upcoming tasks:
1. New Diagram.Use circle intersection method to determine 60
^{o} lead/lag of co orbiting habitats in diagram of Terran orbit.
...............a) Find old slide with Earth orbit about Sol.
...............b) Find old slide with proposed habitat (with mirrors)
...............c) Construct same size circle as Terran orbit.
...............d) Center new circle on Earth, and use two intersections as Alpha/Omega.
...............e) place habitats at 60
^{o} lead/lag on Earth orbit; suggest names: Alpha and Omega
2. Use v
_{fuel} range of .91 c to .99 c to determine if well past Kuiper Belt distances of 1,000 AUs, 2,000 AUs, and so on are within range of spaceship.
3. Expand on more definitions for quick look tables.
Ranges and Planets
v_{fuel} : 10%c to 90%c
Destination | CoHabitat | Mars | Jupiter | Saturn | Uranus | Neptune |
---|
t_{mid}=(2*(D_{mid})/g)^{1/2} | t_{mid}=SQRT(d/g) | d = Typical Dist. (AUs) | 1 | 2 | 5 | 10 | 20 | 30 |
---|
t_{accel} = t_{mid} = t_{decel} | t = t_{accel} + t_{decel} | t= 2 * t_{mid} (days) | 2.83 | 4 | 6.32 | 8.94 | 12.65 | 15.49 |
---|
D_{mid} = d/2 | c=300,000 km/sec
AU = 150,000,000 km | t_{2-way}= 2 * t (days) | 5.66 | 8 | 12.65 | 17.89 | 25.3 | 30.98 |
---|
g = 864 km/sec/day | v_{mid}= g * t_{mid} | v_{mid} (km/sec) | 1,223 | 1,728 | 2,730 | 3,862 | 5,465 | 6,692 |
---|
g = 10m/s^{2}=0.5AU/dy^{2} | planetary escape velocity, e, (km/sec) | n/a | 5 | 60 | 35 | 21 | 23 |
---|
v_{fuel} | %TOGW / day | R_{prac} | Total Two Way %TOGW Needed To Travel |
---|
dec. c | % / day | Days | %TOGW | %TOGW | %TOGW | %TOGW | %TOGW | %TOGW |
---|
0.1 | 2.87% | 8.71 | 16.24% | 22.96% | OUT OF RANGE | OUT OF RANGE | OUT OF RANGE | OUT OF RANGE |
0.2 | 1.41% | 17.73 | 7.98% | 11.28% | 17.84% | OUT OF RANGE | OUT OF RANGE | OUT OF RANGE |
0.3 | 0.92% | 27.17 | 5.2% | 7.36% | 11.64% | 16.46% | 23.27% | OUT OF RANGE |
0.4 | 0.66% | 37.88 | 3.73% | 5.28% | 8.35% | 11.81% | 16.7% | 20.45% |
0.5 | 0.5% | 50.00 | 2.83% | 4% | 6.32% | 8.94% | 12.65% | 15.49% |
0.6 | 0.38% | 65.79 | 2.15% | 3.04% | 4.81% | 6.8% | 9.61% | 11.77% |
0.7 | 0.29% | 86.21 | 1.64% | 2.32% | 3.67% | 5.19% | 7.34% | 8.99% |
0.8 | 0.22% | 113.64 | 1.24% | 1.76% | 2.78% | 3.94% | 5.57% | 6.82% |
0.9 | 0.14% | 178.57 | 0.79% | 1.12% | 1.77% | 2.5% | 3.54% | 4.34% |
IV (increments) | | | = t_{2-way}* (%TOGW/day) |
(Clearly, as fuel particle's exhaust speed, v_{fuel}, increases, the spaceship's two way practical range correspondingly increases. While a v_{fuel} of one tenth light speed, c, might get us to Mars, we need nearly four tenths c to reach Neptune.)
25% is max practical limit. m_{f-LT}= m_{fuel}/(1-v^{2}_{fuel})^{1/2}
k * m_{f-LT} * v_{fuel}/ V_{ship} = M_{ship}
Definitions
m_{fuel} : mass of fuel consumed for each second of flight.
v_{fuel} : velocity of fuel particles as they exit spacecraft (decimal c, light speed). Assume c = 300,000,000 m/s.
m_{f-LT}.: relativistically increased mass of m_{fuel} after being accelerated to v_{fuel}.
V_{ship} : velocity increase of spacecraft during one second of flight (m/sec)
M_{ship} : mass of spacecraft which can be propelled by momentum of fractional light speed, fuel particles.
k: conversion constant. In this case, k= 300.
ff _{day}= (m_{fuel} * 86,400): daily quanity of fuel.
%TOGW/day: Amount of ship's mass needed to convert to energy to propel ship for that day; hence, %TOGW / day = ff_{day} / M_{ship}
R_{prac} : Practical Range. Even perfectly designed propulsion systems have inherent sources of inefficiency. If fuel is 50% of ship's mass, then 25% of total mass can apply toward propulsion.
g = 10 m/s^{2} acceleration due to near Earth gravity. A roughly equivalent value using AUs and days; this turns out to be 0.5 AU/day^{2}. We can also express g (velocity per time) in another way. For example, after accelerating at g for 86,400 secs (number of seconds/day), we achieve 864,000 m/s or 864 km/sec. Thus, we've achieved 864 km/sec per day (g = 864 m/s / day). This, is particularly handy if we want to compare max velocity at mid-trip to planetary escape velocity commonly expressed in km/sec.
CoHabitat :
OUT OF RANGE :
d
v_{mid} velocity of spaceship at midway to destination (or half the distance). Recall that spaceship accelerates to this point then decelerates for 2nd half of travel. Thus, v_{mid} is also v_{max}.
t_{mid}
t_{accel}
t_{decel}
t
t_{2-way}
v_{fuel} : 10%c to 90%c
Destination | | | | | | |
---|
t_{mid}=(2*(D_{mid})/g)^{1/2} | t_{mid}=SQRT(d/g) | d = Typical Dist. (AUs) | 10 | 20 | 30 | 40 | 50 | 60 |
---|
t_{accel} = t_{mid} = t_{decel} | t = t_{accel} + t_{decel} | t= 2 * t_{mid} (days) | 8.94 | 12.65 | 15.49 | 17.89 | 20.00 | 21.91 |
---|
D_{mid} = d/2 | c=300,000 km/sec
AU=150,000,000km | t_{2-way}= 2 * t (days) | 17.89 | 25.30 | 30.98 | 35.78 | 40.00 | 43.82 |
---|
g = 864 km/sec/day | v_{mid}= g * t_{mid} | v_{mid} (km/sec) | 3,864 | 5,464 | 6,693 | 7,728 | 8,640 | 9,465 |
---|
g = 10m/s^{2}=0.5AU/dy^{2} | planetary escape velocity, e, (km/sec) | n/a | 5 | 60 | 35 | 21 | 23 |
---|
v_{fuel} | %TOGW / day | R_{prac} | Total Two Way %TOGW Needed To Travel |
---|
dec. c | % / day | Days | %TOGW | %TOGW | %TOGW | %TOGW | %TOGW | %TOGW |
---|
0.1 | 2.88% | 8.68 | 51.52% | 72.86% | 89.23% | 103.04% | 115.20% | 126.20% |
0.2 | 1.44% | 17.36 | 25.76% | 36.43% | 44.62% | 51.52% | 57.60% | 63.10% |
0.3 | 0.96% | 26.04 | 17.17% | 24.29% | 29.74% | 34.35% | 38.40% | 42.07% |
0.4 | 0.66% | 37.62 | 11.89% | 16.81% | 20.59% | 23.78% | 26.58% | 29.12% |
0.5 | 0.51% | 49.19 | 9.09% | 12.86% | 15.75% | 18.18% | 20.33% | 22.27% |
0.6 | 0.38% | 66.55 | 6.72% | 9.50% | 11.64% | 13.44% | 15.03% | 16.46% |
0.7 | 0.30% | 83.91 | 5.33% | 7.54% | 9.23% | 10.66% | 11.92% | 13.05% |
0.8 | 0.22% | 115.74 | 3.86% | 5.46% | 6.69% | 7.73% | 8.64% | 9.46% |
0.9 | 0.14% | 179.40 | 2.49% | 3.53% | 4.32% | 4.99% | 5.57% | 6.11% |
IV (increments) | ff_{day}
M_{ship} | 25%
%TOGW / day | = t_{2-way}* (%TOGW/day) |
(Clearly, as fuel particle's exhaust speed, v_{fuel}, increases, the spaceship's two way practical range correspondingly increases. While a v_{fuel} of one tenth light speed, c, might get us to Mars, we need nearly four tenths c to reach Neptune.)
m_{f-LT}= m_{fuel}/(1-v^{2}_{fuel})^{1/2}
k * m_{f-LT} * v_{fuel}/ V_{ship} = M_{ship}
Definitions
m_{fuel} : mass of fuel consumed for each second of flight.
v_{fuel} : velocity of fuel particles as they exit spacecraft (decimal c, light speed). Assume c = 300,000,000 m/s.
m_{f-LT}.: relativistically increased mass of m_{fuel} after being accelerated to v_{fuel}.
V_{ship} : velocity increase of spacecraft during one second of flight (m/sec)
M_{ship} : mass of spacecraft which can be propelled by momentum of fractional light speed, fuel particles.
k: conversion constant. In this case, k= 300.
ff _{day}= (m_{fuel} * 86,400): daily quanity of fuel.
%TOGW/day: Amount of ship's mass needed to convert to energy to propel ship for that day; hence, %TOGW / day = ff_{day} / M_{ship}
R_{prac} : Practical Range. Even perfectly designed propulsion systems have inherent sources of inefficiency. If fuel is 50% of ship's mass, and propulsion system is 50% efficient; then, 25% of total mass can apply toward propulsion.
g = 10 m/s^{2} acceleration due to near Earth gravity. A roughly equivalent value using AUs and days; this turns out to be 0.5 AU/day2. We can also express g (velocity per time) in another way. For example, after accelerating at g for 86,400 secs (number of seconds/day), we achieve 864,000 m/s or 864 km/sec. Thus, we've achieved 864 km/sec per day (g = 864 m/s / day). This, is particularly handy if we want to compare max velocity at mid-trip to planetary escape velocity commonly expressed in km/sec.
CoHabitat :
OUT OF RANGE :
d
v_{mid} velocity of spaceship at midway to destination (or half the distance). Recall that spaceship accelerates to this point then decelerates for 2nd half of trip. Thus, v_{mid} is also v_{max}.
t_{mid}
t_{accel}
t_{decel}
t
t_{2-way}
v_{fuel} : 99.1%c to 99.9%c
Destination | Approaching Oort Cloud |
---|
t_{mid}=(2*(D_{mid})/g)^{1/2} | t_{mid}=SQRT(d/g) | d = Typical Dist. (AUs) | 10000 | 20000 | 30000 | 40000 | 50000 | 60000 |
---|
t_{accel} = t_{mid} = t_{decel} | t = t_{accel} + t_{decel} | t= 2 * t_{mid} (days) | 282.84 | 400.00 | 489.90 | 565.69 | 632.46 | 692.82 |
---|
D_{mid} = d/2 | c=300,000 km/sec
AU=150,000,000km | t_{2-way}= 2 * t (days) | 565.69 | 800.00 | 979.80 | 1,131.37 | 1,264.91 | 1,385.64 |
---|
g = .00288c /day | v_{mid}= g * t_{mid} | v_{mid} (dec. c) | 0.41 | 0.58 | 0.71 | 0.81 | 0.91 | 1.00 |
---|
v_{fuel} | %TOGW / day | R_{prac} | Total Two Way %TOGW Needed To Travel |
---|
dec. c | % / day | Days | %TOGW | %TOGW | %TOGW | %TOGW | %TOGW | %TOGW |
---|
0.991 | 0.04% | 642.36 | 22.02% | 31.14% | 38.13% | 44.03% | 49.23% | 53.93% |
0.992 | 0.04% | 682.87 | 20.71% | 29.29% | 35.87% | 41.42% | 46.31% | 50.73% |
0.993 | 0.03% | 729.17 | 19.39% | 27.43% | 33.59% | 38.79% | 43.37% | 47.51% |
0.994 | 0.03% | 789.93 | 17.90% | 25.32% | 31.01% | 35.81% | 40.03% | 43.85% |
0.995 | 0.03% | 865.16 | 16.35% | 23.12% | 28.31% | 32.69% | 36.55% | 40.04% |
0.996 | 0.03% | 966.44 | 14.63% | 20.69% | 25.35% | 29.27% | 32.72% | 35.84% |
0.997 | 0.02% | 1,116.90 | 12.66% | 17.91% | 21.93% | 25.32% | 28.31% | 31.02% |
0.998 | 0.02% | 1,371.53 | 10.31% | 14.58% | 17.86% | 20.62% | 23.06% | 25.26% |
0.999 | 0.01% | 1,938.66 | 7.29% | 10.32% | 12.63% | 14.59% | 16.31% | 17.87% |
IV (increments) | ff_{day}
M_{ship} | 25%
%TOGW / day | = t_{2-way}* (%TOGW/day) | Indicates OUT OF RANGE for 25% TOGW practical limit. |
Clearly, as fuel particle's exhaust speed, v_{fuel}, increases to very near light speed, the spaceship's two way practical range correspondingly increases. While a v_{fuel} of 99.1% c, might increase our practical range to 10,000 AUs; an even greater v_{fuel} of 99.9% might get us to the Oort Cloud and back. (This is a nebulous region of numerous comets; distance varies from 50,000 to 100,000 AUs. Recall that 1 light year is approx. 60,000 AUs.)
m_{f-LT}= m_{fuel}/(1-v^{2}_{fuel})^{1/2}
k * m_{f-LT} * v_{fuel}/ V_{ship} = M_{ship}
Definitions
m_{fuel} : mass of fuel consumed for each second of flight.
v_{fuel} : velocity of fuel particles as they exit spacecraft (decimal c, light speed). Assume c = 300,000,000 m/s.
m_{f-LT}.: relativistically increased mass of m_{fuel} after being accelerated to v_{fuel}.
V_{ship} : velocity increase of spacecraft during one second of flight (m/sec)
M_{ship} : mass of spacecraft which can be propelled by momentum of fractional light speed, fuel particles.
k: conversion constant. In this case, k= 300.
ff _{day}= (m_{fuel} * 86,400): daily quanity of fuel.
%TOGW/day: Amount of ship's mass needed to convert to energy to propel ship for that day; hence, %TOGW / day = ff_{day} / M_{ship}
R_{prac} : Practical Range. Even perfectly designed propulsion systems have inherent sources of inefficiency. If fuel is 50% of ship's mass, and propulsion system is 50% efficient; then, 25% of total mass can apply toward propulsion.
g = 10 m/s^{2} acceleration due to near Earth gravity. A roughly equivalent value using AUs and days; this turns out to be 0.5 AU/day^{2}. Other ways of expressing g (recall accel = speed / time) by using units meters/sec over days (864,000 m/s / day) or fractional light speed per day (.00288c /day).
CoHabitat :
OUT OF RANGE :
d
v_{mid} velocity of spaceship at midway to destination (or half the distance). Recall that spaceship accelerates to this point then decelerates for 2nd half of trip. Thus, v_{mid} is also v_{max}.
t_{mid}
t_{accel}
t_{decel}
t
t_{2-way}
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