Amber G. wrote:
Sudarshanji - Just some quick comments.. , I still found a few things just a little odd in your explanations
- at least some things are not made clear (at least to me it seems that way) and can be misunderstood. But I will not interrupt and side-track you. I will just make one point -- just so that the basic physics is clear(er)...
1- Wrt to albedo(a) and emissivity(e) [.. can be ignored? ].. strictly speaking, of course *not*. A planet surrounded by mirrors will have different temperature than one without mirrors.
(Even in first year physics problems people routinely gives value of (a) and (e) for planets and ask students to calculate steady-state temperature - the calculation is not hard.
I can try and make things clearer. I suggest, though, that we move away from this notion of "albedo," which is a subjective measure of a planet's brightness. This albedo is simply the total reflectivity that I talked about earlier (with the caveat that the albedo is averaged over the visible part of the spectrum, not the entire spectrum), which depends on the spectral distribution of the incident radiation (except when the object is a gray body). The albedo is subjective because it is a measure of how bright the planet will appear to human eyes, so it is the weighted reflectivity over the visible and maybe UV parts of the solar spectrum. Why is it subjective, because different people may have different spectral ranges that they are sensitive to, and also, different eyes may be more sensitive to different colors - for example, some eyes may perceive red as brighter, others might see green or blue as brighter - but even without this, the spectral distribution of energy in sunlight is not necessarily the same as the sensitivity curve of the human eye to various parts of the spectrum.
These first year physics problems you talk about - you can try the calculations yourself, so long as 1-albedo
(or actually, 1 - (total reflectivity)
- albedo is not quite the same thing) is the same as the total emissivity
of the planet, the planet's temperature will always come out to be the same. 1-R
will be identically equal to E
for a gray planet, without an atmosphere, which, further, does not transmit any radiation. But 1-R can also be equal to E for non-gray planets in certain situations.
However, if you set up your problem in such a way that 1-albedo is not the same as the emissivity, then you've already moved away from the "gray body" assumption. Then you get into the kind of behavior exhibited by the polar-bear fur, which I talked about earlier.
As for your statement that a planet surrounded by mirrors will have a different temperature than a planet without these mirrors - nope, not necessarily. I will elaborate further, this will need pictures to make clear.
( Should be emphasized more clearly the (a) and (e) can, and do, depend on the wave-length...As we know inside of a closed car (window glass does NOT reflect but let the light go in.. for IR the glass is not transparent) things get hot.)
Yes, this is the greenhouse effect. I'll try and make things as clear as I can
BTW, an old formula, I remember from my young days, involving holy number 108 (this is the angular diameter of Sun from earth see note below) is all you need to get into right ball park for average temperature of an airless rocky planet. Just take square root of this and multiply by 2, you get about 20.
Just divide Sun's temperature (~6000K) by 20 and you get ~300 K almost right!
.. around the right ball park.
(This happens to be true for any Sun/Planet system - just divide Sun's temperature (surface) by 2 and divide it again by square root of holy number for the planet -- Sun's angular diameter as seen from the planet)
Note: for 108, for example see https://forums.bharat-rakshak.com/viewtopic.php?p=1443569#p1443569
Yajnavalka talked about 108 times of sun diameter as the distance between Sun and Earth which is very close to modern calculations.
Several issues here. First, 300K is the temperature of the earth with its atmosphere, and with the heat generation that you talked about.
Like I said, the moon, which is thought to be geologically dead (which means no internal heat generation), and which has no atmosphere, has a peak temperature due to solar radiation more like 400K (385K, to be precise).
Secondly, the square-root dependence on diameter to distance
of the planet's temperature is not at all surprising, since the heat flux reduces as the square of the distance to diameter, while the temperature goes with a fourth power dependence. In fact, you take f=distance of planet to sun's radius,
which is twice the value of distance to diameter.
You divide the sun's temperature by the square-root of this factor f
. You will get the maximum temperature of a gray planet with no atmosphere, which is directly exposed to radiation from this sun.