The amount of energy coming from the sun to the top of the atmosphere is 1364 w/m² = 393.8 kelvin or 120°C, and not 340 w/m² = 278 kelvin or 4.85°C.

 

Author; Rogelio Perez C

Abstract

The amount of energy coming from the sun to the earth is measured by the solar constant. Which has a value of 1364 w/m², this energy is the value of radiation emission from the sun for the area of a sphere 4πr², at the distance of an area of a sphere 4πr² from an astronomical unit, as the earth only receives sunlight the area of a circle πr², then 4 parts of that energy are not reaching the earth, then the value of the constant is divided by four (1364 w/m²/4), therefore the amount of energy at the top of the atmosphere is approximately 340 w/m², which is equivalent to a temperature of 278 kelvin or 4.85°C, but this work shows that the value of the solar constant does not change when we measure the energy emitted by the sun, in an area of the solar circle (πr²), between the value of the area of a circle (πr²), of an astronomical unit. That is the area that looks at the earth, so the amount of energy entering the earth is the value of the solar constant of 1364 w/m², which is equivalent to 393.8 kelvin or 120°C, and not the 340 w/m² which is equivalent to 278 kelvin or 4.85°C and the evidence is that astronauts on the space station which is located approximately in the high atmosphere when they look at the sun the measured temperature is approximately 120°C.

Introduction

The greenhouse effect theory teaches that the amount of energy entering the earth is 340 w/m² = 278 kelvin or 4.85°C, that after subtracting the albedo, the amount of energy absorbed by the earth is 240 w/m²= 255 kelvin or -18°C, but thanks to the greenhouse effect the average temperature of the earth is 15°C.

According to this work the amount of energy entering the earth is 1364 w/m² = 393.8 kelvin or 120°C, and after subtracting the albedo which is approximately 30%, then the amount of energy absorbed by the earth is 954.8 w/m² = 360.23 kelvin or 87°C.

To know the value of the energy entering the planet, we must know the solar constant that has a value of 1364 w / m² which is equivalent to 393.8 kelvin or 120 ° C, but as the part of the energy that enters the planet is in the area of a circle (πr²), and the solar constant is the energy value for the area of the sphere (4πr²) of the Sun, then the value of the solar constant has to be divided into 4 parts, because the value of the sun's energy in its circle (πr²) is a quarter of its sphere. But this work shows that the energy of the solar constant is the same when we take the area of the solar sphere, than when we take the area of the solar circle, so the solar constant should not be divided into 4 parts to know the value of the energy of the sun entering the earth at a distance of one astronomical unit.

Theory;

The solar constant, SO, is the total amount of solar radiation (including all wavelengths of the solar spectrum) per unit of area that affects in a plane normal to the direction of the solar rays on the outside of the earth's atmosphere at the average distance between the sun and tierra.1

The average annual solar radiation reaching the upper part of the Earth's atmosphere (1364W/m²) represents the power per unit of solar irradiation area through the spherical surface surrounding the sun with a radius equal to the distance to Earth (1 AU).

This means that the Earth's approximately circular disk, as seen from the sun, receives approximately stable 1361W/m² at all times. The area of this circular disk is πr², in which r is the radius of the Earth. Because the Earth is approximately spherical, it has a total area of 4πr² which means that solar radiation reaching the top of the atmosphere,, averaged over the entire surface of the Earth, is simply divided by four to obtain 340 W/m².2

Albedo is the measure of the diffuse reflection of solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body that reflects all incident radiation.3.

The greenhouse effect theory teaches that the amount of energy entering the earth is 340 w/m² = 278 kelvin or 4.85°C, that after subtracting the albedo, the amount of energy absorbed by the earth is 240 w/m²= 255 kelvin or -18°C, but thanks to the greenhouse effect the average temperature of the earth is 15°C.4

 

Development;

What is the value of the solar constant for the area of a sphere 4πr²?

The radiant energy that reaches us from the sun will decrease inversely to the area formed by a sphere of radius of 1 U.A., that is:

An astronomical unit =1.496E 11M

Astronomical unit in M²=

m²=1.496E 11M x 1.496E 11M= 2,238022E 22m²

Astronomical unit for the radius of a sphere;

=2,23802E+22m² x  4π 3,14 =2,23802E+22m² x π 12.56=

=2,81095E+23.

 

Total energy from the sun by the area of a sphere 4πr²;

Formula; E = σ * A * T⁴

E = sun-radiated heat (Luminosity).

Σ= Stefan-Boltzmann constant.

A =Area of a body (Sun)

T⁴=Temperature raised to 4 power.

 

Result;

σ =    5,67E-08   W/(M²K4)

A=     6,06679E+18     m²

T⁴=   1,11458E+15     Kelvin4

E =    3,834E+26         Wm²

An area 6.066C10 18m² with a temperature of 5778°k at the fourth power, multiplied by the Stefan-Boltzmann constant, has an energy of 3.834E 26wm²

Then;

The value of the solar constant= to the energy emitted by the sun in the area 4πr² of a sphere= 3.834E 26w/m², between the astronomical unit in the area of a sphere 4πr²=2, 81095E+23m²

3.834E 26w/m² /2, 81095E+23 = 1363.953709w

The value of the solar constant is equal to 1364wm²

 

What is the solar constant value for the area of a circular disc πr²?

An astronomical unit =1.496E 11M

Astronomical unit in M²=

m²=1.496E 11M x 1.496E 11M= 2,238022E 22m²

Astronomical unit for the radius of a circle πr²;

=2,238022E 22m² x π 3.14 = 7,027E 22m²

Energy emitted by the sun for the area of a circle πr².

Formula; E = σ * A * T⁴

E = sun-radiated heat (Luminosity).

Σ= Stefan-Boltzmann constant.

A =Area of a body (Sun)

T⁴=Temperature raised to 4 power.

 

Result;

σ =    5,67E-08   W/(M²K4)

A=     1,5167E+18m²,  m²

T⁴=   1,11458E+15     Kelvin4

E =    9,58501E+25 wm²,

An area 1,5167E+18m², with a temperature of 5778°k at the fourth power, multiplied by the Stefan-Boltzmann constant, has an energy of 9,58501E+25 wm², 

Then;

The value of the solar constant= to the energy emitted by the sun in the area of a circle (πr²).= 9,58501E+25 wm², between the astronomical unit in the area of a circle (πr²).= 7,027E 22m²

9,58501E+25 wm²/ 7,027E 22m² = 1363.953709w

Value of the solar constant for the circle (πr²) of the sun is equal to 1364wm².

 

Mathematical formula for knowing the kelvin degrees of energy in watts

To find out how many kelvin degrees are equivalent to all these energy values in watts, which are related to the temperature of the Sun and the planet, I use the following mathematical formula from Stefan-Boltzmann's law;

E= A* σ * T⁴

A* σ * T⁴=E

σ * T⁴=E /A

T⁴= E /A* σ

T=⁴√E/A σ

Where;

E = heat radiated by the one body (Luminosity).

σ = Stefan-Boltzmann constant.

A =Area of a body

T⁴=Temperature raised to 4 power.

Conversion of watts to kelvin:

Kelvin value of the solar constant

σ =    5,67E-08   W/(M²K⁴)

A=     1     m²

E = 1364 W

Results.

T=⁴√E/A σ

Te=⁴√1364 W= / 1 m²*5,67E-08 W/(M²K⁴)

Te=⁴√1364 W / 5,67E-08 W/K⁴)

Te=⁴√24056437390 k⁴ = 393.83 kelvin. or 120°C.

Conclusion;

The solar constant for the Earth is equal to the energy emitted by the sun for a radius of a sphere, than for the radius of a circle, so the temperature that reaches us from the sun to the top of the atmosphere, should not be divided by 4, since the Solar constant does not change the energy value.

According to this work the amount of energy entering the earth is 1364 w/m² = 393.8 kelvin or 120°C, and after subtracting the albedo which is approximately 30%, then the amount of energy absorbed by the earth is 954.8 w/m² = 360.23 kelvin or 87°C.

Bibliography;

1-      file:///C:/Users/MASTER/Desktop/radiacion.pdf

 

2-      Stickler, Greg. "Educational Brief - Solar Radiation and the Earth System". National Aeronautics and Space Administration. Archived from the original on 25 April 2016. Retrieved 5 May 2016.

 

 

3-      "Thermodynamics | Thermodynamics: Albedo | National Snow and Ice Data Center". nsidc.org. Retrieved 14 August 2016.

 

4-         https://www.acs.org/content/acs/en/climatescience/climatesciencenarratives/what-is-the-greenhouse-effect.html