Star jumping

This astronomy problem set is a bit of a fantasy wrapped into a reality. The speed of an object such as a space ship carrying you is calculated using applied acceleration.

This is a visual image of the Sun with some sunspots visible on the photosphere. The two small spots in the middle have about the same diameter as our planet Earth. Credit: NASA.{{free media}}

A simple calculation is v = v₀ + a*t. Here a speed with a specific direction (called a velocity, v) is calculated by applying an acceleration for a specific amount of time (t).

Generally, you probably won't survive accelerations above a couple of g's.

Your ship is in orbit above the Earth and your shuttle has just uploaded you into your ship.

As an endorser of the limits of the speed of light you know it would take you at least 4.1 years to get to Proxima Centauri at just under the speed of light.

Radiation

Connect the stars using Universal coordinate converter NASA angle of separation and stellar distances from trigonometric parallax measurements with a finite jump fuel level.

Problem 1

The Earth's standard acceleration due to gravity is g = 9.80665 m/s². Using right ascension and declination, locate Proxima Centauri.

Your ship is now moving toward Proxima Centauri at 100 m/h. Your ship has sub-relativistic drive up to about 50% c. Begin applying a two g acceleration. How much time will it take your ship to reach 0.5 c? How close to Proxima Centauri are you?

If you are less than half way there you may want to cut in your field accelerator. This device converts the local electromagnetic environment into an acceleration inside a chamber much like a rocket engine.

The difference is that this engine's accelerational capability is subject to local fluctuations in the electromagnetic environment. Once you initiate it, you may continue to accelerate as before. It is fundamentally speed of light independent. What is the maximum speed your ship and you can reach before you need to start slowing down for your arrival at Proxima Centauri?

At sub-relativistic speeds your ship consumes nuclear fuel at the rate of 1 liter per one day application of this accelerating engine.

At above 50% c, your electromagnetic accelerating engine consumes about twice as much nuclear fuel equivalents.

Fuel sources can be obtained near stars by absorbing as much low atomic number gas as possible or by consuming through fission elements above iron.

Each liter of hydrogen gas absorbed is equivalent to your current fuel consumption. But, one gram of fissionable elements yields a year's supply of fuel.

How much fuel will your journey to Proxima Centauri consume?

Elements lower in atomic number than iron are consumed in the fusion process. These are approximately consumed as indicated for hydrogen.

Although I aimed your ship toward Proxima Centauri, now that you are there and know how your fuel is consumed you can return to Earth orbit if you wish and pick your own direction to proceed in.

Or, if you like Proxima Centauri you can finish taking on fuel and pick your next location.

Problem 2

File:Aladin2014.04.25-00-43-54.611.png

This is a diagram of the astronomical sources within 20 arc minutes of Proxima Centauri. Credit: Aladin at SIMBAD.{{fairuse}}

The round trip to Proxima Centauri at about 4.1 lyrs is a good estimate of the total fuels capacity of your vessel. If you dare to go elsewhere either from Earth orbit or from Proxima Centauri, you now know your various fuel consumption rates for sub-luminal, near-luminal, and super-luminal travel.

Refueling at Proxima Centauri depends on its neighborhood similarity to that of the Earth's regarding the Sun. Proxima Centauri has more of a proto-planetary disc so you may be able to refuel in 25 % of the time it would take to cruise around the solar system if no hominin bases were present.

Your next destination depends on the availability of local or on-the-way fuel sources and how far it is.

HD 126793 is at RA 14 30 12.65686 Dec -62 51 44.4650 and 176 lyrs from Earth, based on its trigonometric parallax. Can you find a way to travel to it?

How long would the trip take? How many times would you need to refuel?

If you could bring along reserve tanks where 1 % must be used to tow and each contains 100 times as much fuel as your ship similarly distributed in type, would one or two be enough?

If your ship can absorb from the ISM as you travel, how much additional fuel will this provide based on its column density?

At the right is a diagram of the astronomical sources within 20 arc minutes of Proxima Centauri (at the center). HD 126793 is almost due South and has an arrow leading out from it. The various symbols are circle with an arrow (a star), red square (a nebular, PN or SNR), red plus (HII region), red diamond (IR object), * (UV object), X (X-ray object), and Dk Neb is a dark nebula.

Problem 3

One major limitation of your ship is its limit on acceleration due to you and any of your friends inside. The inhabited planet around HD 126793 has a novel charge monitoring device that could be fitted into your ship. Its benefit is that for one field accelerator unit per 5 c units it can pull on all your internal and suit charge units so that you and each of your friends can accelerate with your ship without harm up to ten accelerations before needing to be recharged.

Do you want one?

If you can trade for one on the planet around HD 126793 with four fissionable units of such fuel, how much faster can you go returning to Earth orbit?

How much less time would the return trip take?

What is the maximum velocity you can attain considering that you can decelerate comparably?

Problem 4

You probably noticed in your trip to the star of your choice or from your knowledge of the ISM gained in this course that the ISM between any two stars is not empty. Depending on what's out there, your ship may need some kind of protection from radiation.

At the maximum speed you attained in problem 3, mass may be considered to calculate energy independent of relative speed. If your ship as presently configured can only withstand the equivalent of a kiloton of TNT, had you hit anything, would you have survived?

Vega is about 25 lyrs from Earth. A planet there in orbit may allow you to trade for a kind of deflector that will protect you up to speeds of 100 c for objects below 1 kg. Would this be worth several fissionable fuel units?

Problem 5

Problem 4 brought up a matter of great importance: the possible presence of ship-damaging particles between destinations.

While a good shielding system is clearly necessary, what about a forward looking sensory system?

When traveling at 100 c, regular radiation transceivers may not work. In addition to communication with home, how do you detect larger particles or denser particles?

Tachyonic radar may be a reasonable idea. Tachyonic infrared, X-ray, ultraviolet, and microwaves may work as well.

This technology is not available on Earth. Are there possible superluminal sources nearby that you can reach with your ship's current configuration? Perhaps an inhabited planet near such sources would be willing to trade such a detection or communication system.

From superluminal astronomy and your current location, find three to five nearby stars along the approximate line of sight to one of these superluminal sources or another you may have found. Plot an exploratory course to at least one.

Is your ship's present status sufficient to undertake such an exploration?

Hypotheses

Traveling faster than light is possible.

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