Quote (Azrad @ Mar 28 2014 12:22am)
The amount of work required to lift an object off a planet (from its equator) is:
http://s10.postimg.org/ma7xse9nt/woot.png
This is also the amount of potential energy that is added to the object, that can be retrieved by allowing it to fall back onto the planet.
Let's say that it requires A joules to lift the object normally. If you had a way to lift it cheaper, for say A-5 joules, you could then drop it again and get back A joules. So the full process nets you:
A - 5 - A = 5 joules. Now you can just repeat this process and get as much energy as you want. This is a violation of the conservation of energy. Therefore if the conservation of energy is true, there can not exist a method for lifting the object which costs less than A joules.
Matter being transported from titan to earth would
lose potential energy (in a closed system), since the gravity on earth is much stronger than on titan.
The siphon effect is a a result of pressure differentials... when oil near the exit moves, it creates a vacuum pulling the rest of the oil in the pipeline toward it.
So when the oil near the exit is "falling" towards earth, some of that energy is transferred back along the pipeline via the siphon effect and used to lift the oil at the entry point off of the moon.
There's no conservation of energy violation.
(the most common example of the siphon effect is siphoning gas out of a car... the gas "falls up" to get out of the tank... which works as long as the exit point is lower than the entry point, so the net effect is a loss of potential energy)
Entering extreme geekzone... brace yourselves
titan surface gravity: 1.352 m/s^2
titan radius: 2576km
earth surface gravity: 9.807 m/s^2
earth radius 6371km
saturn surface gravity: 10.44m/s^2
saturn radius: 60268 km
distance between saturn and titan: 1257060 km
distance from titan to earth: 1,200,217,664 km
Assumptions:
Titan is between Saturn and earth.
Gravity from other bodies is negligible (we'll see later that we shouldn't ignore the sun ;))
Everything is a perfect sphere and centers of gravity are in the center (close enough for the purposes of this approximation)
Gross gravitational acceleration from Earth, Titan, and Saturn:

Adding those gives us a net gravitational acceleration of 28863 m/s^2 towards earth
Then dividing by the distance gives an average gravitational acceleration of .00002405 m/s^2 on the system
Which is very, very small acceleration... but still accelerating towards earth, and reaching some terminal velocity determined by the amount of friction in the pipeline.
Some surprising things to note:
The gravity from Titan is nearly negligible... with earth exerting an average acceleration 18 times stronger.
The gravitational effect from Saturn is about half that of earth's, despite the fact that it's not close at all to the pipeline (the exit point is about 21 times Saturn's radius away, making the gravitation of Saturn 1/400 of earth's gravity, at the strongest point).
Now let's see what happens if we include the sun's gravity...
sun surface gravity: 274 m/s^2
radius of sun: 695500km
distance from sun to earth: 149,597,870km
And assuming Earth is between the sun and titan...

That's a 13 times stronger effect than even the earth... which dominated the closed system.
So the future of the Titan pipeline may likely depend on the positioning of the sun relative to Titan and Earth.
Though even with the sun's gravity helping, it'd likely be too slow of a terminal velocity to be economically efficient (and pumping force would have to overcome a TON of friction along that extremely long path that it would probably not help at all).
This post was edited by taekvideo on Mar 28 2014 01:49am