A Pale Blue Dot from across Interstellar Space

[lpetrich]

The Earth is well-known for looking like a pale blue dot across interplanetary space, and it would look like that over interstellar space also. But how blue is the Earth?

Simulations of Light Curves from Earth-like Exoplanets - Planetary Habitability Laboratory @ UPR Arecibo shows some simulations of the Earth's appearance from above its equator at the equinoxes, simulations for full Earth and half Earth.

The Earth is indeed bluish most of the time, but when Eurasia and Africa are at or near the view center, the Earth becomes grayish, because it is then much brighter in the red and the green. For the full Earth, the peak is when Arabia is closest to the view center, while for the crescent Earth, the peak is when Africa is, with a nearby peak for India, and a lesser peak for the Americas.

The Earth will have variations due to cloud variation, but the authors did not show off any calculations of those variations there. Given how the Earth always has some clouds, that variation may be relatively small.

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The authors also did a simulation of the Earth's appearance during the Cambrian Period. Back then, the Earth was bluish, and grayish when Gondwana is at or near the view center. There is very little overall difference from the present-day Earth. That means that the Earth's vegetation will not show up very well. That's likely because the more vegetated areas are relatively dark and often clouded over. The most reflective and least cloudy land areas are deserts.

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The authors also simulated Mars, and it also has brightness variations. However, it is orange all the time.

Mercury is grayish, with not much variation in brightness. The authors did not show simulations of the Moon, but it likely is grayish with more brightness variation.

Venus is yellowish, and it shows almost no variation. The authors state that that is typical of planets with thick atmospheres.

So if one finds that a planet of another star has very noticeable periodic brightness variation, one may conclude that it has lots of geological activity, or else that it has had a lot of geological activity in its past. The Moon and Mars both have abundant relics of earlier geological activity, despite having little or no recent such activity.

 

[lpetrich]

The Earth's past is an underappreciated resource for exoplanet comparisons, IMO. Fortunately, the people at the Planetary Habitability Laboratory have decided to fill that gap (Visible Paleo-Earth - Planetary Habitability Laboratory @ UPR Arecibo).

Analysis of the Distribution of Land and Oceans - Planetary Habitability Laboratory @ UPR Arecibo shows estimates of how much land and ocean area there were for the last 750 million years (late Proterozoic). The continents have moved around quite a bit over that time. They formed two supercontinents over that time, Rodinia about 750 million years ago, and Pangaea 240 million years ago. In between, the continents were more fragmented. Also, while about 2/3 of the continent area is now in the Northern Hemisphere, over the most of the Paleozoic and before it, most of the continent area was in the Southern Hemisphere.

I'm half-thinking of taking some reconstruction maps and quantifying how much of a spread the continents had had. I'd do that by taking position vectors n of the land and finding N(i,j) = <n(i)*n(j)>. I'd then take "eigenvalues" of matrix N, roughly fitting to an ellipsoid and then finding out how long the ellipsoid's axes are. I'd get (1,0,0) for only one small spot of land and (1,1,1)/sqrt(3) for evenly-distributed land. I'd also get the centroid of the land area as the direction of the longest axis.


Habitability of the Paleo-Earth as a Model for Earth-like Exoplanets - Planetary Habitability Laboratory @ UPR Arecibo lists some results for:

• Solar luminosity
• Spin-axis obliquity
• Day length
• Temperature
• Atmospheric carbon-dioxide fraction
• Atmospheric oxygen fraction
• Atmospheric pressure
• Atmospheric relative humidity
• Atmospheric water-vapor fraction
• Their Relative Vegetation Density (RVD) and Standard Primary Habitability (SPH) estimates

The RVD is by surface area, while the SPH is estimated from the temperature and relative humidity. Standard Primary Habitability (SPH) - Planetary Habitability Laboratory @ UPR Arecibo shows how it varies over the year on our planet -- the SPH is much higher in the summer than in the winter for the northern temperate regions.

Vegetation, Ice and Deserts of the Paleo-Earth - Planetary Habitability Laboratory @ UPR Arecibo has graphs of the land fractions of all three over the last 750 million years. The upward curve of the vegetation fraction in the Cambrian and Ordovician (540 - 440 mya) is due to the emergence of multicellular land plants, rather than to any climate effect.

Looking at those curves, there is a remarkable trend. Over most of the Phanerozoic (Paleozoic, Mesozoic, Cenozoic), the Earth was warmer, wetter, and more vegetated or vegetation-capable than it was today. The main exception was near the Carboniferous-Permian boundary, about 300 million years ago. Also much like the present, it was a time of Ice Ages, large continental glaciers.

So according to the SPH's habitability indices, the Earth was more habitable over most of the Phanerozoic than it was today, with the exception of near the Carboniferous-Permian boundary.

 

[lpetrich]

Updating this thread to say that I've completed a Mathematica notebook that calculates simulated light curves.

My results for the Earth and Mars broadly agree with the PHL's, and I've also done the Moon and Jupiter.

Our homeworld from a great distance does indeed look like a pale blue dot, but the Sahara Desert is big enough, light enough, and yellow enough to make our planet look neutral-colored when it is in view.


If there is any simple message to get from these simulations, it is that one can tell over interstellar distances if a celestial body has lots of geological activity, at least if it makes big enough asymmetries. Asymmetries like the Sahara Desert, the Moon's near-side lava plains, and Mars's Tharsis Plateau with its big volcanoes.

But Mercury has much less asymmetry, and Venus, Jupiter, and the other clouded-over planets are close to axially symmetric. So they have relatively flat light curves.