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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 4πR2, so the total emergent radiant flux from the Sun is = 4πRσT4. 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 279 K 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 330 K 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.