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.

Comets

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.