Halfway to Anywhere

When reading popular descriptions of our solar system, one often comes upon descriptions of its sheer vastness. We are to be sent reeling by various analogies to grapes and billiard balls and the distance between US cities, with the upshot being that anything of interest out there is separated from everything else by a gulf of emptiness vaster than we can comprehend. This is true in every way except, perhaps, the most important.

Robert Heinlein, one of the fathers of science fiction, quipped that “once you’re in orbit, you’re halfway to anywhere.” He had a very specific (and nearly literal) interpretation in mind for “halfway” when he said that, and it wasn’t about point-to-point distance. Heinlein was referring to the “Delta-V” required to reach various locations in the solar system.

Delta-V is most generally defined as the change in velocity (both speed and direction) needed to reach one point in space from another. So, to reach a stable Earth orbit (over 100 km from sea level) you must be moving at over 7.9 km/s. In reality, losses due to air resistance on the way up mean that your rocket needs to thrust long enough that, were it in ideal vacuum, it would have changed its velocity by at least 9 km/s. For reference, the super-fast SR-71 spyplane maxes out at 950 m/s and few rifle bullets can crack 1 km/s.

Spaceships and launch vehicles are not rated by “speed” in the sense of the greatest speed they can maintain, which is a meaningless concept in the frictionless environment of space anyway.They are rated  by their maximum Delta-V, which determines what kind of maneuvering they can do and where they can go. In a very real sense, it is more reasonable to talk about somewhere like Mars as being a “speed” away from Earth than to talk about its geometric distance from us. It is the Delta-V between it and us that determines what sort of vehicle can reach it.

When measured by Delta-V the solar system shrinks a great deal, as I’ve illustrated in the diagram below. It shows the Delta-V required to reach the planets of our solar system from Earth. The first leg, from the Earth’s surface up to 8 km/s,  is shown roughly to scale, with the atmosphere petering out almost to nothing by 100 km (the lowest practical orbit as judged via the Kármán line). As you can see, from the Delta-V perspective Earth orbit is just about halfway to anywhere, or at least anywhere in the inner solar system. It’s only a third of the way to the gas-giants.

Click to Enlarge

Data courtesy of the ever-outstanding Atomic Rockets site. Click to Enlarge

It’s immediately noticeable that the planets aren’t in their typical order here. This is largely because the big gas giants, Jupiter and Saturn, have very deep gravity wells. This makes getting down to a 100 km orbit around them very expensive in terms of Delta-V. The requirements are greatly reduced (by around 20%) if you aim for one of their moons and don’t bother going down into the central planet’s gravitational death-grip.

There is one way in which this is misleading, and that is transit time. The chart lists the Delta-V for a minimum-energy “Hohmann” transfer between the Earth and the target world. The downside to this is that it is the slowest way to get there: 9 months to Mars, nearly 3 years to Jupiter, and half a century to Pluto.

You can always get there faster, but only if you build more Delta-V into your spaceship. Willing to spend 35 km/s instead of 5.8? You can get to Mars in 20 days instead of 9 months. 50 km/s will get you to Jupiter in only a year. Better yet you can get to its moon, Ganymede, in the same time with only 30 km/s – the higher the energy of your trajectory the greater the gains from not going so deep into the gravity well.

The fly in the ointment is that you aren’t getting 35 km/s out of a spaceship with chemical rocket engines. Even with the highest theoretical performance that would require 2400 tons of fuel for every ton of ship. Assuming you want to send more than a probe, it almost certainly means you’re going nuclear – either as a power source for a plasma propulsion system or as the engine itself in the case of a nuclear thermal rocket or fusion drive. The good thing is that such propulsion systems are within our technological reach, in some cases since the ’60s.


One response to “Halfway to Anywhere

  1. Just a reminder, it’s been almost two years since your last update!

    Maybe write something about liquid fluoride thorium reactors for your glorious return, akin to the molten lead cooled fast reactors post. Even if it’s only half as good as Kirk Sorensen claims it to be, it would still be a game changer, i wonder why governments are not all in on thorium/LFTR.

    Any thoughts? Cheers!

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