The albedos of Saturn and Uranus are 0.50 and 0.65 respectively while the ratio of the planets radii is 2.50, Satur's being the larger. Their heliocentric distances (orbits being assumed circular and coplanar) are 9.5 and 19.2 AU respectively. Neglecting the effect of Saturn's rings, calculate the magnitude difference in the brightness of the two planets when both are observed at opposition.
2. If the two planets have mean distances from the Sun and (in AU) then their distances from the Earth at opposition are and AU (assuming circular orbits anyway).
3. The Solar flux at the planets are and respectivly, where is a constant who's value does not matter for this calculation. So the fluxs at the Earth due to reflected sunlight are:
where and are the albedos of the two planets and again is a constant who's value does not matter and and are the planets radii.
Also you have an error in your arithmetic, your result should be: 2.9 magnitude (the difference between this and the above is the approx. 2 magnitudes from my having forgotten the planetary radii (the way that you have written your answere suggests you handled the powers of 10 incorrectly)).Code:>F1=(0.5*2.5^2)/(9.5^2*8.5^2) 0.000479253 >F2=0.65/(19.2^2*18.2^2) 5.32314e-006 > > >2.5*log10(F1/F2) 4.88599 >
Reality check: Maximum brightness of Saturn 0.7 Mag, maximum brightness of Uranus 5.5 Mag.