Uranus' Mean Temperature Calculation at 1 bar level

Uranus' Mean Temperature Equation at 1 bar level Tmean.uranus.1bar is:

Tmean.uranus.1bar = [Φ (1-a) So (1/R²) (B*N)¹∕ ⁴ /4σ]¹∕ ⁴

Uranus' sidereal rotation period is17 h 14 min 24 sec, or 0,71833 day

N = 1/0,71833 rotations/per day, or 1,3921 rotations/day

R = 19,2184 AU, 1/R² = 1/19,2184² = 0,002707 times lesser is the solar irradiation on Uranus than that on Earth.

So = 1.361 W/m² is Solar constant

Uranus' albedo, auranus = 0,300 

Uranus is a gaseous planet, Uranus' surface irradiation accepting factor Φuranus = 1 (Uranus has not surface to reflect the incident sunlight. Accepted by a Gaseous Hemisphere with radius r sunlight is S*Φ*π*r²(1-a), where Φ = 1)

Atmosphere composition 83% ± 3% H₂, 15% ± 3% He, 2,3% CH₄.

B = 850 days/rotation – it is the Rotating Gaseous Planet at 1 bar level (Jupiter, Saturn, Uranus and Neptune very similar atmosphere composition) Rotating Planet Solar Irradiation INTERACTING-Emitting constant

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

So we have:

Uranus' mean temperature at 1 bar level Tmean.uranus.1bar is:

Tmean.uranus.1bar = {1*(1-0,300)1.361*0,002707(W/m²) [850*(1/0,71833)]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.uranus.1bar = {0,7*1.361*0,002707(W/m²) (850*1,3921)¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.uranus.1bar = [0,7*1.361*0,002707(W/m²)*5,865 /4*5,67*10⁻⁸(W/m²K⁴) ]¹∕ ⁴ =

Tmean.uranus.1bar = (66.691.995,25)¹∕ ⁴ = 90,37 K

Tmean.uranus.1bar = 90,37 K is the calculated. Near the Equinoxes.

And below is the measured by satellites

Tsat.mean.uranus = 76 K (at 1bar level)

Tsat.mean.uranus = 47 K (at 0,1 bar level).

Let's for very special reason calculate Uranus' Effective Temperature Incomplete Equation Te.uranus.incompl is:

Te.uranus.incompl = [ (1-a) So (1/R²) /4σ]¹∕ ⁴

Te.uranus.incompl = [(1-0,300)1.362*0,002707(W/m²) /4*5,67*10⁻⁸(W/m²K⁴) ]¹∕ ⁴ =

Te.uranus.incompl = 58,08 K is the calculated. Near the Solstices. 

And calculated with the Mean Temperature at 1 bar level Equation Tmean.uranus.1bar = 90,37 K.

Uranus is a unique case of a planet where both the planet effective temperature and the mean temperature at 1 bar level equations should be applied.

When around the Solstices there is only a hemisphere pointed towards the sun irradiated. It is exactly the unique case of a one hemisphere solar irradiated spherical planet.

This case is in accordance with the Planet Effective Temperature equation Definition. So during the Solstices we may apply the planet effective temperature equation:

Te.uranus = [ (1-a) So (1/R²) /4σ]¹∕ ⁴

Te.uranus = [(1-0,300)1.362*0,002707(W/m²) /4*5,67*10⁻⁸(W/m²K⁴) ]¹∕ ⁴ =

Te.uranus = 58,08 K

When Uranus is around Equinoxes the Mean Temperature at 1 bar level should be applied, because at the time Uranus behaves as an ordinary planet with the regular day-night pattern.

Tmean.uranus.1bar = {1*(1-0,300)1.361*0,002707(W/m²) [850*(1/0,71833)]¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.uranus.1bar = {0,7*1.361*0,002707(W/m²) (850*1,3921)¹∕ ⁴ /4*5,67*10⁻⁸(W/m²K⁴) }¹∕ ⁴ =

Tmean.uranus.1bar = [0,7*1.361*0,002707(W/m²)*5,865 /4*5,67*10⁻⁸(W/m²K⁴) ]¹∕ ⁴ =

Tmean.uranus.1bar = (66.691.995,25)¹∕ ⁴ = 90,37 K

Tmean.uranus.1bar = 90,37 K is the calculated. Near the Equinoxes.

At the year 2019, December, where we are now, Uranus is orbiting around the Sun in its 84 earth's years long uranian year. Uranus now is about at the middle between the Equinox of the year 2007 and the Solsctice of the year 2028.

What we do now is:  (Tmean.uranus = 90,37 K + Te.uranus.incompl = 58,08 K) /2 =

Te.2019.uranus = (90,37 K + 58,08 K) /2 = 74,29 K

And below is the measured by satellites

Tsat.mean.uranus = 76 K (at 1bar level)

Here is an abstract from Wikipedia:


"Uranus orbits the Sun once every 84 years.

The Uranian axis of rotation is approximately parallel with the plane of the Solar System, with an axial tilt of 97.77° (as defined by prograde rotation). This gives it seasonal changes completely unlike those of the other planets. Near the solstice, one pole faces the Sun continuously and the other faces away. Only a narrow strip around the equator experiences a rapid day–night cycle, but with the Sun low over the horizon. At the other side of Uranus' orbit the orientation of the poles towards the Sun is reversed. Each pole gets around 42 years of continuous sunlight, followed by 42 years of darkness.[58] Near the time of the equinoxes, the Sun faces the equator of Uranus giving a period of day–night cycles similar to those seen on most of the other planets. Uranus reached its most recent equinox on 7 December 2007.[59][60]

Northern hemisphere Year Southern hemisphere Winter solstice 1902, 1986 Summer solstice Vernal equinox 1923, 2007 Autumnal equinox Summer solstice 1944, 2028 Winter solstice Autumnal equinox 1965, 2049 Vernal equinox

One result of this axis orientation is that, averaged over the Uranian year, the polar regions of Uranus receive a greater energy input from the Sun than its equatorial regions. Nevertheless, Uranus is hotter at its equator than at its poles. The underlying mechanism that causes this is unknown.

Uranus' south pole was pointed almost directly at the Sun at the time of Voyager 2's flyby in 1986. The labelling of this pole as "south" uses the definition currently endorsed by the International Astronomical Union, namely that the north pole of a planet or satellite is the pole that points above the invariable plane of the Solar System, regardless of the direction the planet is spinning.[63][64] A different convention is sometimes used, in which a body's north and south poles are defined according to the right-hand rule in relation to the direction of rotation.[65]

Although the model considered above is reasonably standard, it is not unique; other models also satisfy observations. For instance, if substantial amounts of hydrogen and rocky material are mixed in the ice mantle, the total mass of ices in the interior will be lower, and, correspondingly, the total mass of rocks and hydrogen will be higher. Presently available data does not allow a scientific determination which model is correct.[69] The fluid interior structure of Uranus means that it has no solid surface. The gaseous atmosphere gradually transitions into the internal liquid layers.[13] For the sake of convenience, a revolving oblate spheroid set at the point at which atmospheric pressure equals 1 bar (100 kPa) is conditionally designated as a "surface". It has equatorial and polar radii of 25,559 ± 4 km (15,881.6 ± 2.5 mi) and 24,973 ± 20 km (15,518 ± 12 mi), respectively.[8] This surface is used throughout this article as a zero point for altitudes.

Internal heat

Uranus' internal heat appears markedly lower than that of the other giant planets; in astronomical terms, it has a low thermal flux.[20][80] Why Uranus' internal temperature is so low is still not understood. Neptune, which is Uranus' near twin in size and composition, radiates 2.61 times as much energy into space as it receives from the Sun,[20] but Uranus radiates hardly any excess heat at all. The total power radiated by Uranus in the far infrared (i.e. heat) part of the spectrum is 1.06±0.08 times the solar energy absorbed in its atmosphere.[14][81] Uranus' heat flux is only 0.042±0.047 W/m2, which is lower than the internal heat flux of Earth of about 0.075 W/m2.[81] The lowest temperature recorded in Uranus' tropopause is 49 K (−224.2 °C; −371.5 °F), making Uranus the coldest planet in the Solar System.[14][81] One of the hypotheses for this discrepancy suggests that when Uranus was hit by a supermassive impactor, which caused it to expel most of its primordial heat, it was left with a depleted core temperature.[82] This impact hypothesis is also used in some attempts to explain the planet's axial tilt. Another hypothesis is that some form of barrier exists in Uranus' upper layers that prevents the core's heat from reaching the surface.[13] For example, convection may take place in a set of compositionally different layers, which may inhibit the upward heat transport;[14][81] perhaps double diffusive convection is a limiting factor.[13]

In 1986, NASA's Voyager 2 interplanetary probe encountered Uranus. This flyby remains the only investigation of Uranus carried out from a short distance and no other visits are planned. Launched in 1977, Voyager 2 made its closest approach to Uranus on 24 January 1986, coming within 81,500 km (50,600 mi) of the cloudtops, before continuing its journey to Neptune. The spacecraft studied the structure and chemical composition of Uranus' atmosphere,[87] including its unique weather, caused by its axial tilt of 97.77°. It made the first detailed investigations of its five largest moons and discovered 10 new ones. It examined all nine of the system's known rings and discovered two more.[19][108][141] It also studied the magnetic field, its irregular structure, its tilt and its unique corkscrew magnetotail caused by Uranus' sideways orientation.[101]"

Atmosphere composition

83% ± 3% H₂, 15% ± 3% He, 2,3% CH₄.




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

Tmin↑→ Tmean ← Tmax