Transcript No Slide Title

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 = 4πRσT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
a
Fraction
2
4 r
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:
4 R  T 1  A a
Flux absorbed 
2
4 r
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
Sun
4
Sun
2
Flux reemitted 4 a  T
2
4
bb
For equilibrium, the total radiant energy
absorbed by the sphere must be equal to the
total radiant energy reemitted, so.
4 R  T 1  A a
4 a  T 
2
4 r
2
4
bb
or:
T 
4
bb
2
Sun
2
4
Sun Sun
R T
4
Sun
2
1  A
2
4r
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.
Insertion of values for the Sun, and
normalization of the distances in terms of
A.U. produces:
1  A 279K
0.5
rA.U.
0.25
Tbb 
For a slowly-rotating planet the temperature
of the sunlit side, Tss, is given by:
1  A 330K
0.5
r A.U.
0.25
Tss 
Planet
Mercury
Venus
Earth
Moon
Mars
Jupiter
Predicted Tbb Observed T
440K
~650 K
625 K (noon)
229 K
210 K (clouds),
750 K (surface)
246 K
290 K
273 K,
~205 K
386 K (noon)
216 K
~230 K
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
Mercury
Venus
Earth
Moon
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
a (A.U.)
R/R
M/M
0.387
0.723
1.000
0.999
1.524
5.202
9.528
19.164
29.962
39.482
0.382
0.949
1.000
0.272
0.532
11.209
9.449
4.007
3.883
0.187
0.0553
0.8150
1.000
0.0123
0.1075
317.83
95.161
14.536
17.148
0.0022
Distances from the Sun:
Mercury
0.4 D
Venus
0.7 D
Earth
1.0 D
Mars
1.5 D
Jupiter
5.2 D
Saturn
9.6 D
Uranus
19.2 D
Neptune
30.1 D
Pluto
39.8 D
Some
Men
Very
Early
Made
All
Jars
Stand
Up
Nearly
Perpendicular
Say !
My
Very
Energetic
Maiden
Aunt
Just
Served
Us
Nine
Pizzas
Sun
Mercury
Venus
Earth
Mars
Asteroids
Jupiter
Saturn
Uranus
Neptune
Pluto
Mnemonic
Mostly
Nonsense
Easing
Memorization
Of
Names
In
Columns
The
Asteroid
Belt
Mercury + 0
The Terrestrial Planets
Venus + 0
Earth + 1
Mars + 2
Moon
Saturn + 62
Neptune + 14
Jupiter + 67
Uranus + 27
The Ringed Gas Giants
Earth + 1
The Plutinoes
Pluto + 5
Eris + 1
Kuiper-Edgeworth Belt
Objects
Earth + Moon
Planets − Bright “stars” on the ecliptic.
Jupiter and Venus
Waning Crescent Moon, Venus & Jupiter.
Comets
Comet Tails
Comet Origins
Kuiper Cloud
Comet Origins
Oort Cloud
Shepherd Satellites
Tides
F~1/r3
Tidal Friction
Displays of the aurora
borealis imaged by Wilf
Meyer from Yellowknife.