Io, the innermost of Jupiter's Galilean satellites, is the most volcanically-active object in the Solar System, thanks to tidal heating of its interior by gravitational interactions with Jupiter and the other 3 Galilean satellites. Estimate the Roche limit for tidal disruption of Io by Jupiter (you may ignore any constant in front of the formula, a rough estimate will suffice here). Use the data in the table to choose the correct statement about the location of the Roche limit relative to Jupiter and Io. Jupiter mass -1.9 x 1027 kg
Jupiter radius 70,000 km
lo mass 9x 1022 kg
lo radius 1800 km
lo orbital radius 420,000 km
A. The Roche limit is about twice lo's radius, which is much smaller than lo's orbital radius.
B. lo orbits very near the Roche limit, which is about 8.5 Jupiter radii.
C. The Roche limit is about 4.5 times farther out than lo's orbit.
D. The Roche limit approximately coincides with the top of Jupiter's atmosphere, which is about 8.5 times closer to Jupiter than lo's orbital radius.