Frontier, final: correctly attributed to ►space, which borders on the infinite and is the cruising radius of the ►starship Enterprise, whose mission is to boldly explore strange new worlds and solar systems where no man has gone before.

The Enterprise possessed a warp propulsion system, which enabled it to travel with superluminal velocity and thus within a theoretically infinite cruising range. But what about the cruising range of a real interstellar spacecraft? ►Special relativity theory suggests that we can travel pretty fast even at subluminal speed. A spacecraft continuously accelerating by 1 g — the gravitational acceleration of the Earth — during the first half of its voyage and decelerating by 1 g during the second half will require the following travel times for interstellar destinations:

With Beta CVn we can reach what could be an ►extraterrestrial civilization in less than seven years; a mere 30 years would get us to the ►Andromeda Nebula. How are these short travel times for such gigantic distances possible? As soon as the spacecraft has reached a noticeable fraction of the speed of light — which at a 1-g acceleration rate would take only a few months — the relativistic length contraction of the travel route is reduced in the direction of the destination. The greater the speed, the shorter the distance to the spacecraft's destination. From the Earth's point of view, however, the spacecraft's travel speed slows down due to time dilation. Both phenomena have the effect of radically diminishing the subjective travel time inside the spacecraft. Thus, despite its restriction to the speed of light, relativity theory does not rule out interstellar travel.

Unfortunately, a glance at the last column of the table dampens our travel hopes. Here we have a list of the amounts of propellant that we need to take with us for accelerating and decelerating a relatively small spacecraft weighing a mere 100 tons. The amount required just for a trip to the center of the Milky Way is far outside the realm of possibility — and that even on the assumption that our hypothetical spacecraft has the most effective propulsion system conceivable, and not some measly chemical rocket engines like those of a space shuttle or the Saturn V moon rocket.

The Rocket Formula

A rocket engine's** efficiency was first calculated in 1903 by the space pioneer Constantine Ziolkowsk. The propellant requirement per kilograms of cargo depends on the gas jet velocity of the propulsion jet. Standard chemical rocket engines reach a gas jet velocity of about 5 km per second — by far not enough for interstellar voyages. Since the maximum possible velocity is the speed of light, the most efficient propulsion system would be a photon rocket engine, which uses light particles to provide the thrust. Such an engine could consist, for example, of a strong laser for X-ray or gamma radiation.

To generate the light energy, our spacecraft directly transforms matter and antimatter into energy. But even with this hypothetical superengine with its 100% efficiency, the above table shows that we would have to carry matter-antimatter propellant weighing roughly the same as a smallish moon to reach the next galaxy. And we have not even included in our calculation the propellant required for the return flight.

The lion's share of propellant is used for accelerating the propellant mass required for the deceleration phase. How would the above table change if we dispensed with deceleration altogether and arrived at our destination almost at the speed of light?

This table already looks much better. But how can we bring our spacecraft to a halt at the destination without using any propellant for deceleration? One possible braking maneuver is to simply collide with the destination planet. However, the impact of a spacecraft with a weight of millions of tons (due to relativistic mass increase) at almost the speed of light will not likely do any good to either the spacecraft or the planet. In addition, such an act would probably result in substantial diplomatic difficulties with the extraterrestrial civilization that we intend to visit.

Black Holes as Rocket Brakes

A superior alternative may be to enter the destination planet's orbit and allow the friction from the atmosphere to gradually decelerate the spacecraft. However, to keep a spacecraft almost as fast as the speed of light in place on an orbit we would need a very strong gravitational field of the kind that exists only in the vicinity of a ►black hole. Moreover, not just any black hole will do. Rather, we need a supermassive object lest we will lose both our spacecraft and our life due to ►spaghettification.

Fortunately, there are supermassive black holes in the centers of nearly all galaxies that we could use for our braking maneuvers, especially since they usually also have some kind of atmosphere in the form of a gas accretion disk. With skillful navigation they could also be used as "gravitational slingshots" to further accelerate our spacecraft and catapult it into another direction without the use of any propellant. The narrowly bundled jets ejected by many black holes toward their rotational axes could also prove to be a source of alternative operating power.

In this way, by "jumping" from one black hole to the next, we could visit a number of galaxies one after the other — outdoing even the Enterprise, which (owing to a hypothetical galactic barrier) was generally confined to this galaxy. To be sure, it would be something of a thrill ride, since we could never be sure that the black hole in our destination galaxy really is suitable for deceleration. In this respect, space travel without propellant for deceleration is somewhat like a leap from a ten-meter springboard into an unfamiliar body of water. But astronauts are traditionally courageous. Perhaps there are already entire fleets of spacecraft from various civilizations in the centers of galaxies using black holes as springboards for their adventures.

The Infinity Engine

We should not neglect to mention a certain disadvantage of the propulsion system just described. Although we can produce antimatter as antiprotons in particle accelerators, even the largest available accelerators could not produce more than some parts in a billion grams per year. There is to date no practical solution to the problem of generating tons of antimatter. Other propulsion systems, such as the fusion of deuterium and helium 3 to helium 4, require multiples of the propellant quantities listed above.

There is also the screening problem. A spacecraft traveling almost as fast as the speed of light experiences a strong blueshift (the opposite of the ►redshift) of objects in the direction of travel. Depending on the speed, the light of the stars and of the cosmic ►background radiation in front of the spacecraft is first blue, then ultraviolet, and eventually starts bombarding the spaceship as a strong X-radiation. Even the vicinity of black holes is a source of deadly radiation. Interstellar spaceships therefore require solid lead armor as a screen, which would again increase our propellant requirements.

The best solution would be a spacecraft that does not need any propellant for either acceleration or deceleration. This would also provide the spaceship with a theoretically infinite cruising range. The simplest way to achieve this would be by separating spaceship and propulsion system. We could station our propulsion laser on Earth and direct the laser beam toward a mirror on the rear of the spaceship, which is powered exclusively by the pressure of the beam.

Does this solve the propulsion problem? Unfortunately not. For one thing, this principle cannot be applied to deceleration, unless the same kind of laser were also installed on our destination planet. Secondly, the laser experiences a redshift from the point of view of the spaceship. The faster is the ship, the weaker is the energy coming from the laser and the less efficient is the propulsion.

The physicist Robert Bussard proposed to obtain our propellant directly from space. Even the empty space between galaxies contains hundreds of hydrogen atoms per cubic meter. In Bussard's proposal, a huge magnetic field located at the lean bow of the ship collects these ►atoms. They are subsequently fused into helium in a reactor, and the generated energy is used for propulsion. The volume of collected atoms depends on the speed of the spacecraft. The spaecraft does have to carry some propellant in order to accelerate to roughly ten percent of the speed of light. The rest is covered by the reactor. With such a propulsion system we could travel from one end of the ►Hubble volume to the other, and even further than that, without refueling.

But even this infinity engine has some little problems. To enable the magnetic field to collect the atoms, the latter have to be ionized (electrically charged). But while matter in intergalactic space is indeed largely ionized, galaxies predominantly contain uncharged, neutral atoms. We could electrically charge them by means of a laser located on the ship's bow. But this would presumably require more energy than the fusion could generate. To make sure that the fusion is possible in the first place, the particles in the reactor have to be accelerated up to the speed of the spaceship. But doing so will decelerate the ship itself. Thus the infinity engine is much better suited for deceleration than for acceleration.

It is conceivable that future interstellar spaceships will use a combination of all the propulsion methods discussed above. Unfortunately, the warp engine will not be involved. Captain Kirk will stay ahead of us by a nose.

* Here are the formulas for relativistic computation of the spaceship's travel time t, the time on Earth T, and the traveled distance D under the assumption of a constant acceleration value a.

T = c/a * sinh(at/c) = sqrt((D/c)² + 2D/a)
t = c/a * asinh(aT/c) = c/a * acosh(aD/c² + 1)
D = c²/a * (cosh(at/c) - 1) = c²/a * (sqrt((aT/c)² + 1) - 1)

If the spacecraft has accelerated over the first half of the route and subsequently decelerates, then times and distances in the first table above are to be reduced by half prior to their insertion in the formulas and the consequent results are to be doubled. We shall use years and light-years as units for time and space, which simplifies the formulas because the speed of light c will then amount to 1 and the acceleration a = 9,81 m/s² to approximately 1.

** Ziolkowski's rocket formula can be used to calculate the mass ratio of propellant and cargo:

m₀/m_e = exp(v_e/ v_c)

where v_e is the final velocity, v_c the gas jet velocity of the thrust medium, m₀ the initial mass of the rocket including propellant, and m_e the final mass. As you can see, with equal final velocity the ratio between initial mass and final mass — that is, the volume of propellant to be carried on the spaceship — systematically decreases with an increase in gas jet velocity. The above formula is non-relativistic, hence applicable only to low speeds. Assuming a constant acceleration a as well as v_c = speed of light c, the relativistic rocket formula for the required mass ratio for a travel period t is:

m₀/m_e = exp(at/c) - 1

For deceleration both sections have to be calculated separately, with the final mass of the acceleration route corresponding to the initial mass of the deceleration route.

Links Related to the Topic

■ U.S.S Enterprise NCC-1701

© Johann Christian Lotter   ■  Infinity  ■  Links  ■  Forum