by Jenab6 » Mon 07 Jul 2008, 23:28:38
$this->bbcode_second_pass_quote('BigTex', 'N')o, no, no, this can work... Problem solved.
No, it can't work, either. The fundamental problem is the fact that more energy is required, in even the most favorable shipping scenario, for making the delta-vees (particularly that for Earth arrival) than could be recovered by burning any hydrocarbon cargo.
Saturn's perihelion distance is 9.05 AU. The best Saturn-to-Earth Hohmann transfer orbit would have a semimajor axis of
a = (9.05+1)/2 = 5.03 AU
The sun-relative speed of a cargo ship following that transfer orbit, at its arrival at Earth's orbit, would be
GM = 1.32712440018E+20 m^3 sec^-2
AU = 1.49597870691E+11 meters
v = sqrt{(GM/AU) (2 - 1/5.03)} = 53648 m/s
Assume that the cargo ship is playing catch-up with Earth, a condition that minimizes the energy needed for the cargo ship to make orbital rendezvous with Earth. Earth's orbital speed is
ve = sqrt(GM/AU) = 29784 m/s
The difference is
dv'' = v-ve = 23864 m/s
Now, Earth's gravity will speed up the cargo ship somewhat on approach. On the other hand, the cargo ship doesn't have to come to a full stop, relative to Earth, since it's bound for a parking orbit. The speed up from Earth's gravity is a conservation of energy problem. Let's assume the parking orbit has an altitude of 1000 kilometers.
R = Re + 1000 km = 7378000 meters
GMe = 3.986E+14 m^3 sec^-2
dv' = sqrt{ (dv'')^2 + 2GMe/R }
dv' = 26030 m/s
However, the circular orbit speed around Earth will be
vc = sqrt{GMe/R} = 7350 m/s
So the delta-vee needed to park the cargo ship, arriving from Saturn via transfer orbit, has a minimum of
dv = dv' - vc = 18680 m/s
Roughly estimated, of course.
Now, how much energy is required to accelerate a kilogram of payload to 18680 m/s, assuming that the fuel itself has no mass?
E = (1/2) (1 kg) (18680 m/s)^2 = 1.745E+8 Joules
The energy from burning 1 kilogram of gasoline is 4.5E+7 Joules, which is only about 1/4 of what you'd have to spend to slow that kilogram of gasoline down at the arrival end of the transfer orbit. And that's assuming that you have a massless fuel and a massless cargo ship superstructure. It also neglects the energy used in the departure delta-vee at the Saturn end of the transfer.
So forget bringing Titan hydrocarbons to Earth. Costs too much.
Jerry Abbott