TO NEIGHBOR STARS
Alpha Centauri (AC) is Sol's nearest neighbor.
AC is a cluster of three stars about 4.3 light years (LYs) away.
Our thought experiment notionalizes an interstellar spaceship with an particle accelerator propulsion system which constantly accelerates the vessel at gforce. Such a spacecraft could get us to nearby planets within days AND also simulate near Earth gravity throughout the trip; but interstellar travel would take much longer.
Recall that interplanetary trips require following gforce profile . Gforce accelerate for a few days to the midpoint of the trip. Precisely at midpoint, reverse direction of spacecraft so the ship's exhaust vectors now points opposite direction of flight. Gforce decelerate for the remaining half of journey until ship reaches destination. Thus, after one day of gforce travel, a vessel could achieve velocity of 847.8 kilometers per second (kps) about .283 percent of the speed of light, c.
Interstellar travel requires a new profile. Consider following points: 1. Acceleration to Midpoint is impractical. Interplanetary distances are just a few AUs; thus, gforce acceleration will take just a few days. However, midpoint to the nearest star, AC, is over 2 LYs, over 120,000 AUs; this takes years of gforce propulsion which could easily consume the ship's weight in fuel. 2. Interstellar Gforce Velocities approach c, light speed. In contrast, interplanetary gforce flights never even approach c. For example, a gforce flight to Mars will usually require less than three days of acceleration and will achieve max velocity less then 1%c. 3. Special Relativity Theory maintains that any observer always measures c at 299,792 kps regardless of observer's own velocity. Numerous published works in both theory and experiment continue to confirm that no object with mass can exceed c; but continuing acceleration will take you closer and closer to that relativistic limit. Consider cases where a gforce vessel accelerates for 100 days, 200 days or any number of days. After any given duration, let the gforce vessel release a module with no propulsion; that module stops accelerating and maintains velocity at time of release. An occupant on that module will observe the gforce vessel accelerating away; as a matter of fact, TE assumes the module observer will always observe a velocity increase of .283%c after an additional day has elapsed. 
A year of constant gforce acceleration can achieve significant fraction of light speed.
For longer durations, "t × g" no longer works. EXAMPLE: After one year of gforce propulsion, V_{1Year}= 365.25 days ×Δ = 1.033c, an impossibility!!! Resulting velocity exceeds c, which contradicts Einstein's Special Theory of Relativity. Thus, previous work proposes the Remainder (R) concept to determine gforce velocities. After one day, an Earth bound observer measures gforce vessel velocity at .283%c with remaining velocity of 99.717%c till the speed of light. Thus, R = c (1Δ). After any given number (n) of gforce days of travel, above module is released. After another day (n+1), TE assumes that module occupant will observe gforce vessel increase velocity to .283%c with a R of 99.717%c until light speed. Furthermore, TE assumes that Earth bound observer can use Remainder (R) exponentials to predict velocity for any number of gforce days. Following table predicts vessel velocity after one year (365.25 days) of gforce.
EXAMPLE: After one year of gforce propulsion,
an Earth bound observer measures velocity of 64.5% c.  
For Interplanetary Destinations:
Traditional Newtonian Agrees with Relativistic Einsteinian
Newton formulas: V_{t} = t × Δ and d_{t} = t × g work well for the special case of extremely slow velocity, the portion of the speed spectrum where humanity lives.
EXAMPLE: For a trip to Mars, a vessel might need two days of gforce acceleration to reach midway of the journey. After two days of gforce propulsion, interplanetary gforce spaceship velocity is still less then 1% of light speed.
V_{t} = 2 days × .283%c/day = .566c
We see the Einsteinian velocity formula V_{t }= c [1(1Δ)^{t}] gives almost the same velocity for two days of gforce.
V_{2 }= c [1(1.002826)^{2}] = 0.564%c
ANOTHER EXAMPLE: A Kuiper Belt Object (KBO) destination might need 10 gforce days to reach midpoint.

For Interstellar Destinations:
Traditional Velocity Values Diverge from Relativistic
If we expand gforce duration from days to years, we see a wide divergence between Newton and Einstein.
After one year of gforce acceleration, we see following difference:
Newtonian value is clearly wrong; nothing exceeds c.
Previous work leads TE to the Einsteinian method.
Newtonian is clearly wrong; vessel cannot exceed light speed. Previous work leads TE to assume Einsteinian method produces a reasonable gforce velocity.

Gforce acceleration to the midpoint between stars would take too long; a starship would easily consume well over 100% of its mass in fuel during the multiyear voyage.
Thus, interstellar flights need three phases:
1) ACCELERATION brings ship to a near light speed velocity which facilitates a reasonable cruise duration. If our spaceship accelerates at gforce for 323 days;
It will consume perhaps 25% of available fuel (depending on design efficiencies and exhaust particle velocity). However, acceleration distance
2) CRUISE. Interstellar flights will need a lengthy constant velocity duration to conserve fuel. This profile assumes a cruise phase at .6c for several years. Earth bound observers will see the cruise portion take several years; but onboard crew and passengers will observe the trip taking much less time due due to relativistic time dilation. Maintaining Earthlike environment will be very important during this multiyear period; however, humans will have been living in asteroid habitats (which rotate to simulate Earth gravity) for many decades and probably generations prior to going interstellar. Thus, going interstellar will require some midflight reconfiguration for the cruise portion. 3) DECELERATION. About .3 LY from destination, spaceship must decelerate from .6c to an operational velocity. Assuming consistent gforce, this will take same duration as the acceleration phase (323 days) and another large portion of fuel. 
Propulsion time sums durations for acceleration (t_{Acc}) and deceleration (t_{Dec}); propulsion needs fuel to apply gforce. However, cruise duration is excluded since no propulsion is applied during this lengthy phase. TRADEOFFS. Duration of 323 days for acceleration/deceleration was chosen arbitrarily. Flight planners can choose any duration as long as they observe the tradeoffs between fuel availability and total trip time.
Consider following interplanetary flight assumptions:
Simulate Earth Gravity Throughout Voyage.
During gforce acceleration, a spaceship can attain enormous speeds and simulate earthlike gravity.
During cruise portion of voyage, vessel simulates gravity via centripetal force due to spin about its longitudinal axis (same as asteroidal habitats throughout the Solar System).
For final portion of flight, the vessel must use gforce to decelerate for same time/distance as for acceleration phase.
 
 
SUMMARY  

AXIOM. Light speed is absolute and puts limits on interstellar travel. Even at light speed, interstellar flights take years for photons, virtually massless particles. Since human spaceships will contain large quantities of mass, the best we can hope for is to approach light speed; we can never attain it and certainly never surpass it. ASSUMPTION1. Self Contained Fuel. Prior to departure, notional spaceship will collect and carry sufficient fuel for planned propulsion durations: acceleration (t_{Acc}) and deceleration (t_{Dec}). ASSUMPTION2. Earthlike Gravity. We currently know two methods to achieve Earth like gravity on an interstellar vessel. 1) Constant Gforce Acceleration. If an onboard propulsion system can increase ship's velocity by 9.80665 m/s for every second of "powered" flight'; then, ship's contents will feel a force equivalent to Terran gravity. 2) Centrifugal Force. During nonpowered cruise phase, the gforce alternative is a carefully controlled spin to generate gforce by 'pressing' contents against the inside of the outer hull. If ship was cylindrical in shape and rotated around its longitudinal axis; spin rate (degrees per second) will be inversely proportional to radius (as cylinder size increases, less spin rate is needed to maintain centripetal acceleration of 9.80665 m/s/s).  ASSUMPTION3. Three Phases. Initial calculations indicate that a vessel powered throughout entire interstellar voyage could easily consume fuel greater than ship's total mass. Thus, TE assumes following flight profile. Acceleration Phase. Ship starts off trip by accelerating at gforce for 365.26 days, this will bring it to a velocity of .6443c (64.43% of light speed). Occupants will feel a gravity like force drawing them back to departure. Cruise Phase. Due to fuel considerations, ship will stop propulsion after 1 year and lose gforce from back of ship. Thus, ship will maintain constant velocity of 64.43c for entire cruise phase (majority of voyage). To maintain Earth like gravity, ship will then have to reconfigure to gain gforce against inside of outer hull by starting sufficient spin to gain gforce. Deceleration Phase. For 1 year prior to arrival at destination, ship will end this trip by slowing down from 64.43% c at same gforce rate of acceleration phase. 
VOLUME I: ASTEROIDAL 

VOLUME II: INTERPLANETARY 
VOLUME III: INTERSTELLAR 
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