Hidden Wonders of the Southern Sky

Here in southern Arizona, we can theoretically see 92.4% of the celestial sphere. I say “theoretically” because atmospheric extinction, light pollution, local topography, and obstructions limit the amount of the celestial sphere that we can see well. Also, far southern objects (down to δ = -58° at φ = 32° N) spend very little time above our horizon each day.

Practically speaking, then, we see somewhat less than 92% of all that there is to see from spaceship Earth.

Percent of the Celestial Sphere Visible

\% = 50\left [ 1-sin\left ( \left|\varphi \right| -90^{\circ}\right ) \right ]

where |φ| is the absolute value of your latitude in degrees

What are the most prominent objects we are missing, and what objects that we can see are they closest to?

Alpha Centauri

Never visible north of latitude 27° N, the nearest star system beyond our solar system is Alpha Centauri. Alpha Centauri A & B are bright stars, having a visual magnitude of 0.0 and +1.3, respectively, and in 2023 they are separated by just 8 arcseconds, about 1/4 of the angular separation between Albireo A & B. While Alpha Centauri A & B—which orbit each other once every 79.8 years—lie just 4.36 ly away, a faint red dwarf companion, Proxima Centauri (shining at magnitude +11.1), is even closer at 4.24 light years. It is not yet known whether Proxima Centauri, discovered in 1915, is gravitationally bound to Alpha Centauri A & B, or just presently passing through the neighborhood. Proxima is a full 2.2° away (over four moon-widths) from Alpha Centauri A & B.

When Arcturus (α Boo) and Zubenelgenubi (α Lib) are crossing our celestial meridian, so are Alpha & Proxima Centauri below the southern horizon.

Large Magellanic Cloud

The Large Magellanic Cloud (LMC), the largest satellite galaxy of our Milky Way galaxy and easily visible to the unaided eye, lies directly below our southern horizon when Rigel has crossed the meridian and Bellatrix is preparing to do so.

Small Magellanic Cloud

The Small Magellanic Cloud (SMC), the second-largest satellite galaxy of the mighty Milky Way lies underneath our southern horizon when M31, the Great Andromeda Galaxy, crosses the meridian near the zenith.

47 Tucanae

The 2nd brightest globular cluster in the sky (after Omega Centauri) is impressive 47 Tucanae. It is just 2.3° west and a little north of the Small Magellanic Cloud, so crosses the meridian below our horizon just as M31 is nearing the meridian.

Eta Carinae Nebula

Four times larger and brighter than the Orion Nebula, NGC 3372, the Eta Carinae Nebula, is a spectacular star-forming region containing a supermassive (130 – 180 M) binary star (Eta Carinae) that may go supernova at any time. When Leo the Lion is straddling the meridian, the Eta Carinae Nebula sneaks across as well.

Any other spectacular objects I should be including that are south of declination -58°? If so, please post a comment here.

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?