April 25, 2000

Abstract: Consider a science-fictional starship: a relativistic ramship that accelerates to very near the speed of light and scoops up the interstellar medium as propellant. But what conditions will such a ship encounter?

Outline:

• The science-fictional setting
• Travel between stars and ramjet propulsion
• The local interstellar medium

"The Structure of the Warm Local Interstellar Medium. I. Methodology," Linsky et al, Ap. J. 528 (2000) 756-766.

Slower than Light - a novel in progress

Ten thousand years in the future, humans have colonized over a hundred planets, using relativistic ramships to travel at near the speed of light from star system to star system. Earth (referred to as "Home") is lost in myth, and the lushest inhabitable planets are colonized by our rivals, the delphines. Humans colonize marginally inhabitable worlds, deserts and ice planets.

A message from a long-vanished alien race hints at the existence of a faster-than-light drive on a planet orbiting a red dwarf star, forty light-years from the nearest inhabited planet. A plucky crew of humans mount an expedition to try to beat their delphine competitors to this prize.

Side note: the message is actually found in interstellar dust. Some grains of dust have an unusual pattern of iron inclusions whose x-ray diffraction yield a fragment of the message, which must then be pieced together. This is analogous to how we decode DNA, by breaking into smaller fragments and reading each fragment. So the message is all around us, floating in space for three million years, waiting to be found.

(1) Distance between inhabited planets

(2) Travel at near the speed of light

(3) Ramscoop propulsion

(1) Distance between inhabited planets.

I need the density of stars, and most important density of G-class stars, in the solar neighborhood. To do that formally one would need an initial mass function. In lieu of that, I simply look at a table in The Starflight Handbook, which lists 74 star systems within 21.0 light years of Sol.

Approximately 3% are A, F stars.

10% are G stars.

20% are K stars.

67% are M stars.

1/3 of the systems are double or triple systems.

There are about 0.002 stars per cubic light-year, or the average distance to the nearest star is 5 light years. To the nearest G star is 11 light years.

Assume a constant acceleration, usually 10 m/s² (approximately 1 standard gravity), in the ship’s rest frame. Everything can be expressed in terms of the rapidity y, which increases linearly in the ship’s frame:

y = a t /c, where a = acceleration and t = ship’s elapsed time.

v/c = tanh y

Dilation factor

Let t be time elapsed in galactic frame;

or

Velocity in galactic frame is

Dilation factor

Distance traveled in galactic frame

Now let me consider a "typical" flight plan. Assume acceleration = 10 m/s

Keep in mind: 1 light-day (l.d.) = 25.9 billion km; Pluto’s orbit = 40 A.U; Heliopause approx 100 A.U.

ship days	galactic days	g	km
10	10	1.00	3.7 billion	25 AU
20	20	1.00	14.9 billion	99 AU
30	30	1.00	33.6 billion	224 AU
40	40.1	1.01	59.8 billion	2.3 l.d
50	50.2	1.01	93.5 billion	3.6 ld
100	101.4	1.04	376 billion	14.5 ld
150	154	1.09	853 billion	33 ld
200	211	1.17	1.3 trillion	50 ld.
300	338	1.40	3.6 trilion	0.38 ly.
400	494	1.74	6.6 trillion	0.70 ly.
500	692	2.23	11.1 trillion	1.17 ly
750	1485	4.39	30.5 trillion	3.23 ly.
1000	3083	8.94	71.4 trillion	7.55 ly.
1100	4117	15.9		10.4 ly.
1200	15 yrs	21.1		14.1 ly.
1300	20 yrs	21.5		19.1 l.y.
1400	26.8 y	28.2		25.9 ly.

(3) Ramscoop Propulsion

The Bussard Ramjet (1960)

ISM is both propellant and fuel. However, pp fusion reaction too weak. Need pd, dd or dt reaction—and deuterium is rare. Later analyses suggest insufficient energy from fusion. (I solve this by invoking an as-yet-unknown type of mini-black hole that destroys protons and spits out their energy—essentially invoking a miracle.)

Assume crew of 150, mass of ship 10,000 metric tons.

To accelerate at 10 m/s² requires force of 10⁸ N.

Assume interstellar matter is accelerated from rest to speed of light: then need 0.3 kg/s. Assume 0.1 H atoms per cubic cm. This will then require, while traveling at 0.1 c through the ISM, a scoop 4000 km in radius!!

Ramscoop radius for constant acceleration so as the density changes the radius must change.

Note: most of the scoop will not be solid material. As the ram moves against the ISM, it will build up a shockwave that ionizes the material. The dense plasma will conduct current and guide magnetic field lines. The self-consistent magnetic field from the "plasma bloom" will guide the ions. The powerful magnetic field will also help to shield the ship from charged particle radiation.

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