Space Travel Under Constant 1g Acceleration

The basic principle behind every high-thrust interplanetary space probe is to accelerate briefly and then coast, following an elliptical, parabolic, or mildly hyperbolic solar trajectory to your destination, using gravity assists whenever possible. But this is very slow.

Imagine, for a moment, that we have a spacecraft that is capable of a constant 1g (“one gee” = 9.8 m/s2) acceleration. Your spacecraft accelerates for the first half of the journey, and then decelerates for the second half of the journey to allow an extended visit at your destination. A constant 1g acceleration would afford human occupants the comfort of an earthlike gravitational environment where you would not be weightless except during very brief periods during the mission. Granted such a rocket ship would require a tremendous source of power, far beyond what today’s chemical rockets can deliver, but the day will come—perhaps even in our lifetimes—when probes and people will routinely travel the solar system in just a few days. Journeys to the stars, however, will be much more difficult.

The key to tomorrow’s space propulsion systems will be fusion and, later, matter-antimatter annihilation. The fusion of hydrogen into helium provides energy E = 0.008 mc2. This may not seem like much energy, but when today’s technological hurdles are overcome, fusion reactors will produce far more energy in a manner far safer than today’s fission reactors. Matter-antimatter annihilation, on the other hand, completely converts mass into energy in the amount given by Einstein’s famous equation E = mc2. You cannot get any more energy than this out of any conceivable on-board power or propulsion system. Of course, no system is perfect, so there will be some losses that will reduce the efficiency of even the best fusion or matter-antimatter propulsion system by a few percent.

How long would it take to travel from Earth to the Moon or any of the planets in our solar system under constant 1g acceleration for the first half of the journey and constant 1g deceleration during the second half of the journey? Using the equations below, you can calculate this easily.

Keep in mind that under a constant 1g acceleration, your velocity quickly becomes so great that you can assume a straight-line trajectory from point a to point b anywhere in our solar system.

Maximum velocity is reached at the halfway point (when you stop accelerating and begin decelerating) and is given by

The energy per unit mass needed for the trip (one way) is then given by

How much fuel will you need for the journey?

hydrogen fusion into helium gives: Efusion = 0.008 mfuel c2

matter-antimatter annihilation gives: Eanti = mfuel c2

This assumes 100% of the fuel goes into propelling the spacecraft, but of course there will be energy losses and operational energy requirements which will require a greater amount of fuel than this. Moreover, we are here calculating the amount of fuel you’ll need for each kg of payload. We would need to use calculus to determine how much additional energy will be needed to accelerate the ever changing amount of fuel as well. The journey may well be analogous to the traveler not being able to carry enough water to survive crossing the desert on foot.

Now, let’s use the equations above for a journey to the nearest stars. There are currently 58 known stars within 15 light years. The nearest is the triple star system Alpha Centauri A & B and Proxima Centauri (4.3 ly), and the farthest is LHS 292 (14.9 ly).

I predict that interstellar travel will remain impractical until we figure out a way to harness the vacuum energy of spacetime itself. If we could extract energy from the medium through which we travel, we wouldn’t need to carry fuel onboard the spacecraft.

We already do something analogous to this when we perform a gravity assist maneuver. As the illustration below shows, the spacecraft “borrows” energy by infinitesimally slowing down the much more massive Jupiter in its orbit around the Sun and transferring that energy to the tiny spacecraft so that it speeds up and changes direction. When the spacecraft leaves the gravitational sphere of influence of Jupiter, it is traveling just as fast as it did when it entered it, but now the spacecraft is farther from the Sun and moving faster than it would have otherwise.

Reference: https://www.daviddarling.info/encyclopedia/G/gravityassist.html

Of course, our spacecraft will be “in the middle of nowhere” traveling through interstellar space, but what if space itself has energy we can borrow?

Brightest Event Ever Observed

On June 14, 2015, perhaps the intrinsically brightest event ever recorded was detected at or near the center of the obscure galaxy APMUKS(BJ) B215839.70−615403.9 in the southern constellation Indus, at a luminosity distance of about 3.8 billion light years.

ASASSN-15lh (All–Sky Automated Survey for SuperNovae), also designated SN 2015L, is located at α2000=22h02m15.45s, δ2000=-61° 39′ 34.6″ and is thought to be a super-luminous supernova—sometimes called a hypernova—but other interpretations are still in play.

Let’s put the brightness of SN 2015L in context.  Peaking at an absolute visual magnitude of -24.925 (which would be its apparent visual magnitude at the standard distance of 10 parsecs), SN 2015L would shine as bright as the Sun in our sky if it were 14 light years away—about the distance to van Maanen’s Star, the nearest solitary white dwarf.  SN 2015L would be as bright as the full moon if it were at a distance of 8,921 light years.  SN 2015L would be as bright as the planet Venus if it were at a distance of 333,000 light years.  Since the visible part of our galaxy is only about 100,000 ly across, had this supernova occurred anywhere in our galaxy, it would have been brighter than Venus.  If SN 2015L had occurred in M31, the Andromeda Galaxy, 2.5 million light years away, it would take its place (albeit temporarily) as the third brightest star in the night sky (-0.47m), after Sirius (-1.44m) and Canopus (-0.62m), but brighter than Alpha Centauri (-0.27m) and Arcturus (-0.05m).

The Open Supernova Catalog (Guillochon et al. 2017) lists three events that were possibly intrinsically brighter than SN 2015L.  Two events were afterglows of gamma ray bursts GRB 81007 and GRB 30329: SN 2008hw at -25.014m and SN 2003dh at -26.823m, respectively.  And the other event was the first supernova detected by the Gaia astrometric spacecraft, Gaia 14aaa, 500 Mly distant, shining perhaps as brightly as -27.1m.

References
Chatzopoulos E., Wheeler J. C., Vinko J., et al., 2016, ApJ, 828, 94
Dong S., Shappee B. J., Prieto J. L., Jha S. W., et al., 2016, Science, 351, 257
Guillochon J., Parrent J., Kelley L. Z., Margutti R., 2017, ApJ, 835, 64

Stars Like Our Sun

The spectral type of our Sun is G2V, that is to say, a G2 main-sequence star.

Sun
Zodiacal Constellations
mv = -26.75, mb = -26.10, B-V = 0.65
Ecliptic
0.0000158 ly
Single star

Here are the brightest stars visible in the nighttime sky that have the same spectral type and therefore are, arguably, most like our Sun.  All have an apparent visual magnitude brighter than +6.00.

Rigil Kentaurus A, Alpha Centauri A (α Cen A)
Centaurus
mv = 0.01, mb = 0.72, B-V = 0.71
α2000 = 14h 39m 36s, δ2000 = -60° 50′ 02″
4.30 – 4.34 ly
Triple star system

Alula Australis B, Xi Ursae Majoris B (ξ UMa B)
Ursa Major
mv = 4.73, mb = 5.38, B-V = 0.65
α2000 = 11h 18m 11s, δ2000 = +31° 31′ 46″
28 – 30 ly
Quintuple star system

HR 4523 A
Centaurus
mv = 4.88, mb = 5.55, B-V = 0.67
α2000 = 11h 46m 31s, δ2000 = -40° 30′ 01″
30.0 – 30.1 ly
Binary star system; exoplanet

Eta Coronae Borealis A & B (η CrB A & B)
Corona Borealis
A: mv = 5.577, mb = 6.123, B-V = 0.546
B: mv = 5.95, mb = 6.48, B-V = 0.53
α2000 = 15h 23m 12s, δ2000 = +30° 17′ 18″
57 – 59 ly
Triple star system

HR 8323
Grus
mv = 5.58, mb = 6.18, B-V = 0.60
α2000 = 21h 48m 16s, δ2000 = -47° 18′ 13″
51.9 – 52.5 ly
Single star

Mu Velorum B (μ Vel B)
Vela
mv = 5.59, mb = 6.10, B-V = 0.51
α2000 = 10h 46m 46s, δ2000 = -49° 25′ 12″
116 – 119 ly
Binary star system

HR 7845 A
Capricornus
mv = 5.65, mb = 6.34, B-V = 0.69
α2000 = 20h 32m 24s, δ2000 = -09° 51′ 12″
79 – 80 ly
Binary star system

HR 3578
Hydra
mv = 5.86, mb = 6.39, B-V = 0.53
α2000 = 8h 58m 44s, δ2000 = -16° 07′ 58″
68 – 69 ly
Single star

HR 2007
Orion
mv = 5.97, mb = 6.61, B-V = 0.64
α2000 = 5h 48m 35s, δ2000 = -4° 05′ 41″
49.2 – 49.8 ly
Single star with exoplanet

The Eta Coronae Borealis system is noteworthy in that its two primary components are both G2V stars orbiting each other every 41.6 years.  The third component of this system is a distant infrared dwarf, spectral type L8V.

Two of these G2V stars host at least one exoplanet: HR 4523A in Centaurus and HR 2007 in Orion.

HR 4523A has a planet midway in mass between Uranus and Neptune orbiting every 122 days between 0.30 and 0.62 AU from the star (similar to orbital distance of the planet Mercury in our own solar system).  The other stellar component of this system. HR 4523B, is a distant M4V star currently orbiting about 211 AU from HR 4523A.

HR 2007, a single star like the Sun, has a planet about 78% more massive than Neptune, orbiting every 407 days, more or less.  If this planet were in our own solar system, it would range between the orbits of Venus and Mars, roughly.