### Rotating Planet Spherical Surface Solar Irradiation Absorbing-Emitting Universal Law

**Planet Energy Budget: **

**Solar energy absorbed by a Hemisphere with radius "r" after reflection and dispersion: **

**Jabs = Φ*πr²S (1-a) (W) **

**What we have now is the following:**

** Jsw.incoming - Jsw.reflected = Jsw.absorbed **

**Here**

**Jsw.reflected = 0,53 * a * Jsw.incoming **

**And**

**Jsw.absorbed = Φ* (1-a) * Jsw.incoming**

**Where Φ = (1-0,53) = 0,47 Φ = 0,47 **

**Φ is the planet's spherical surface solar irradiation accepting factor. Conclusion: The planet's absorbed fraction of the SW incoming radiation in total is:**

** Jsw.absorbed = 0,47 * (1-a) * Jsw.incoming **

**Total energy emitted to space from entire planet: **

**Jemit = A*σΤe⁴ /(β*N*cp)¹∕ ⁴ (W)**

**Α - is the planet's surface (m²) **

**(β*N*cp)¹∕ ⁴ - dimensionless, is a Rotating Planet Surface Solar Irradiation Warming Ability**

**A = 4πr² (m²), where r – is the planet's radius **

**Jemit = 4πr²σTe⁴ /(β*N*cp)¹∕ ⁴ (W)**

**global Jabs = global Jemit**

**Φ*πr²S (1-a) = 4πr²σTe⁴ /(β*N*cp)¹∕ ⁴ **

**Or after eliminating πr²**

**Φ*S*(1-a) = 4σTe⁴ /(β*N*cp)¹∕ ⁴ **

**The planet average Jabs = Jemit per m² planet surface: **

**Jabs = Jemit**

** Φ*S*(1-a) /4 = σTe⁴ /(β*N*cp)¹∕ ⁴ (W/m²)**

** Solving for Te we obtain the effective temperature: **

*Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴ (K) *

**β = 150 days*gr*oC/rotation*cal – is a Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law constant**

** N rotations/day, is planet’s sidereal rotation spin**

** cp – is the planet surface specific heat **

**cp.earth = 1 cal/gr*oC, it is because Earth has a vast ocean. Generally speaking almost the whole Earth’s surface is wet. We can call Earth a Planet Ocean. **

**Here (β*N*cp)¹∕ ⁴ - is a dimensionless Rotating Planet Surface Solar Irradiation Warming Ability**

**σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant**

** Rotating Planet Spherical Surface Solar Irradiation Absorbing-Emitting Universal Law:**

** Jemit = σΤe⁴/(β*N*cp)¹∕ ⁴ (W/m²)**

** The year-round averaged energy flux at the top of the Earth's atmosphere is Sο = 1.362 W/m². **

**With an albedo of a = 0,3 and a factor Φ = 0,47 we have Te = 288,36 K or 15°C. **

**This temperature is confirmed by the satellites measured Tmean.earth = 288 K.**

* Jemit = σΤe⁴/(β*N*cp)¹∕ ⁴ (W/m²)*

**http://www.cristos-vournas.com**

** The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean: **

**Tmin↑→ T↑mean ← T↓max**

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