop of $0.7K$.

That is the long term equilibrium if the sun's output dropped by the equivalent of a solar eclipse (using the estimate in the question). Over a period of a few hours, the effect is going to be much smaller. I think any effect is going to be much smaller than normal variations in temperature and be basically unnoticeable.

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