A couple of posts back I looked at the historical time scale of space. Now let's look at the human time scale, the pace of travel.
We know how long this takes with current technology: about 9 months to Mars, and in the example of Cassini, three years to its Jupiter flyby and seven years to Saturn. Happily we do not have the choice of chemfuel or waiting for magic; the Dawn mission to Ceres and Vesta is already using that classic SF standby, ion drive. This is not suitable for large, human-carrying spacecraft, but other electric drives are.
Drive details matter less than the drive's power output, because for deep space travel with Realistic [TM] high specific impulse drives we must be concerned not only with speed (technically, delta v) but also acceleration. High specific impulse drives require enormous power in relation to thrust, and a top speed of 100 km/s will not get you to Mars quickly if it takes you a year to build up to it.
My convenient figure of merit for drive power density is one kilowatt per kilogram - on the same order as gasoline engines (and about 10x better than present day shipboard nuclear power plants.) At this power density, a drive with an exhaust velocity of 50 km/s has a thrust/mass ratio of 0.004, meaning it can just push itself along at 4 milligees. Attached to a ship, it might might waft it forward at 1 milligee or so.
By the bone crushing standards of SF acceleration - or actual Earth liftoff - this is feeble stuff, less than freight train acceleration. But keep it up for a month and you're booking along at 25 km/s - well above solar escape velocity for a tangential burn departing Earth's orbit.
Here are outline characteristics for a small ship, with a 100 megawatt power plant and full load mass of 750 tons, half of it propellant:
Drive engine, 100 tons
Tankage and structure, 75 tons
Payload section, 200 tons
Propellant, 375 tons
Given an exhaust velocity of 50 km/s this ship has a mission delta v of 34.7 km/s. It burns off propellant at 80 grams/second for a total burn time of 4.375 million seconds, 51 days, giving it an average acceleration of 0.81 milligees. It can reach Mars in about three months - its delta v is sufficient for a two month orbit, but the prolonged burns will add another month; in fact, the ship is under power for more than half the trip.
Replace the payload section with a much larger one, 750 tons, and mission delta v falls to 17.0 km/s, just enough for the Hohmann transfer to Mars, plus the (inefficient) spirals a low-thrust ship must use to enter and leave a planetary gravity well. This is good enough for slow freight, which in a thriving space economy will be the great majority of traffic.
All of these details are pretty arbitrary, except for the important ones, the basic relationships of drive power output, acceleration, and specific impulse that determine how fast you can get wherever you are trying to go.
Our concern is with passenger traffic in the broad sense, human travel, and for that we want fast orbits. Orbit calculations are far above my math pay grade. Happily the Atomic Rockets site has a wealth of information plus some handy links. For those who want to play along at home, this online calculator will give you the orbit parameters, delta v requirement, and travel time for orbits ranging from the economical Hohmann transfer to semi-fast orbits at just below solar escape speed. For faster orbits a flat space approximation starts to give decent results.
For travel in the inner Solar System, at least out to Mars, I am partial to solar electric drive. It has about as good a prospect as nuke electric does of hitting the 1 kW/kg benchmark, and it has the enormous virtue of having practically no moving parts. Whereas a nuclear electric plant is the ultimate steampunk maintenance nightmare, a steam engine in space.
The only problem with solar electric is that it gasps for light beyond the orbit of Mars. Sunlight at Ceres has only a seventh of its intensity at Earth, so a drive good for 1 km/s per day at 1 AU now takes a week to put on 1 km/s. A trip that might take 6 months by nuclear electric drive might take 9 months by solar electric due to sluggish performance in the asteroid belt.
For outer system exploration a VASIMR style variable specific impulse drive also becomes handy, and is probably not too difficult to achieve. If, for a given drive power output, you double the specific impulse and halve your thrust and thus acceleration, your total power requirement is (ideally) unchanged, but total delta v is doubled, while your propellant consumption falls by a factor of four.
The result? With a VASIMR type drive, travel time increases not in direct proportion to distance, but as the 2/3 root of distance. Suitably tuned, the drive outlined here reaches the main asteroid belt in about 6 months, Jupiter in a year, Saturn in a year and a half, Neptune in three years, and Eris, beyond the Kuiper Belt near 90 AU, in about 7 years. (These are careful guesses, not worked out orbits!)
In rocketpunk days they did not blink at multi-year journeys, and you could say that the true first orbital mission was Magellan's, three years to go once around. We can explore Jupiter and Saturn; human missions to the outer planets and beyond are problematic, at this techlevel, on human factors grounds.
I've suggested that a benchmark for 'routine' travel is about three months, experience with submarines showing that being cooped in a can becomes progressively difficult beyond this time. Even aboard luxury liners, shipboard romances start getting complicated, and threats to the piano player get serious. Oh yes, also the little detail of radiation - the longer your travel time, the more shielding you need, meaning penalty mass.
This doesn't mean that we can't go to the asteroid belt, especially if it turns out to be full of Valuable Asteroid Stuff; it just means that cabin fever becomes a challenge. (As does radiation shielding.)
For the bloodthirsty among my readers, which is most of you, note that warlike expeditions will tend to follow slower orbits than civil passenger transports, because they had better carry delta v for a round trip, or least an abort to a friendly base. Drop tanks won't really speed you up, because their mass reduces acceleration, making transfer burns more sluggish. For a faster military trip you'll have to revert to staging, and ditch power plants as well as tanks.
Faster travel would be helpful - for peaceful as well as warlike purposes - but speeding things up will be surprisingly difficult. For faster orbits we must increase not only peak speed but acceleration; in fact, for brachistochrone and semi-brachistochrone orbits the required acceleration goes up as the square of peak speed. (To make the trip in half the time you must go twice as fast in half the time, calling for four times the acceleration.)
Halving travel time - three months to Ceres, six months to Jupiter - thus requires an eightfold increase in drive power density, into the same range as jet engines, several kilowatts per kilogram. For this we will probably need a drive that generates its power directly, rather than requiring a separate power plant. Fusion drive is the classic if speculative example, though there are alternatives.
So what does all of this mean? For some period in the midfuture, perhaps a lengthy one, the pace of travel will be more or less as outlined here - about three months to Mars, six to Ceres and other points in the main asteroid belt, a year to Jupiter. Coming next, a look at the social and political implications of these travel times.
Related post: Last year I wrote a bit on getting around the Solar System, under much the same tech assumptions I've described here.