45 minutes seems like an awfully long time for a ballistic missile aimed at a mobile target.
Chronos:
There’s a minimum size at which the Roche limit applies? Also, are the rings of Saturn et al. former satellites that were below the Roche limit?
Are you considering tidal forces to not be Newtonian?
Tidal forces are Newtonian, but they can’t destabilize an orbit. And the Roche limit only applies for things which are held together primarily by gravity: If I have a baseball, say, or the Space Shuttle, in low Earth orbit, then the tidal forces pulling the baseball apart will be stronger than the gravitational force holding the ball together… But so what? The gravitational force holding a baseball together is pitifully small anyway, compared with the electromagnetic forces holding it together.
I’m pretty sure that the rings of the gas giant planets are below the Roche limits, but it’s hard to say whether they were once a larger body which got pulled apart, or if they just never formed a moon to begin with.
But don’t they decrease the momentum of the orbiting body?
And from the article, I don’t understand this:
Are you saying that the closer you are to Earth, the slower the orbiting speed is?
Tidal forces don’t do anything to the momentum of an orbiting body. All they do is try to pull the body apart. Where did you hear otherwise?
And a closer circular orbit is faster than a further circular orbit, but when you go down, you gain speed (from potential energy being converted to kinetic). The net effect is that, if you try to thrust yourself down, the circular orbit speed for your height will increase, but your speed will increase even more. So you end up too fast to stay at that height.
Perhaps we’re talking about different things. In physics, “tidal forces” usually refers to the differential in the gravitational force, but in this case I’m using the term to refer to the forces regarding tides (as in changes in sea level). The Earth is losing angular momentum because of the tides, right? So isn’t that momentum being transfered to the moon?
Hmm, I think I’m starting to see what you’re saying. As the ball “falls”, it starts to move towards the Earth faster and faster. But unless it hits the Earth on the first pass, all that velocity will be turned into velocity away from the Earth, like a bull whose velocity towards the matador is transformed into velocity away from him by the simple act of the matador stepping aside.
OK, I think I see what you’re getting at. While in principle, dragging the oceans around the planet will change the momentum of an orbiting body, the effect will be negligible for any artificial satellite, since they have so little effect on the oceans. Even for the Moon, which is easily the most tidally-significant object for the Earth, the effect is miniscule. I can’t imagine that this would be enough to bring down a satellite before the Sun engulfed the Earth, regardless of whether the satellite is within the Roche limit.
Essentially correct, if you allow for the fact that this isn’t all happening in a straight line, like with the bull.
Description of gravity assist maneuvers.
http://www.jpl.nasa.gov/basics/bsf4-1.html
Though I think the term is really not accurate. It is not the gravity that is assisting, but the angular momentum. The gravity slows down as much as it speeds up, it’s the orbit of the sun that gives the extra speed.
Picture of Phobos. It mentions the decaying orbit, but doesn’t explain.
http://antwrp.gsfc.nasa.gov/apod/ap030701.html