PROFILE TO THE PLANETS
Mankind currently orbits to other planets.
It takes no fuel, but it takes a while.
Much quicker gforce will need fuel.
Gforce acceleration will need a profile.
It takes no fuel, but it takes a while.
Much quicker gforce will need fuel.
Gforce acceleration will need a profile.
KBO  Neptune  Uranus  Saturn  Jupiter  Mars 

40 AU  30 AU  20 AU  10 AU  5 AU  2 AU 
A gforce vessel could travel a LOS path much, much quicker then an orbiting vessel can travel a corresponding transfer orbit.
Destination  Transfer Orbit  Gforce Propulsion  

SemiMajor Axis  ^{2}Typical LOS  ^{3}SO Dist  Travel Times  ^{4}Constant  ^{5}Gforce Profile  
a_{D}  d  C_{T}/2  T_{Y}  T_{d}  Accel  t_{Acc}  t_{Dec}  t_{Ttl}  
^{1}NEO  n/a  1 AU  n/a  n/a  n/a  2.00 dy  1.41 dy  1.41 dy  2.83 dy  
Mars  1.52 AU  2 AU  5.54 AU  0.71 Yr  258 dy  2.83 dy  2.00 dy  2.00 dy  4.00 dy  
Jupiter  5.2 AU  5 AU  12.33 AU  2.73 Yr  997 dy  4.47 dy  3.16 dy  3.16 dy  6.32 dy  
Saturn  9.51 AU  10 AU  19.14 AU  6.02 Yr  2,200 dy  6.32 dy  4.47 dy  4.47 dy  8.94 dy  
Uranus  19.18 AU  20 AU  34.58 AU  16.03 Yr  5,854 dy  8.94 dy  6.32 dy  6.32 dy  12.65 dy  
Neptune  30.06 AU  30 AU  51.55 AU  30.61 Yr  11,179 dy  10.95 dy  7.75 dy  7.75 dy  15.49 dy  
Kuiper Belt  40 AU  40 AU  67.47 AU  46.42 Yr  16,954 dy  12.65 dy  8.94 dy  8.94 dy  17.89 dy  
Observed  Assumed  π√(a_{τ}^{2}+b_{τ}^{2}) √2  (1+a_{D})^{3/2} 5.656  365.26×T_{Y}  √(2×d) √g  √(2(d/2)) √g  √d √g  2√d √g 
Note: 
2×(d/2)
 =  d 
Thus, 
√(2×(d/2)/g)
 =  √(d/g) = t_{Acc} = t_{Dec} 
Destination  Transfer Orbit  Gforce Propulsion  

Transfer Distance  Typical LOS  SemiMajor Axis  Velocities  No Slowdown  Gforce Profile  
d_{τ}  d  a_{τ}  v_{max}  v_{ave}  v_{min}  v_{Max}  v_{Dept}  v_{Final}  v_{Dest}  
NEO  3.14 AU  1 AU  n/a AU  n/a  n/a  n/a 
1,728 k/s
 0  1,222 k/s 
0
 
Mars  5.54 AU  2 AU  1.26 AU  32.75 k/s  26.25k/s  21.54 k/s 
2,444 k/s
 0  1,728 k/s 
0
 
Jupiter  12.33 AU  5 AU  3.1 AU  38.61 k/s  14.85k/s  7.43 k/s 
3,864 k/s
 0  2,732 k/s 
0
 
Saturn  19.14 AU  10 AU  5.255AU  40.11 k/s  10.65k/s  4.22 k/s 
5,464 k/s
 0  3,864 k/s 
0
 
Uranus  34.58 AU  20 AU  10.09AU  41.11 k/s  7.23 k/s  2.14 k/s 
7,728 k/s
 0  5,464 k/s 
0
 
Neptune  51.55 AU  30 AU  15.53AU  41.48 k/s  5.67 k/s  1.38 k/s 
9,465 k/s
 0  6,693 k/s 
0
 
K.B.  67.47 AU  40 AU  20.5 AU  41.65 k/s  4.87 k/s  1.04 k/s 
10,929 k/s
 0  7,728 k/s 
0
 
TABLE1  Assumed  1+a_{D} 2 
 _{dτ ÷ tτ} 



G = 6.67428 × 10^{11} m^{3}/(kgsec^{2})
 M_{☉ }= 1.98892 × 10^{30} kg 

 


Gotta Slowdown well prior to Destination
As a matter of fact, if we applied a consistent gforce vector all the way to Jupiter, TABLE5 shows that ship velocity would achieve almost four thousand kilometers per second. EXAMPLE: A typical LOS distance between Earth and Jupiter could be 5 AU (depends on relative orbital positions).
Time required to gforce accelerate for 5AU is
This would be way too fast. Jupiter itself orbits the Sun at about 13 km/sec; at 3,864 km/sec, ship could not land, orbit or do anything except glimpse at Jupiter as it quickly passes by.
 
OPTIMAL SLOWDOWN
To maintain constant gforce for entire flight, reverse propulsion vector at midpoint.
Gforce Profile: Acceleration + Deceleration.
To choose the appropriate SLOWDOWN point, consider that we want constant gforce throughout the entire flight; thus, we want acceleration time/distance to equal deceleration time/distance. Therefore, it makes sense to reverse propulsion vector at midpoint (or midtime) of our trip. TABLE5: Three "Gforce Profile" columns:

Transfer Orbit

Gforce Profile
 

Flight Path
 
Shape
 ⇓ No enroute propulsion constrains vehicle to the path of an elliptical orbit.  ⇑ Constant gforce propulsion enables vehicle to closely approximate a straight line. 
Length
 ⇓ Longer  ⇑ Shorter 
Control
 ⇓ No enroute propulsion means unable to adjust flight path prior to intercepting destination orbit.  ⇑ Adjust propulsion vector as required to maintain flight path. 
Target Aspect
 ⇓ Due to everchanging direction of flight, destination remains obligue throughout most of flight.  ⇑ Line of Sight (LOS) really applies to this profile, target remains straight ahead throughout entire flight. 
Timing
 ⇓ Launch Window must be considered. Since nonpowered flight must fly an orbit from dept to dest, duration will take years, thus considerable effort and waiting time required to sync prop dept from Earth to arrive at dest.  ⇑ Launch Window is not important. Powered flight enables vehicle to fly LOS path from dept to destination at any time. Very slight lead required, which can be accomplished enroute. 
Flight Duration

Orbital Speeds Take
Months to Years

Gforce Flights Reduce to
Weeks and Days 
Training
Time  ⇑ Lots of time to prepare for mission at destination. Enough time to study entire college courses.  ⇓ No time to train; crew will be extremely busy getting ready for subsequent flight phases. 
Social
Time  ⇑ Lots of time to establish essential relationships. Marry, have babies and many other things.  ⇓ Much shorter durations barely give passengers enough time to know each other. 
Inflight Morale
 ⇓ Cabin Fever! If ship's population is too few, lack of social interaction will likely cause severe depression amongst many of those onboard. 
⇑ No time for cabin fever.
Crew and pax are far too busy 
Public
Interest 
⇓ Eventually public will lose interest.
Media will turn to other matters.  ⇑ With impending mission accomplishment, public will more likely maintain interest for first few missions. Eventually, interplanetary gforce flights will become routine and will cease to be "news". 
Fuel

⇑ Extremely fuel efficient.
Virtually no fuel is required other then small amount needed to change orbits.  ⇓ Large Quantity Needed. Relative amount is small (very small %TOGW due to near light speed exhaust particles); however, even a small percentage could be thousands of tons). 
Large
Populations

⇓ Extremely difficult!
Quantity of food storage nearly impossible.
Alternatives: Inflight agriculture; Stasis: (inflight hibernation) is currently a risky proposition  ⇑ Still challenging, but transporting large pop for short durations has got to be easier then for long durations. 
Small
Populations

⇓ Quantity of food to be stored is more practical but still challenging.
As pop shrinks, socializing opportunities correspondingly decrease.
 ⇑ Even for short durations, smaller populations have less problems then large pops. 
Radiation
Hazards

⇓ Longer durations mean more REMs to hit ship and likely affect crew/pax.
Must add shielding to infrastructure which affects construction process and performance.
 ⇑ Shorter durations mean fewer REMs. However, gforce ships will still need to shield occupants from inflight radiation. 
Need to Bleed Speed
(Deceleration Requirement)  
⇑ No need.
Transfer orbital velocity stays within a relatively close range.  ⇓ Indeed, need is great. Considerable energy is needed to gforce accelerate to enormous speeds at midpoint. Same amount of energy needed to bring velocity back to operational levels. Trade off for extremely short duration of flight.  
Inflight Navigation
 
⇓ Moot point! Without viable inflight propulsion, unable to adjust course. Even though destination will not be "straight ahead" for most of flight, there is no choice but to stand fast and wait for orbit change.  ⇑ Flying nearly straight line course, destination stays within sight for entire flight. (Thus, Line of Sight (LOS)!) If course adjustments must be made, there is plenty of available propulsion capability to do so.  
Gravitational Environment
 
Free
Fall  ⇑ Continuous free fall can be fun! It might even prove useful, for example, takes less effort to move heavy loads.  ⇓ No free fall until gforce is turned off. If that happens, ship stays at that velocity until gforce starts again. 
Earth
Like  ⇓Long term effects of gravity deprivation can be substantial: muscles atrophy, bones get brittle, and other medical dysfunctions.  ⇑ Maintaining Earth like gravity facilitates transitions to/from residing on Earth via residing in space. 
Technology
 
⇑Current.
TO has been used many times  ⇓ Achievable but not there yet. Particle accelerators are old news and ion drives are new news, but maintaining a tightly controlled, consistent flow of kilograms per second for extended periods (days) is very much future news. Thus, a spaceship with such a propulsion system remains a TE for now. 
Assume: Exhaust particle speed: V_{Exh} = .866c;
then, d_{c} = .866 and m_{r} = 2 = 1÷√(1d_{c}²)
For first half of flight, propulsion vector points opposite to direction of flight (in the same manner that current rocket propulsion systems work).
For adequate slowdown, the spaceship must reverse the propulsion vector's direction at midpoint.
SUMMARY: Gforce profile uses constant stream of accelerated exhaust particles throughout the flight.
TE assumes water as source of plasma (ionized particles to form propulsion stream), because it's plentiful, readily obtained and easily heated to steam, thence to plasma (just heat it!!). Water has many other useful qualities.
Momentum Exchange
From previous work, TE assumes mass and speed of exhaust particles directly affect propulsion capacity. Thus, Expelling one gram per second at 10% light speed can propel a ship of 3 metric tons (mTs) with gforce. 1,000 grams per second (1 kg/s) can propel a 3,000 metric Tonne (mT) vessel (size of small ship or yacht). 1 kg/s at 20% light speed can gforce propel 6,000 mTs. TE farther assumes relativistic growth also contributes to propulsion effect of exhaust particles. For example, if original mass of 1 kg is accelerated to .866 c, then Lorentz Transform shows a doubling in size to 2 kg of exhaust particles. Thus, 1 kg/s accelerated to 86.6% light speed can gforce 50,000 mTs. From previous work, TE further simplifies by determining fuel requirements as a percentage of ship's Take Off Gross Weight (TOGW).
Thus, TE makes hypothesis:

TE assumes efficiency factor, ε, to account for ineffective use of exhaust particles. This is due to inevitable design flaws as well as peripheral energy needs.
Thus, TE arbitrarily assumes ε = 2 to include all energy needed to insure adequate gforce propulsion. To further clarify, TE adjusts a couple of statements from Table3 as follows:
To propel a ship of 3 metric tons (mTs) with gforce, ship's power system must consume 2 grams per second.
Actual efficiency will need to be determined;
it will no doubt improve as gforce technology advances.
 
TWO WAY TRAVEL:DEPARTURE AND RETURN
TE assumes it'll be a while before mankind learns to harvest fuel from spaceborne resources; thus, initial gforce missions will have to carry enough fuel to go and return.
TE assumes that scope of interplanetary missions includes a return leg. Circumstances compell TE to further assume that fuel for return must be included in ship's Take Off Gross Weight (TOGW). Thus, TE must double fuel requirements from corresponding cells in Table 4.
Onboard fuel must suffice to travel to destination and return since there are no other fuel supplies available.
Very little fuel will be required for in orbit operations while at destination; we'll assume it to be small enough to disregard. Perhaps our interplanetary vessel will immediately discharge an orbiting payload and quickly return.
Good judgment dictates considerable margin in addition to fuel planned for consumption during the two way trip. However, our thought experiment will live life on the edge and just determine how much fuel is needed to travel to our interplanetary destination and return.

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