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Relationship between temperature and mass of astronomic object

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Spectrum of sun and earth

x axis is wave length in the unit of nm y axis is intensity of the astronomic object in an arbitrary unit. Temperature of earth was 290K for calculation

Radiation spectrum of planet

x axis is wave length in the unit of nm y axis is intensity of the astronomic object in an arbitrary unit. Temperature of planet used for calculation was mean value.

Define Photogravitational mass as follows,

 m_{pg} = k_{pg} T_s^4

Where  m_i is inertial mass and k_{pg} is photogravitational constant. However without bulk, the surface temperature couldn't be maintained. With T cube inertial mass assumption,

 T^4 = k_x m_i T_s

and can be written as follows.

 m_{pg} = m_i T_s /T_0


Astronomic object Surface Temperature(C) Remark
Earth 40~-50
Sun 6000
Moon

T cube inertial mass assumptionEdit

T cube inertial mass assumption fits large planets including moon. Small planets also have characteristic R/Ts values excluding Earth as the satellite of the moon. It is properable to use  del T instead of T.   Small values of R/Ts for inner planet are due to the influence of the sun.  Satellite near the planet shows small R/Ts values.

PlanetEdit

Planetary attributes
Name Equatorial
diameter(sq)[a]
Mass(sq)[a] Density(sq) Orbital
radius(sq) (AU)
Equatorial diameter
(biq,shortest distance)
Mass(biq) Density(biq,norm) Orbital
radius(biq)
Orbital period
(years)
SurfaceTemperature (degree) R/Ts;
Sun Sun 109 332900   1.408 0 109 8.79M 6.79 0 - 5855K 5.343
Terrestrials Mercury 0.382 0.06 5.427 0.39 0.271 0.565 0.24

103/623 

90/440/700

0.177
Venus 0.949 0.82 5.2504 0.72 0.605 0.826 0.62 228/737/773 0.236
Moon 0.275 1/81 3.364 1.00 2.626 18.11 1.00 1.00 1.00 40/250/396K  3.015
Earth[b] 1.00 1.00 5.515 1.00 1.00 1.00 1.00 1.00 1.00 185/287/331  1.00
Mars 0.532 0.11 3.934 1.52 0.292 1.287 1.88 133/210/293 0.399
Gas giants Jupiter 11.209 317.8 1.326 5.20 4.508 2.689 11.86 110/152/ - 8.512
Saturn 9.449 95.2 0.69 9.54 3.176 3.870 29.46 82/143/- 6.374
Uranus 4.007 14.6 1.27 19.22 1.077 5.885 84.01 59/68/- 4.546
Neptune 3.883 17.2 1.638 30.06 0.896 7.705 164.8 50/53/-  4.852








a  Measured relative to the Earth.
b  See Earth article for absolute values.


Big sattellitesEdit

Satellite near the planet shows small R/Ts values.

Name
Diameter
(km,sq)[note 1]
Mass
(×1016 kg,sq)
Semi-major axis
(km,sq)[1]
Orbital period
(d,sq)[1][note 2]
Diameter
(km,biq)
Mass
(×1016 kg,biq)
Semi-major axis
(km,biq)
Surf.Temp. R/Ts
Earth 1.000 12,756 384,000 27.3 1.0 3,663,360 184/287/331 1.0
Io 0.4022 3,660.0×3,637.4
×3,630.6
8,900,000 421,700 +1.769 137 786 0.1154 169,607.7 ?/130/200 0.2548
Europa 0.4022 3,121.6 4,800,000 671,034 +3.551 181 041 0.09842 269,889.9 50/102/125 0.2769
Ganymede 0.4022 5,262.4 15,000,000 1,070,412 +7.154 552 96 0.16593 430,519.7 70/110/152 0.4329
Callisto 0.4022 4,820.6 11,000,000 1,882,709 +16.689 018 4 0.1520 757,225.6 80 ± 5/134 ± 11/165 ± 5 0.3255
Rhea 0.3361 1529 (1535×1525×1526) 2306.518 ± 0.353 527 108 +4.518 212 0.0429 177,161.0 53/ /99 0.1521
Titan 0.3361 5151 134520 ± 20 1 221 930 +15.945 42 0.13572 410,690.7 93.7 K (−179.5 °C) 0.4157

References Edit

  1. 1.0 1.1 "Natural Satellites Ephemeris Service". "Note: some semi-major axis were computed using the µ value, while the eccentricities were taken using the inclination to the local Laplace plane" 
  1. Diameters with multiple entries such as "60×40×34" reflect that the body is not a perfect spheroid and that each of its dimensions have been measured well enough.
  2. Periods with negative values are retrograde.

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