If Jupiter were to orbit the sun at the same distance of the earth, what would happen to the orbits of the moons if its mass suddenly disappeared? Would they still be cometary (at the least) or would they settle into a planetary orbit?
At 1AU, orbital velocity is 42.3 km/s. Io does 17.3 km/s relative to Jupiter. Io would be gone. Calliso does 8.2 km/s and I highly suspect that would be too fast to maintain a planetary orbit at 1AU.
The orbital velocity of Earth is the escape velocity of the solar system, from Earth (42.1 km/s). Fun fact, this means that if we ever wanted to dispose of nuclear waste by dumping it in a star, we'd need much less rocket fuel to hit Alpha Centauri than the Sun.
Jupiter has an orbital velocity of only 13.7 km/s, so even if Io is going the right direction and all the elliptical planes are parallel, isn't that still just a max orbital velocity of ~40 km/s, which is slow enough for orbit at 1AU?
It'd be interesting to see what happens at Jupiter's orbit, thouh. Does Io always leave? What about Callisto? It seems like there would be a large part of their orbit that would send them off into cometary orbits (or worse) depending on what direction they are going when scotty beams jupiter aboard the enterprise.
Can you explain (or link to) "Fun fact, this means that if we ever wanted to dispose of nuclear waste by dumping it in a star, we'd need much less rocket fuel to hit Alpha Centauri than the Sun."
It's not making much sense to my tired mind today.
It takes less energy to accelerate an object away from both the Earth and sun (assuming your launch pad is on an appropriate spot on the Earth surface), than to accelerate an object away from the Earth but into the sun without just getting the object stuck in an orbit like Venus or Mercury.
