Flying to Titan will be easier than flying to the large Moons of Jupiter. The thick atmosphere as thick as Titan’s is a boon to space-travelers trying to shed excess speed. Plus Titan is held in its orbit by a lighter planet – Jupiter masses 318 times Earth, while Saturn masses 95 times.
Using ITS Tankers as stages, it’s pretty easy to compute the number required for a given Spaceship payload and delta-vee. Even with 0 payload, not even 10 stages gets 19.4 km/s delta-vee. A Hohmann trajectory, which takes ~1,000 days to get to Callisto, can be done with a single Tanker as a booster, if we’re carrying just 100 tons. However landing – an extra 2 km/s delta-vee – requires an extra booster. ALternately a Tanker can be sent separately to supply the landing propellant on arrival, as the dry-mass of the Tanker is less, so there’s less fuel required for a given delta-vee.
The SpaceX Spaceship, with a full tank, has a mass of 2,100 tons, of which 150 tons is vehicle structure. Mass ratio is 2100/150 = 14. With an Isp of 382 seconds – call it 3,750 m/s – the MAXIMUM delta-vee is thus LN(14)*3,750 = 9,896 m/s.
The Tanker is a simpler vehicle, with 90 tons structure and 2500 tons propellant, thus a mass-ratio of 2590/90 = 28.78. Thus a maximum delta-vee of 12,598 m/s.
Let’s contemplate two full Tankers used as boosters for a Spaceship, also with a full tank. What’s the maximum delta-vee?
The mass-ratio of the first stage is thus (2100 + 2590 x 2)/(2100 + 180) = 3.193
Second stage is 14, and as stage mass-ratios multiply, overall it’s 44.702 i.e. a delta-vee of 3.8 x 3.75 = 14.25 km/s.
This assumes no payload. If it could all be added instantaneously at a point in Low Earth Orbit, with 7.75 km/s orbital velocity, then 19 km/s would be added to the vehicle’s solar orbital speed it shares with the Earth.
Let’s rework the figures for a fully loaded Spaceship:
Stage 1: (2550 + 2590 x 2)/(2550 + 180) = 2.83
Stage 2: 2550/600 = 4.25
Total mass-ratio = 12.034
Delta-vee: 9.329 km/s
The minimum delta-vee for a parabolic solar orbit is 8.75 km/s from LEO. Working out gravity losses from finite time boosts in LEO isn’t easy, but at a guess it’ll be roughly 0.1 km/s. That leaves about 0.4 km/s in the tank. We’ll need that aerobrake at Titan to land.
Fuel from Titan
Methane exposed to UV light from the Sun undergoes chemical reactions that polymerises it into make the quasi-opaque haze that obscures Titan’s surface. In the process it should crack methane and cause it to combine into ethane and longer chain hydrocarbons – alkanes like propane, butane etc. – and a slightly more exotic hydrocarbons, the alkynes. The simplest is acetylene, C2H2, featuring two carbons united by a triple bond. Large amounts have been identified on the surface of Titan, identified thanks to clever processing of data from ‘Cassini’, which leads to thoughts of using acetylene as a propellant. Oxy-Acetylene is the first reaction that springs to mind, but free oxygen is in short supply on Titan. Oxygen will need to be cracked from water or carbon dioxide, both of which are part of the ‘lithosphere’ in the cryogenic conditions on Titan.
Getting to Callisto
Three orbits can be contemplated – the Hohmann transfer, 1,000 days and lowest delta-vee; an Elliptical arc, which halves the time, and the aforementioned Parabolic orbit, which launches at Solar escape velocity from Earth’s solar orbit. Boosting from LEO, then braking into the L2 Point about 50,000 km up from Callisto’s surface, before touching down, the total delta-vee, with a 15% increase for the landing is as follows:
Hohmann (1,000 days): LEO Boost = 6.2 km/s; Braking into Orbit = 4.7 km/s; Landing = 2 km/s; Total = 12.9 km/s
Elliptical (500 days): LEO Boost = 7.2 km/s; Braking into Orbit = 8.4 km/s; Landing = 2 km/s; Total = 17.6 km/s
Parabolic (400 days): LEO Boost = 8.8 km/s; Braking into Orbit = 12.9 km/s; Landing = 2 km/s; Total = 23.7 km/s
SOURCES- Spacex, Crowlspace