load 'd:\j602\user\mynewbob.ijs'
/////////////////////////////////////////////////////////////////////////////////////////
//K modeling of basic black body planetary temps .
/////////////////////////////////////////////////////////////////////////////////////////

+-----------------------------------------------------------------+
|The Stefan-Boltzmann law is a simple equation with a complicated |
|constant derived from fundamentals which states that the Power   |
|radiated by a body is its Emissivity times the Stefan-Boltzmann  |
|constant times its Temperature raised to the 4th power.          |
+-----------------------------------------------------------------+
+--------------------------------------------------------------------------------------+
|sb   =:  5.6704e_8            NB. Stefan-Boltzmann constant in  ( W % m ^ 2 ) % K ^ 4 |
+--------------------------------------------------------------------------------------+
+-----------------------------------------------------------------------------------+
|Psb  =:  verb : 'sb * T ^ 4 [ T =. y  NB. Stefan-Boltzmann Law . returns W % m ^ 2'|
+-----------------------------------------------------------------------------------+
+------------------------------------------------+
|R_Sun_    =:  6.96e8             NB. Sun radius |
+------------------------------------------------+
+------------------------------------------------+
|temp_Sun_ =:  5778               NB. deg Kelvin |
+------------------------------------------------+
+-----------------------------------------------------------------------------+
|'aphelion_Earth_ perihelion_Earth_' =: 1.52097701e11 1.47098074e11 NB. metres|
+-----------------------------------------------------------------------------+
+-----------------------------------------------------+
|Dist_Earth_ =: avg aphelion_Earth_, perihelion_Earth_|
+-----------------------------------------------------+
1.49598e11

+---------------------------------------------------------------------+
|apply Trd with R fixed to each of ap- , peri- , and mean distances . |
+---------------------------------------------------------------------+
+------------------------------------------------------------------------------------------------------+
|Trd =: verb : '%: R % D * 2 [ ''R D'' =. y' NB. Temperature ratio for disk of radius R at distance D .|
+------------------------------------------------------------------------------------------------------+
+-----------------------+
|Trd R_Sun_ ,Dist_Earth_|
+-----------------------+
0.0482311

+------------------------------------------------------------------------------+
|trd_Earth_ =: Trd"1 R_Sun_ ,. aphelion_Earth_, perihelion_Earth_, Dist_Earth_ |
+------------------------------------------------------------------------------+
0.0478331 0.0486392 0.0482311

+--------------------------------------+
|temp_Earth_ =: trd_Earth_ * temp_Sun_ |
+--------------------------------------+
276.38 281.037 278.679

+-----------------------------------------------------------------------------------------------------------+
|(%/ ; -/) 1 0 {temp_Earth_ NB. This > 1% diff between ap- and peri-helion temps should be easy to confirm .|
+-----------------------------------------------------------------------------------------------------------+
+-------+------+
|1.01685|4.6576|
+-------+------+

+-------------------------------------------+
|similarly calculated temperature for Venus |
+-------------------------------------------+
+-----------------------------------------------------------------------------------------+
|AU_Venus_   =:  0.72333                    NB. distance from sun as ratio of earth ( AU )|
+-----------------------------------------------------------------------------------------+
+-----------------------------------------------------------------------------+
|Dist_Venus_ =:  AU_Venus_ *  Dist_Earth_   NB. Venus orbital distance metres |
+-----------------------------------------------------------------------------+
1.08209e11

+---------------------------------------------------------------------------+
|trd_Venus_  =:  Trd  R_Sun_, Dist_Venus_   NB. Temperature ratio for Venus |
+---------------------------------------------------------------------------+
0.0567099

+--------------------------------------------------------------------------------------------------+
|temp_Venus_ =:  trd_Venus_ * temp_Sun_     NB. SB calculated temperature for object in Venus orbit|
+--------------------------------------------------------------------------------------------------+
327.67

//////////////////////////////////////////////////////////////////////////////////////////
//Sphere Partition 
/////////////////////////////////////////////////////////////////////////////////////////

+-------------------------------------------------------------+
|SAd  =: tacitvb : 'pi * %/ RD ^ 2 [ RD =.y ' NB. solid angle |
+-------------------------------------------------------------+
+----------------------------------------------------------------------------+
|SunSA_Earth_ =: SAd R_Sun_, Dist_Earth_  NB. agrees w @ Wikipedia/SolidAngle|
+----------------------------------------------------------------------------+
6.80013e_5

The celestial sphere is divided into the solid angle of the sun and the rest of night and
day as portions of the total pi4 steradians .

+---------------------------------------------------------------------------------+
|SfP =: tacitvb : '|pi4%~( SunSA - 0, pi2), pi2 [ SunSA =. y' NB. Sphere partition|
+---------------------------------------------------------------------------------+
+-------------------------------------+
|SfeerPart_Earth_ =: SfP SunSA_Earth_ |
+-------------------------------------+
5.41137e_6 0.499995 0.5

//////////////////////////////////////////////////////////////
//Other than the disk of the sun , the celestial sphere presents the approximately 3 degree K 
//microwave background radiation . We'll include it altho taken to the 4th power it ends up 
//being quite negligible .
//////////////////////////////////////////////////////////////

+-----------------------------------------------+
|CMB =: 3.0  NB. 3K  Cosmic Microwave Background|
+-----------------------------------------------+
+---------------------------------------------------------------------+
|Tcs =: temp_Sun_ , 2 # CMB   NB. Temperature of each sphere partition|
+---------------------------------------------------------------------+
5778 3 3

//////////////////////////////////////////////////////////////
//Finally ,  there is the absorptivity/emissivity , the grayness , of each sphere partition . 
//We will look at several cases starting with all black .
//////////////////////////////////////////////////////////////

//////////////////////////////////////////////////////////////
//Total radiated power from shaded gray ball
//////////////////////////////////////////////////////////////
 Multiplying the "grayness" , portion of the sphere , and power for the celestial
sphere and "earth" at 279K give the following numbers for each part of the sky .

+-----------------------------------------------------------------------+
|r =: flip > tacitvb : ' AE * SfeerPart_Earth_ * Psb y ' each  Tcs ; 279|
+-----------------------------------------------------------------------+
   342.004 0.00185925
2.29649e_6    171.789
2.29651e_6    171.791

Summing across each sphere partition :

+-------------------------------------------------------+
| ,.r ; +/ r   NB. Summing across each sphere partition |
+-------------------------------------------------------+
+---------------------+
|   342.004 0.00185925|
|2.29649e_6    171.789|
|2.29651e_6    171.791|
+---------------------+
|342.004 343.582      |
+---------------------+

+---------------------------------------------------------------------------------------+
|Newton =: adverb : 'y - (u % u D. 1) y' NB. find zero of verb u (y) by Newton iteration|
+---------------------------------------------------------------------------------------+

+------------------------------------------------------------------------------+
|Tgen  NB. verb to solve temperature given AE, temperature array, SunSolidAngle|
+------------------------------------------------------------------------------+
+---------------------------------------------------------------------------------+
|'AE Tcs SunSA' =. 3{.y, <SunSA_Earth_  NB. default Solid Angle to Earth orbit    |
| PgrayBall =: (AE; SunSA) & (tacitvb : '+/AE * (SfP SA) * Psb y [''AE SA'' =. x')|
| Tdif      =: Tcs& (tacitvb : ' -/ PgrayBall every x ; y  ')                     |
| (Tdif Newton)^:_ (300)                  NB. converges ok starting from 300      |
+---------------------------------------------------------------------------------+
+---------------+
|Tgen 1 1 1; Tcs|
+---------------+
278.679

+---------------------------------------------------------------------------------+
|Tgen 1 1 1; 3#temp_Sun_ NB.  A point totally surround by a uniform temperature . |
+---------------------------------------------------------------------------------+
5778

+----------------------------------------------------------------+
|Tgen 1 1 0; 3#temp_Sun_ NB. Makes no difference how it's shaded |
+----------------------------------------------------------------+
5778

 //////////////////////////////////////////////////////////////
 A disk in earth orbit , black on the day side , totally reflective and non emissive
 on the night side . This is the maximum any object in the orbit can get .
 //////////////////////////////////////////////////////////////

+---------------------------------+
| Tgen 1 1 0; temp_Sun_ , 2 # CMB |
+---------------------------------+
331.407

//////////////////////////////////////////////////////////////
//And finally , a maximally hot body in Venus orbit :
//////////////////////////////////////////////////////////////

producing a sphere partition 

+--------------------------------------------------------------------------------------+
|SunSA_Venus_     =: SAd R_Sun_ , Dist_Venus_    NB. Solid angle of sun seen from Venus|
+--------------------------------------------------------------------------------------+
0.00012997

+----------------------------------------------------------------------------------------+
|SfeerPart_Venus_ =: SfP SunSA_Venus_            NB. not needed explicitly in the next...|
+----------------------------------------------------------------------------------------+
1.03427e_5 0.49999 0.5

+------------------------------------------------------------------------------------+
|Tgen 1 1 0; (temp_Sun_ , 2 # CMB); SunSA_Venus_ NB. black day side reflective night |
+------------------------------------------------------------------------------------+
389.667

+---------+----+
|Sun      |    |
+---------+----+
|R        |temp|
+---------+----+
|696000000|5778|
+---------+----+
+----------+----------+----------+----------+----------+-------+---------+
|Earth     |          |          |          |          |       |         |
+----------+----------+----------+----------+----------+-------+---------+
|Dist      |SfeerPart |SunSA     |aphelion  |perihelion|temp   |trd      |
+----------+----------+----------+----------+----------+-------+---------+
|1.49598e11|5.41137e_6|6.80013e_5|1.52098e11|1.47098e11| 276.38|0.0478331|
|          |  0.499995|          |          |          |281.037|0.0486392|
|          |       0.5|          |          |          |278.679|0.0482311|
+----------+----------+----------+----------+----------+-------+---------+
+-------+----------+----------+----------+------+---------+
|Venus  |          |          |          |      |         |
+-------+----------+----------+----------+------+---------+
|AU     |Dist      |SfeerPart |SunSA     |temp  |trd      |
+-------+----------+----------+----------+------+---------+
|0.72333|1.08209e11|1.03427e_5|0.00012997|327.67|0.0567099|
|       |          |   0.49999|          |      |         |
|       |          |       0.5|          |      |         |
+-------+----------+----------+----------+------+---------+