Sunday, December 23, 2012

ACCELERATE TO THE PLANETS


G-force to the planets in days.





Consider a thought experiment:
Let a notional spaceship accelerate
at rate g (10 m/sec²)

between points within the Solar System.





 During first half of journey,
g-force spaceship gains so much speed ,
 that it must spend second half slowing down.





Nicholas Copernicus (1473-1543) postulated the Sun as the center of the Universe.

Born in Torun, Poland, Copernicus first studied astronomy and astrology at the University of Cracow (1491-94). After considerable more study in mathematics, medicine and law; he returned home for an extremely fruitful life.
In 1514, he began to circulate in manuscript the 'Commentariolus' (A Brief Description), in which he criticised then prevalent Ptolemaic system for not adhering to the principle of uniform circular motions and offered instead his own system in which the earth and all the other planets rotate around the sun.
By the 1530s, Copernicus's reputation as a skilled mathematician had even reached the ears of the Pope. Thus, the distinguished Professor Georg Joachim Rheticus (1514-1574), University of Wittenburg, included Copernicus on a tour of distinguished scholars and visited Copernicus in 1539. Thus, Rheticus reported Copernicus' heliostatic theory in his subsequent book, Narratio Prima (First Report on the Books of Revolution) in 1540 at Gdansk. Following the favourable reception of the Narratio Prima, Rheticus persuaded Copernicus to publish a full account. This became the De Revolutionibus Orbium Coelestium.
Of course, we currently use non-powered spacecraft to orbit throughout the Solar System. They routinely travel between planets via "transfer orbits", which take months and years. Furthermore, interplanetary trips must be timed to accommodate planetary positioning; such synchronization requirements can add years of further delay. Thus, human transport via transfer orbit is infeasible, and practical payloads are limited to Artificial Intelligence (AI) devices.  Transfer orbits between planets at constant velocity will take months and years. This might work for robots and other AI devices; it probably would not work so well for humans and other biologics.











On the other hand, g-force spacecraft would enable humanity to routinely travel between planets within days. Such vessels would no longer be constrained to transfer orbits, and humans could routinely transit the planets in days and weeks. 





G-force acceleration will quickly take the vessel to enormous speeds; thus, such voyages must observe a flight profile:
  • PHASE I: 1st Half of Flight.  Due to continuous "g-force" acceleration, vessel attains very high speed.
  • PHASE II: 2nd Half of Flight. Vessel decelerates to orbital velocity at destination.
  • Interplanetary positioning is not nearly so great a factor. g-force propulsion adds considerable capability.
Thus, g-force propulsion can make human transport routine with unlimited payloads.





Copernicus ordered the planets and proposed the universe to be centered on Sol (our sun) versus Terra (our Earth) then considered as the center of the universe. Thus, Copernicus is often incorrectly portrayed as a controversial figure who advocated a heliocentric system for the express purpose of overthrowing existing systems and institutions. In fact, his monumental work follows parameters and data from Ptolemy, and it's even dedicated to the Pope in a fashionable style.
He presents a model in which the earth rotates daily and orbits the sun, but the sun itself was not quite in the center of the universe. He established the order of planets and devised a system which accounted for the movements of planets without equants, but he was motivated by the desire to establish uniform circular motion, itself a classical ideal. Copernicus certainly believed that this was the true system of the physical universe, but this conviction was not shared widely by his peers for contemporary reasons.
"On the Revolutions of the Heavenly Spheres" was published in March 1543 at Nuremberg. Copernicus died two months later. (For more.)
PHASE I. G-FORCE ACCELERATION TO MIDWAY
Departing Earth at an initial velocity of essentially zero, our notional spaceship constantly accelerates at g (0.5 AU/day2)
  • simulates gravity; great comfort for the many humans and animals inside the vessel.
  • travels much quicker then orbiting vessels.
EXAMPLE: After only 3.16 days, we reach midway (2.5 AU) of our 5 AU journey to Jupiter.
Max speed is achieved at the midway point because the vessel must slowdown for the 2nd half of the voyage.
Typical Accelerate Max Velocity
Distance
fm Earth
Departure
to Midway
(at midway)
d dAcctAccVMax
NEO
1 AU
0.5 AU
1.41 dy
1,218 km/s
Mars
2 AU
1.0 AU
2.0 dy
1,728 km/s
Jupiter
5 AU
2.5 AU
3.16 dy
2,730 km/s
Givend / 2√(d/g)

g= 0.5AU/day2
tAcc×g

g=864kps/day
Let d be total distance from departure to destination; then, distance to midway is d/2.  Since we've chosen to accelerate to midway, this is also the value of the acceleration distance:  dAcc = d/2 
Then, compute acceleration time: tAcc = (2 × dAcc/g) = (d/g)
Finally, compute max velocity:  VMax = tAcc × g
g 10 m/sec

sec
864 km/sec

day
0.5 AU/day

day
0.289%c

day
Equivalent Expressions of g
1) Since g-force vessels can travel AUs in days, describe acceleration value as g=.5 AU/day², a value very close to 10 m/sec2.
2) Vessel increases speed 864 kilometers per second (kps) for each day of g-force acceleration; thus, g = 864 kps/day.
G-force profiles would make for simpler and quicker interplanetary flights. If a spaceship could travel throughout the inner Solar System in days and weeks, then interplanetary travel would become routine for human passengers and all kinds of cargo.

Routine??? Well, millions of people now travel by air every day, but many people would still consider flying a novel experience. Just as international air flights will never become as common as vehicular travel between cities, interplanetary space flights will never become as common as air travel on Earth. However, interplanetary flights can become much more frequent and accessible then now.

G-force spacecraft will constantly accelerate at 10 meters per second per second (10 m/sec2), the same acceleration as a free falling object near Earth's surface. To paraphrase Einstein: "If gravity causes objects to accelerate at a certain rate; perhaps, same rate acceleration can apply gravity like force to an elevator." Thus, we could accelerate at rate, g, in space (far away from Earth's gravitation field) to simulate Earth surface gravity (thus, the term "g-force" acceleration). This inflight gravity would make flights much more comfortable for our human occupants.

 Even better, constant g-force acceleration would reduce flight times from months and years to just DAYS; this would make interplanetary travel much more feasible for ordinary folks versus only available for an exclusive group of well trained astronauts.

Fortunately g-force can be used to both accelerate and decelerate a vessel. After a certain duration of g-force acceleration, vessel will achieve a very high "max velocity". Same duration of g-force deceleration can bring vessel to orbiting speed at destination.
Max Velocity Decelerate Time Total Time
VMax tDectTtl
NEO
1,218 km/s
1.41 dy
2.83 dy
Mars
1,728 km/s
2.00 dy
4.00 dy
Jupiter
2,730 km/s
3.16 dy
6.32 dy
Saturn
3,864 km/s
4.47 dy
8.94 dy
tAcc×g

g=864kps/day
VMax/g 

√(d/g)=tAcc=tDec=VMax/g
2×√(d/g)

tTtl=tDec+tAcc
Copernicus suggested the following order of heavenly spheres:
  • highest heavenly sphere is the heaven of the fixed stars
  • highest planet is Saturn
  • Jupiter is next
  • followed by Mars
  • Venus
  • Mercury
  • the Earth (with the attendant Moon)
  • the Sun is at the center of the universe
He admitted: 'all these statements are difficult and almost inconceivable, being of course opposed to the beliefs of many people'.

He hoped: 'as we proceed, with God's help I shall make them clearer than sunlight, at any rate to those who are not unacquainted with the science of astronomy'.

Copernicus introduced a new cosmological view: At rest in the middle of everything is the sun.
Accelerate to Very High Velocities.
v = g * t = 864 km/sec per day.
With constant g-force acceleration, vessel increases speed to several hundred times Earth's escape velocity (e = 11 km/sec).

This is way too fast to do anything useful at our interplanetary destination; thus, the spacecraft must SLOW DOWN!!!

Thus, we need PHASE II. G-FORCE DECELERATION FROM MIDWAY TO JUPITER
PHASE II. Midway between Earth and Jupiter (i.e., d/2 = 2.5 AU), spaceship velocity exceeds 2,700 km/sec. To decrease this speed and still simulate gravity, spaceship reverses direction of fuel exhaust and decelerates at g for remaining 3.16 days of travel.
Typical g-force Flight Profiles to Nearby Planets
Typical Accelerate Max Velocity Decelerate Total
Dist. fm Earth Dept to Midway (at midway)Midway to Dest Travel Time
d dAcctAccVMax tDectTtl
NEO
1 AU
0.5 AU
1.4 dy
1,218 km/s
1.41 dy
2.83 dy
Mars
2 AU
1.0 AU
2.0 dy
1,728 km/s
2.00 dy
4.00 dy
Jupiter
5 AU
2.5 AU
3.2 dy
2,730 km/s
3.16 dy
6.32 dy
Saturn
10 AU
5.0 AU
4.5 dy
3,864 km/s
4.47 dy
8.94 dy
Uranus
20 AU
10 AU
6.3 dy
5,464 km/s
6.32 dy
12.64 dy
Neptune
30 AU
15 AU
7.8 dy
6,693 km/s
7.75 dy
15.50 dy
Givend / 2√(d/g)

g= 0.5AU/day2
tAcc×g

g=864kps/day
√(d/g)

tDec = tAcc
2×√(d/g)

tTtl = tDec + tAcc




VOLUME I: ASTEROIDAL
VOLUME II: INTERPLANETARY
VOLUME III: INTERSTELLAR



SUMMARY:  Given the proper planetary alignment, a transfer orbit could take 7 months to travel to Mars. However, our thought experiments contends that a g-force accelerating spaceship could reduce the travel time to a few days to any of the nearby planets.        SLIDESHOW.

0 Comments:

Post a Comment

Links to this post:

Create a Link

<< Home