SpaceX’s proposed reusable Interplanetary Transport System is an interesting concept and certainly eminently feasible. Last part of Elon Musk’s presentation indicated its ability to travel beyond Mars to targets further afield, illustrated by images of landings on Europa, Enceladus, and a pretty flight above the rings of Saturn. Yet the exact details of such ambitious missions warrants discussion.
Minimising the specific energy of the mission means a Hohmann transfer orbit, but minimising the supplies required for the crew means a trade-off against trip-time. The proposed orbit to Mars, for example, uses a faster partial ellipse to get to Mars in 80 days during the most favorable conditions.
Jupiter and Saturn are challenging for life-support especially if Hohmann transfers are used. On average a Hohmann to Jupiter takes 2.75 years and to Saturn takes 6 years. Partial elliptical orbits can improve that somewhat, but let’s look at a parabolic orbit – where the vehicle launches from Earth’s orbit at just over 12 km/s. Such an orbit is on the cusp, as it has zero net energy, making it an open orbit that escapes the Sun. At Earth’s orbit distance the speed required is 42.122 km/s, but as Earth is already doing 29.785 km/s, the total delta-vee required is 12.34 km/s. If the ITS vehicle launched directly from Earth’s surface it would need an initial boost of over 16.65 km/s, but fortunately it’s leaving from Low Earth Orbit, where it’s taken on a full tank of propellant and is already orbiting at 7.75 km/s. Thanks to starting at near the bottom of a gravity well, the actual delta-vee to leave Earth’s gravity with a net speed of 12.34 km/s is significantly reduced. In this case 8.75 km/s, with some amount of gravity losses if the acceleration is low.
So just what can SpaceX’s ITS do? Fortunately SpaceX have provided some numbers on their vehicle’s dry mass (150 tons) and total propellant load (1950 tons). That’s a maximum mass-ratio of 14 (= 2100/150) which would boost an empty ITS by 9.87 km/s. Fully loaded with payload the ITS masses 2550 tons, thus a mass-ratio of 4.25, just 5.42 km/s delta-vee. To achieve a delta-vee of 9 km/s (parabolic orbit and some reserve) the mass-ratio needs to be 11. Thus 80 tons of payload. Not enough for a full 100 colonist load, but enough for an initial mission. A parabolic orbit to Jupiter takes 1.1 years and 2.5 years to Saturn. Of course that does mean that we have no propellant to actually stop at Jupiter’s moons, so I won’t discuss those, but in the case of Saturn there’s the option of aerobraking at Titan. The re-entry speed works out at ~11.3 km/s, best case, and about 16.9 km/s worst case. The ITS Spaceship is designed to re-enter Earth’s atmosphere at 12.5 km/s on a fast return from Mars, so Titan’s nitrogen atmosphere and lower gravity should mean a similar re-entry is manageable. Perhaps a bit higher.
Higher payloads and/or higher delta-vees may be possible if a fully loaded ITS Tanker is used as a first stage. The empty mass of the Tanker is only 90 tons and if used as an expendable booster, there’s no need for return propellant. A Tanker can hold a full propellant load of 2,500 tons. A fully loaded Spaceship can then be boosted to 8 km/s delta-vee. With a lighter payload, the system can actually land on the airless moons of Jupiter.