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7-15. Solar System Fundamentals
Goals:
1. Learn the basic astrophysics of solar system objects.
2. Introduce basic solar system terminology, which differs from other areas of astronomy.
3. Discuss some of the rationale behind searches for other planetary systems.
Consider the case of a small black sphere of radius a and albedo A orbiting the Sun at a distance of r A.U. from it. Albedo = fraction of incident light reflected.
The radiance at the Sun’s surface is σT4
where T = 5779 K. The surface area of the Sun is 4πR
2, so the total emergent radiant flux from the Sun is = 4πRσT
4.
At a distance r from the Sun, a small disk of radius a intercepts a fraction of the Sun’s light amounting to:
2
2
4Fraction
r
a
The amount absorbed by the sphere is (1−A), where A is the albedo of the sphere. So the radiant flux absorbed by the sphere is:
The absorbed energy heats the sphere, which reradiates it into space. If Tbb is the black body temperature of the ball when it reaches equilibrium, then the total energy reradiated by the sphere is:
2
24Sun
2Sun
4
14absorbedFlux
r
aATR
4bb
24reemittedFlux Ta
For equilibrium, the total radiant energy absorbed by the sphere must be equal to the total radiant energy reemitted, so.
or:
For R = 6.9598 108 m and T = 5779 K one can calculate the expected temperature of various spheres of differing A as a function of orbital radius r in the solar system.
2
24Sun
2Sun4
bb2
4
144
r
aATRTa
2
4Sun
2Sun4
bb 4
1
r
ATRT
Insertion of values for the Sun, and normalization of the distances in terms of A.U. produces:
For a slowly-rotating planet the temperature of the sunlit side, Tss, is given by:
5.0
25.0
bbA.U.
K2791
r
AT
5.0
25.0
ssA.U.
K3301
r
AT
Planet Predicted Tbb Observed TMercury 440K ~650 K
625 K (noon)Venus 229 K 210 K (clouds),
750 K (surface)Earth 246 K 290 K Moon 273 K, ~205 K
386 K (noon)Mars 216 K ~230 KJupiter 102 K 150 K (cloud tops)
Note that this also predicts an exponentially decreasing temperature T with increasing distance r from the Sun (or any star).
Planet a (A.U.) R/R M/M
Mercury 0.387 0.382 0.0553Venus 0.723 0.949 0.8150Earth 1.000 1.000 1.000 Moon 0.999 0.272 0.0123Mars 1.524 0.532 0.1075Jupiter 5.202 11.209 317.83Saturn 9.528 9.449 95.161Uranus 19.164 4.007 14.536Neptune 29.962 3.883 17.148Pluto 39.482 0.187 0.0022
Distances from the Distances from the Sun:Sun:
MercuryMercury 0.4 D0.4 D
VenusVenus 0.7 D0.7 D EarthEarth 1.0 D1.0 D MarsMars 1.5 D1.5 D JupiterJupiter 5.2 D5.2 D SaturnSaturn 9.6 D9.6 D UranusUranus 19.2 D19.2 D NeptuneNeptune 30.1 D30.1 D PlutoPluto 39.8 D39.8 D
SomeMenVeryEarlyMade
AllJars
StandUp
NearlyPerpendicular
Say !My
VeryEnergeticMaiden
AuntJust
ServedUs
NinePizzas
SunMercuryVenusEarthMars
AsteroidsJupiterSaturnUranus
NeptunePluto
Mnemonic
MostlyNonsense
EasingMemorization
OfNames
InColumns
TheAsteroid
Belt
The Terrestrial Planets
Earth + 1Venus + 0
Merc
ury
+ 0
Mars + 2
Moon
The Ringed Gas Giants
Earth + 1
Ura
nu
s +
27
Nep
tun
e +
14
Jupiter + 67Saturn + 62
The Plutinoes
Earth + Moon
Pluto + 5 Kuiper-Edgeworth Belt Objects
Eris + 1
Planets − Bright “stars” on the ecliptic.
Jupiter and Venus
Waning Crescent Moon, Venus & Jupiter.
Comet Tails
Comet OriginsKuiper Cloud
Comet OriginsOort Cloud
Shepherd Satellites
TidesF~1/r3
Tidal Friction
Displays of the aurora borealis imaged by Wilf Meyer from Yellowknife.