There are a lot of different topics this weeks but first we need to alert, all of you SpaceX Starlink satellite launch followers, that the next scheduled launch from KSC is now on for Monday, January 6 a 9:19 pm. So get out and follow the satellites and get some photos of the string of pearls. You can check in with www.heavens-above.com website for viewing details in your area.
Anyway, back to other activity, this image of "a sun dog" was taken, where the "x" marks the spot, with just iPhone. It's just at 7:05 AM in the morning and the sun is just barely about 5 degrees above the horizon, but it sure looks like another sun higher up in the sky. Hmm, sun dogs are usually described as being horizontal to the real sun, but what else is this but a vertical sun dog?
|Is this iPhone image at 7:05 AM of a "vertical sun dog"? (Source: Palmia Observatory)|
We know that most descriptions of sun dogs are shown as they usually appear in the horizontal direction. The Wikipedia screenshot below shows the typical scenario where the sun dog appears on the 22 degree cone surrounding the real sun. Why can't the ice crystals be high in the sky and create a vertical sun dog too?
|Example showing how refraction causes sun dogs (Source: Wikipedia)|
Ok, last post we mentioned how there has been a lot of current interest in Betelgeuse and how it seems to be particularly dim right now. We know that Betelgeuse is a variable star, so it doesn't seem to indicate much although we know that as a massive, 10 times the mass of the Sun, it is bound to eventually blow up as a supernova. You can check out the evolutionary path of a star from the main sequence in the screenshot from atnf.csiro.au, below.
|Evolutionary track of stars as they move off the main sequence (Source: www.atnf.csiro.au)|
So, large massive stars, like Betelgeuse, will blow up as supernovas, but what about smaller stars like our sun. You can trace the sun's evolutionary path in the diagram above, but it just seems to end up in the Asymptotic Giant Branch (AGB) area of the diagram. But what happens after that? We know that the sun is not massive enough to end as a supernova and instead ends up as a white dwarf. The screenshot below from the U. of Oregon shows the trajectory to the region where white dwarfs hang out.
|Evolutionary track from main sequence to white dwarfs (Source: www.abyss.uoregon.edu)|
Next up, we received a note from Science Nerd and Theatre Impresario, Scott, who wondered about a post on the AIAA public forum describing a low cost global warming mitigation scheme using large mirrors to reflect more of the incoming solar radiation before it can heat up the Earth. The post by did some calculations that ended with a potential geoengineering solution to global warming that said that using low cost mirrors, say at 1 penny per square meter, could mitigate global warming at a cost of about $10 billion. Hmm, that sounded a little to good to be true, even though geoengineering solutions might prove to be part of the mitigation mixture.
I was skeptical, not of the science, but of the estimate, because of the magnitude of energy that is trapped by greenhouse gases in the atmosphere. Remember that the temperature of the Earth, or any planet for that matter, is just a heat balance, were if the energy coming in does not equal the energy going out, then the temperature of the planet will change. Rather than trying to calculate this whole amount of energy flows, lets use some high level models and do some back of the envelope calculations to see that the actual answer might be.
Check out the screenshot below which summarizes all the incoming energy and the outgoing energy. Some of the incoming solar radiation is reflected and some is absorbed. Some of the blackbody radiation, generated by the actual ground and air temperature, is reflected back into space. If all of the blackbody radiation were reflected back into space the temperature would not change, but we see that currently about 5% of the incoming solar radiation is trapped in the atmosphere and this results in global warming.
|Amount of heat trapping by greenhouse gases (Source: www.earthobservatory.nasa.gov)|
Now we all rely on some greenhouse warming because without some of that resulting from background CO2, we would live on a much colder planet. Check out the screenshot below, which shows the amount of CO2 in the atmosphere over the past 800,000 years. So, for a stable temperature we would like to see something like 300 ppm CO2, but now the amount of CO2 has been increasing due to burning fossil fuels and other land use sources and now passes 407 ppm.
|CO2 Levels over 800,000 years (Source: www.climate.gov)|
So, now we can do our own back of the envelope calculation about how many mirrors would be required to offset global warming effects. We need the following data points:
Luminosity of the sun = 3.828 x 10 to the 26th watts
Distance to sun = 149 x 10 to the 6th km
Radius of Earth = 6378 km
CO2 in the atmosphere = 890 x 10 to the 9th tons
Now we can calculate the power density at the Earth, using inverse square law,
is 1370 watts per square meter.
The amount of total energy hitting the Earth is then just the area of a circle the same size as the Earth. Normally we would have calculated the surface area of the Earth, but the Sun only shines on half of it at a time and another factor of 1/2 is involved because the Earth's surface is not all perpendicular to the incoming flux from the sun. So,
Solar incoming flux on the Earth is 1.75 x 10 to the 17th watts
Now 5% of all of this incoming radiation is absorbed an trapped by the CO2 in the atmosphere, so
the excess trapped power is 8.75 x 10 to the 15th. This is the amount of incoming power that exceeds the balance and causes the temperature to increase and it is also the amount of energy that would have to be reflected by use of mirrors. So, right away we see this is a huge area of reflecting mirrors, something like 5% of the Earth's surface. This does not seem very practical, but maybe!
I also wanted to check and see how much area of mirrors I would need as an individual to offset my own individual carbon footprint. For people in the industrialized parts of the world, we have a carbon footprint of about 20 metric tons per year, for a global per capita average of about 4 tons per year.
Now assuming that the amount of trapped heat is proportional to the amount of CO2, we can see that my annual portion is just 4 tons divided by 890 gigatons or = 2.25 x 10 to the minus 11th. So to reflect back into space enough energy to account for the amount due to CO2 trapping based on my CO2 contribution, we see that I would need (2.25 x 10 to the -11) x (8.75 x 10 to the 15th) divided by 1370, which is equal to 143 square meters of mirrors per year. This estimate would also have to be doubled because the mirrors would only be effective during the daytime.
Hmm, we might not even be able to do that for one year little alone for every year after that.
Ok, that is enough tiring math work, let's look at a couple of interesting articles that caught my tired eye in New Scientist magazine. First up, is an interesting article about the tremendous fuel advantage of using lighter than air flying ships. We know of current balloons that use hot air and blimps that use helium, instead of the lighter but more flammable hydrogen. Well, the availability of helium is getting scare and expensive and might not be that available anymore, but since all blimps work on the principle of displacing the volume of air with a gas that is lighter than air, you can't get any higher buoyant force than that from a volume of vacuum.
Philip Ball describes some of the up and coming ideas in this approach, apparently first considered back in 1670. The issue is making a container that is strong enough not to collapse with vacuum inside and not be so heavy as to outweigh the buoyant force. The article talks about various approaches being considered with new lightweight but very strong fabrics and also of maybe using hot air to launch from the ground and then pumping the air out only at higher elevations where the pressure across the containers will be much less. Hmm, that whole topic is pretty interesting and if materials can be found to make it work, it will be a great way of air travel that uses less carbon based fuels!
|Flying on (vacuum) empty (Source: Philip Ball, New Scientist, 21 Dec 2019)|
The second article that caught my eye, probably when I was getting thirsty, is this one by Sam Wong, who describes putting the old beer can trick where by tapping on the can, before you open the pull tab, can reduce the amount of gas bubbles that ultimately cause a lot of the beer to flow out over the table and not into your mouth. Yep, that is a problem, not that I drink much beer, at least not from cans. But the issue is, does this old often told trick actually work? It seems that once it is put to the scientific test, it is found that tapping the can does not make any significant difference in spilled beer. At least the opened cans of beer were shared with the university students and not wasted. Now there is a an experiment that I would sign up to help out in. Especially if they were investigating if slowly opening the champagne, with a "pop" or not resulted in less of the liquid spilling out onto the table!
|Beer can trick put to scientific test (Source: Sam Wong, New Scientist, 21 Dec 2019)|
Until next time,