Saturday, August 30, 2014

VOLUME I: ASTEROIDAL Table of Contents

Over the next century,
mankind will build and live in habitats
throughout the Solar System.







  • HABITATS:  Some human colonies will live in large, spinning cylinders constructed from "in situ" material from asteroids and comets.
  • EARTH LIKE GRAVITY: Spinning cylinders will simulate g-force via centrifugal force along longitudinal axis.
  • ENERGY SOURCE: Large, adjacent mirrors will reflect sunlight into habitats for plentiful energy.
  • FRESH FOOD: Essential ingredients from Mother Earth will enable robust agricultures.
  • SPENDING MONEY: Harvesting of space bound materials will enable a robust economy among the many habitats as well as Mother Earth
  • POPULATIONS: Smaller habitats will easily house 10,000 people; larger habitats will provide comfortable quarters for well over 100,000.

Volume 1: ASTEROIDAL

Introduction

************HABITATS************
1. HABITATS CAN ORBIT. Transform selected asteroids into orbiting habitats; i.e., "orbiters".
2. HABITAT CAN TRANSFER Habitats can transfer large human populations from Earth orbit to Mars orbit via a simple "semi-orbit".
3. HABITATS CAN CYCLE. Refashion some Near Earth Asteroids (NEAs) as cyclers
4. CYCLERS TO MARS: MARSONANCE: Design Habitat's orbit such that Habitat Period (TH) = period of Mars (T).
5. Transponder on NEA Radio beacon or transponder to NEA.
6. Robotic Operations Necessary precursor to human presence.
7. Robotic observatory. "Dark side of the moon" on steroids best vantage point to observe the Universe.
8.  ELEVATE PAYLOADS FROM EARTH. Resupply for habitats will require frequent and consistent elevation of materials from Earth to space.
9. Terraformation notes To become Earth-like, habitats must transform via export of Earth's soil with both minerals and microbes
10. Centripetal: Rotation is Essential Human habitats, orbiting cylinders of huge dimensions, will rotate around their longitudinal axis. They will orbit the Earth and throughout the Solar System.
11. Impart Spin with Mass Driver Moving a huge habitat from zero spin to g-force spin will take a significant amount of power.
***********BENEFITS***********
12. Mining Operations Asteroids are a plentiful source of materials required to construct and maintain habitats in space.
13. Habitats: Alpha and Omega Orbiting Sol at 60° ahead or behind Earth might have certain advantages.
14. Launching Alpha The most convenient way would leverage Luna and its vast resources.



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




VOLUME II: INTERPLANETARY Table of Contents

Interplanetary flights will become routine
(much like airline travel today)
because travel time will become reasonable.







Furthermore, spacecraft will maintain comfortable Earthlike conditions (gravity, atmosphere, comfortable billets, entertainment, etc) throughout the flight.
Consider Einstein's thought experiment about an accelerating elevator. If the elevator accelerates at same rate as free falling objects near Earth's surface, then occupants will feel same g-force as if they're static on Earth's surface. (Einstein called this "equivalence".)
Instead of Einstein's elevator, our thought experiment notionalizes a high performance spaceship to accelerate at rate, g, to produce gravity like force (g-force). A g-force trip to nearby planets will take days or weeks (orbiting vehicles now take years). We speculate that g-force propulsion can be accomplished with well known science and slight advances in current technology.

Volume 2: INTERPLANETARY

Introduction: Thinking About It.

1. ACCELERATE FOR A DAY: Consider Einstein's famous "Thought Experiment" which states the equivalence between being static on Earth's surface or traveling at 1 g acceleration; it feels the same. Acceleration due to Earth surface gravity, g, about 10 m/sec². This value can be expressed as an equivalent daily rate, g = .5 AU/day².
2. ACCELERATE TO THE PLANETS: G-force to the planets in days, because G-force acceleration greatly increases ship's velocity. However, the ship must reverse propulsion vector at midpoint to SLOWDOWN throughout the second half of trip at g-force deceleration.
3. MOMENTUM MAKES IT HAPPEN: High speed fuel particles propel a space vessel via a rocket like momentum exchange. If exhaust particle speed approaches light speed; then, relativistic masses gain increases momentum to further enhance propulsion.
4. MASS TO MOTION: On board particle accelerators can drive exhaust particles to enormous speeds with enormous momentum to drive spaceships. Resulting mass consumption can be expressed as percentage of take off gross weight (%TOGW) per day.
5. PUSH PARTICLES TO INTERPLANETARY. Particle exhaust speeds from .1c to .5c will adequately transport people, cargo and habitats to the planets inside the KB.
6. CURRENT TECHNOLOGY: ION THRUSTER.  Closest current tech to accelerator drive is "Ion Thruster".  Could be incorporated as an "injector".
7. PROFILE TO THE PLANETS: G-force can propel vessel in straight line to destination. However, flight profile must be carefully planned and executed. Plasma particles can be accelerated to very high, relativistic speeds; resultant momentum imparts g-force and very high speeds to the vessel.
8. G-FORCE TO MARS: Water can get us to our red neighbor quickly.
9. FINITE RANGE: Given a fuel consumption rate, logarithms can quickly approximate a g-force vessel's range.
10.  ACCELERATORS IN SPACE: Particle accelerators can propel g-force vessels.

11. G-FORCE ELEVATORS quickly move pax/cargo from Earth's Equator to GEO.
12. TO URANUS.. Why go?? Helium-3, an isotope of Helium, can produce cheaper, cleaner fuel for onboard power needs for space faring enterprises. He-3 is plentiful on the Gas Giants; with the lowest escape velocity, mining HE-3 from Uranus might prove fruitful.
13. KEEPERS FROM KUIPER Space communities will eventually depend on raw materials from space. Kuiper Belt has plenty.
14. SUPER G-FORCE Can interplanetary cargo travel quicker than passengers at g-force? Yes, less time, more fuel, but it may be worth it.
15. EXTRAPLANETARY: Beyond the Inner Planets. Transition to interstellar.
Eventually, interplanetary flights will become routine. When they do, the practicality of interstellar flights will become imminent. "Going Asteroidal" (leveraging asteroids for traveling and dwelling) will be an integral part of both interplanetary and interstellar travel.



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



Thursday, August 28, 2014

VOLUME III: INTERSTELLAR Table of Contents

INTERSTELLAR flights could take centuries.
Fortunately, g-force could reduce this to a few years.








Unfortunately, fuel can severely limit time/distance for interstellar g-force voyages; though, fuel is not a problem for interplanetary flights.  G-force vessels can easily carry sufficient fuel to accelerate at constant g-force throughout a trip to Mars, which would take a few days and only a few percent of the ship's mass for fuel.  However, interstellar vessels would easily consume well over 100% of its weight in fuel during the multi-year voyage.

Thus, interstellar ships will separate their voyages into three phases:
  • G-force for about a year to accelerate to a high percentage of light speed.
  • Conserve fuel by cruising for a few years at this speed to save fuel (maintain gravity via longitudinal spin).
  • Decelerate back to an orbital speed to conduct interplanetary operations at the destination star.

Volume 3: INTERSTELLAR

1. INTERSTELLAR SCENARIOS.  TE has grouped most common scenarios into 1) Theoretical 2) Feasible 3) Practical.  Which technologies are most likely and therefore most practical? Let's focus on them.
2. PUSH TO INTERSTELLAR. Interplanetary performance envelope will need considerable "pushing" for interstellar flights. Particle exhaust speeds will need to be in the high ninety percentiles of light speed.
3. ACCELERATE FOR A YEAR: Compare spaceship's g-force speeds with c, light speed. See associated 1G TABLE: Accelerate for 1 Year.
4. CALCULUS DOES DISTANCE.  Use exponential to determine g-force interstellar speeds; use integral to determine distance traveled.
5. TO NEIGHBOR STARS: Between accelerating and decelerating, stellar flights need a lengthy cruise phase.
6. GETTING THERE: PRACTICALITY G-force acceleration requires mass/energy conversion. Since spaceship has limited mass; it has limited range. Practicality limits range even further.
7. RECURRING REMAINDER INCREASES PRACTICALITYMake the feasible range more practical with a dynamic efficiency factor which inversely correlates with vessel performance (exit particle velocity).
8. TOTAL TIME DILATION:  Can easily compute large part of time dilation during cruise; much more difficult to compute time dilation for acceleration/deceleration portions of flight.
9. HELIUM-3, WILL IT GET US THERE? No, but it'll keep us warm during the trip; thus, He-3 might very well prove essential for space travel.
10. INTERSTELLAR RAMJET might enable inflight refueling. The interstellar ramjet (proposed by Dr. Bussard in 1960) is a possible solution to the inherent transportation problem of having to carry enough fuel to power entire flight.
11. INTERSTELLAR SUPER G.  Greater than g-force propulsion can be an enormous help to interstellar travelers.   See associated 7G TABLE: Accelerate for 100 Days.
12. SNOWBALL FROM OORT  Sol's boundary cloud contains "trillions of comets" which could benefit humankind enroute to the stars.  See associated 7G TABLE: Decelerate for 48¼ days.
13. MORE SNOWBALLS  More ways to throw more snowballs. See associated 1G TABLE: Decelerate for 1 Year.
14. Maintain Contact: Inflight Communications Maintaining huge data flows over these long distances will likely prove quite challenging.
15. Stellar Lighthouses Going straight to a star reduces risk; if the photons can reach us, there's probably no enroute obstruction.
Eventually, interplanetary flights will become routine. When they do, the practicality of interstellar flights will become imminent. "Going Asteroidal" (leveraging asteroids for traveling and dwelling) will be an integral part of both interplanetary and interstellar travel.



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






Sunday, July 20, 2014

7G TABLE: Decelerate for 48 1/4 Days









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








To effectively accomplish an interstellar resupply mission, an Artificial Intelligent (AI) vessel could use 7G propulsion to quickly intercept the primary 1G vessel.  However,  the 7G vessel must slow down prior to intercept in order to match the 1G vessel cruise velocity. This table describes daily progress throughout the deceleration duration.
7G Deceleration for 48 ¼ Days 

Previous table, 7G Acceleration for 100 Days, describes daily progress of vessel accelerating from zero velocity at 7g.
After 100 days of 7g acceleration, a vessel travels total distance of 9,842 AUs (.155 Light Year, LY).  It gained velocity of about 150 AU/day (.866 c, 86.6% light speed).  
Assume 7G vessel cruises at this velocity until the optimal time/distance to start decelerating at 7g.
Decel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
0 days149.93 AU/dy86.59% c9,811.1 AU0.1551 LY0.0 AU9,811.1 AU27.974% GW0
1 days149.46 AU/dy86.32% c9,661.7 AU0.1528 LY149.4 AU9,960.5 AU28.210% GW0
2 days148.98 AU/dy86.04% c9,512.8 AU0.1504 LY148.9 AU10,109.4 AU28.445% GW0
3 days148.48 AU/dy85.76% c9,364.4 AU0.1481 LY148.4 AU10,257.9 AU28.679% GW0
4 days147.98 AU/dy85.46% c9,216.5 AU0.1457 LY147.9 AU10,405.8 AU28.913% GW0
5 days147.46 AU/dy85.17% c9,069.1 AU0.1434 LY147.4 AU10,553.2 AU29.146% GW0
6 days146.94 AU/dy84.86% c8,922.2 AU0.1411 LY146.9 AU10,700.1 AU29.378% GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t


To accomplish the resupply mission, the 7G vessel must slow down to match the 1G vessel cruise velocity (.644c = 111.5 AU/day).  This table describes daily progress throughout the 48¼ days required to do this.
Interstellar 7G Vessel
In this example, 7G vessel starts its 100 day acceleration at day 260 of 1G vessel’s acceleration.

On day 360, 7G vessel stops propulsion, and cruises at 149.9 AUs per day (.865c).

100 days of 7G acceleration  takes vessel to 9,842 AU, .155 LY.

xDecel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
7 days146.40 AU/dy84.56% c8,775.8 AU0.1388 LY146.4 AU10,846.5 AU29.609% GW0
8 days145.86 AU/dy84.24% c8,630.0 AU0.1365 LY145.8 AU10,992.3 AU29.840% GW0
9 days145.30 AU/dy83.92% c8,484.7 AU0.1342 LY145.3 AU11,137.6 AU30.070% GW0
10 days144.73 AU/dy83.59% c8,340.0 AU0.1319 LY144.7 AU11,282.3 AU30.299% GW0
11 days144.15 AU/dy83.26% c8,195.8 AU0.1296 LY144.1 AU11,426.4 AU30.527% GW0
12 days143.56 AU/dy82.91% c8,052.3 AU0.1273 LY143.6 AU11,570.0 AU30.755% GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t
Points a thru f map out following events:
After 360 days, resupply vessel ends 100 days of 7G propulsion and starts cruise at 149.9 AU/day.
After 365.25 days of 1G acceleration, primary vessel cruises at 111.5 AU/day.
After 400 days, resupply vessel is about 12,000 AU behind primary vessel.
After 500 days, resupply vessel closes the gap to slightly over 8,000 AU.
 600 days, gap closes even more to just over 4,000 AU.
 684 days, gap shrinks to about 1,000 AU in prep for 7G vessel’s deceleration to match speed of primary vessel.

Decel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
13 days142.96 AU/dy82.57% c7,909.3 AU0.1251 LY143.0 AU11,712.9 AU30.982% GW0
14 days142.34 AU/dy82.21% c7,767.0 AU0.1228 LY142.3 AU11,855.3 AU31.208% GW0
15 days141.72 AU/dy81.85% c7,625.3 AU0.1206 LY141.7 AU11,997.0 AU31.433% GW0
16 days141.08 AU/dy81.48% c7,484.2 AU0.1183 LY141.1 AU12,138.1 AU31.658% GW0
17 days140.42 AU/dy81.10% c7,343.7 AU0.1161 LY140.4 AU12,278.6 AU31.881% GW0
18 days139.76 AU/dy80.72% c7,203.9 AU0.1139 LY139.8 AU12,418.3 AU32.105% GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t
Decel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
19 days139.08 AU/dy80.32% c7,064.8 AU0.1117 LY139.1 AU12,557.5 AU32.327% GW0
20 days138.38 AU/dy79.92% c6,926.4 AU0.1095 LY138.4 AU12,695.9 AU32.549% GW0
21 days137.67 AU/dy79.51% c6,788.7 AU0.1073 LY137.7 AU12,833.6 AU32.770% GW0
22 days136.95 AU/dy79.10% c6,651.7 AU0.1052 LY137.0 AU12,970.6 AU32.990% GW0
23 days136.21 AU/dy78.67% c6,515.4 AU0.1030 LY136.3 AU13,106.9 AU33.210% GW0
24 days135.46 AU/dy78.24% c6,379.9 AU0.1009 LY135.5 AU13,242.4 AU33.428% GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t

Remaining Slides:  Plan for Rendezvous
Profiles will be adjusted later; however, initially, assume acceleration profiles as follows:
Main mission vessel accelerates at 1G for one year; then cruises at constant velocity per following distance equation:  d1G = -.267 LY + .644c×t
Resupply vessel starts 7G accel at 265.25 days after mission vessels begins.  100 days later (365.25 days into mission), 7G vessels stops accel and starts cruise:   d7G = -.711 LY + .866c×t
FOR CONVENIENCE: Set t=0 at beginning of  mission; thus, the 2nd mission year is the first cruise year.  During 1st year of cruise, 7G vessel trails 1G vessel.  At cruise start (365.25 days) the 1-g pax vessel is .377 LY (23,841.5 AU) from Sol with velocity of .644c (= 111.5 AU/day = 193,066 km/sec). 7G vessel trails 1G vessel (.155 LY =9,811 AU from Sol); but it has much greater velocity, (.866 c = 149.9 AU/day = 259,620 km/sec) and will catch up.      
d1G = -.267 LY + .644c×t = -.711 LY + .866c×t  = d7G
-16,885AU + 111.5AU/day×t = -44,964 AU + 149.9 AU/day; thus, tInt = 731.2 days and dInt= 64,644 AUs.  Unfortunately, the vessels have a huge velocity differential of about .22c.  Next slide considers the required deceleration of the 7G, resupply vessel.

Decel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
25 days134.70 AU/dy77.79% c6,245.1 AU0.0988 LY134.8 AU13,377.2 AU33.646% GW0
26 days133.91 AU/dy77.34% c6,111.1 AU0.0966 LY134.0 AU13,511.2 AU33.864% GW0
27 days133.12 AU/dy76.88% c5,977.9 AU0.0945 LY133.2 AU13,644.4 AU34.080% GW0
28 days132.30 AU/dy76.41% c5,845.5 AU0.0924 LY132.4 AU13,776.8 AU34.296% GW0
29 days131.47 AU/dy75.93% c5,713.9 AU0.0904 LY131.6 AU13,908.4 AU34.512% GW0
30 days130.62 AU/dy75.44% c5,583.1 AU0.0883 LY130.7 AU14,039.1 AU34.726% GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t
Decel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
31 days129.76 AU/dy74.94% c5,453.2 AU0.0862 LY129.9 AU14,169.0 AU34.940% GW0
32 days128.88 AU/dy74.43% c5,324.2 AU0.0842 LY129.0 AU14,298.1 AU35.153% GW0
33 days127.98 AU/dy73.91% c5,196.1 AU0.0822 LY128.1 AU14,426.2 AU35.366% GW0
34 days127.06 AU/dy73.38% c5,068.9 AU0.0802 LY127.2 AU14,553.4 AU35.577% GW0
35 days126.13 AU/dy72.84% c4,942.6 AU0.0782 LY126.3 AU14,679.7 AU35.788% GW0
36 days125.17 AU/dy72.29% c4,817.3 AU0.0762 LY125.3 AU14,805.0 AU35.999% GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t

Decel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
37 days124.20 AU/dy71.73% c4,692.9 AU0.0742 LY124.4 AU14,929.4 AU36.208% GW0
38 days123.20 AU/dy71.15% c4,569.5 AU0.0723 LY123.4 AU15,052.8 AU36.417% GW0
39 days122.19 AU/dy70.57% c4,447.1 AU0.0703 LY122.4 AU15,175.2 AU36.626% GW0
40 days121.15 AU/dy69.97% c4,325.7 AU0.0684 LY121.4 AU15,296.6 AU36.833% GW0
41 days120.10 AU/dy69.36% c4,205.4 AU0.0665 LY120.3 AU15,416.9 AU37.040% GW0
42 days119.02 AU/dy68.74% c4,086.1 AU0.0646 LY119.3 AU15,536.1 AU37.246% GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t
Decel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
43 days117.92 AU/dy68.11% c3,968.0 AU0.0627 LY118.2 AU15,654.3 AU37.452%GW0
44 days116.80 AU/dy67.46% c3,850.9 AU0.0609LY117.1 AU15,771.4 AU37.657%GW0
45 days115.66 AU/dy66.80%c3,735.0 AU0.0591 LY115.9 AU15,887.3 AU37.861%GW0
46 days114.49 AU/dy66.12% c3,620.2 AU0.0572 LY114.8 AU16,002.1 AU38.065%GW0
47 days113.30 AU/dy65.44% c3,506.6 AU0.0554 LY113.6 AU16,115.7 AU38.268%GW0
48 days112.09 AU/dy64.74% c3,394.2 AU0.0537 LY112.4 AU16,228.0AU38.470%GW0
Resupply Vessel Matches Cruise Velocity of Baseline "Pax" Vessel (1.0 yr of 1G Accel.)
at exactly the time/distance of the intercept.
48¼days111.78 AU/dy64.56% c3,366.3 AU0.0532 LY27.9 AU16,256.0 AU38.520%GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t
Decel.
Time(t)
Spot
Velocity (Vt)
Spot
Distance (dt)
Daily
Dist. (dΔ)
7G
Dist.(d7G)
Total
Fuel (F)
52 days106.98AU/dy61.79%c2,966.6 AU 0.2636LY107.3AU16,667.7AU39.272%GW0
53 days105.64AU/dy61.01%c2,860.5AU 0.2652LY106.0AU16,773.7AU39.471%GW0
Resupply Vessel Matches Cruise Velocity of Slower "Pax" Vessel (0.9 yr of 1G Accel.)
at exactly the time/distance of the intercept.     
53.4 days105.10AU/dy60.70%c2,818.4AU 0.2659LY42.0 AU16,815.7AU39.551%GW0
54 days104.27AU/dy60.22%c2,755.7AU 0.2662LY62.6 AU16,836.3AU 39.669%GW0
Given
(1 - (1-Δ)100-t) × c
c×(100-t)+ Vt

ln(1-Δ)
dt-1 - dt dΔ + ΣdΔ 1-(1-ε∇)100+t

Tuesday, June 03, 2014

High Frontier Extract: Chapter 13 Space Robotics D. P. Gump, Prse. LunaCorp

VOLUME I: ASTEROIDAL
VOLUME II: INTERPLANETARY
VOLUME III: INTERSTELLAR
New era of space exploration will feature an unexpected abundance of robots doing new and unexpected tasks.

Hohlman Transfer

VOLUME I: ASTEROIDAL
VOLUME II: INTERPLANETARY
VOLUME III: INTERSTELLAR
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 necessities can add considerable delay. Thus, human transport via transfer orbit is infeasible, and practical payloads are limited to Artificial Intelligence (AI) devices.



First, consider current spacecraft capabilities for interplanetary travel. Far from a straight line, typical flight path is more like a semi-ellipse. Kepler and Newton initiated our current knowledge of orbital mechanics which demonstrate that non-propelled objects within the Solar System must fly in elliptical orbits around the Sun.
We are currently unable to propel a spacecraft for entire interplanetary trips; instead, we must satisfy ourselves with well planned "fuel burns". Between these "burns", spacecraft orbits the Sun. An orbit that connects two planetary orbits is called a transfer orbit.
Thus, consider possible path of vehicle traveling from Earth to Mars. Following diagram shows three relevant orbits.
  1. Earth's Orbit is nearly circular. Diagram assumes prior launch from Earth's surface; vehicle orbits Earth for a while; then, follows path shown on diagram.
  2. Destination Orbit. Most planetary orbits are nearly circular; diagram shows orbit of Mars as an example.
  3. Transfer Orbit is a highly eccentric orbit which connects two planetary orbits. A simple, well planned transfer orbit would require following events.
    • Enter Transfer  Orbit (*Δ v= 2.947 km/sec): burst of fuel burn to leave Earth orbit and enter transfer orbit. (*Ref: page 357, On Motion by AE Roy)
    •  Exit Transfer Orbit (*Δ v= 0.396 km/sec): burst of fuel burn to exit transfer orbit and enter Mars orbit. (*Ref: page 357, On Motion by AE Roy)
Careful planning is required to ensure that spacecraft arrives near destination planet at completion of orbit transfer. For example, above diagram shows that Mars very far from destination point when vehicle initiates transfer orbit; during the 259 days of zero-g flight, Mars and Earth both travel through considerable portions of their respective orbits.

Hohmann Transfer Orbits. A Hohmann Transfer is a special case of a transfer orbit discovered by Walter Hohmann in 1928. Strictly speaking, a pure Hohmann transfer would exit Earth's orbit at its perihelion (nearest point to Sol) and enter destination orbit at aphelion (farther point from Sol). Typical transit times for relevant Hohmann Transfer orbits can be approximated via an online Hohmann Transfer calculator.

Perihelion, q, is orbit's closest point to Sol. Since we're now considering Hohman Transfers from Earth to outer planets, HT's perihelion must be on Earth's orbit.  Thus, qHT equals Earth's semimajor axis, aE. Thus,
qHT = aE = 1 AU
Aphelion, Q, is orbit's farthest point from Sol. Thus, HT's Q must be destination orbit's semimajor axis, aD. Thus,
QHT = aD
HT's focus, c, is half of difference of aphelion and perihelion:
cHT = .5×(QHT  - qHT) = .5×(aD - 1)
HT's semimajor axis is average of HT's aphelion and perihelion:
aHT = .5×(QHT + qHT) = (aD + 1) / 2
Thus, HT's eccentricity is focus divided by semimajor axis.
eHT = (a -1)/(aD+1)
To determine HT orbital period, recall Kepler's Third Law, square of orbital period is proportional to cube of orbit's semimajor axis. .5×(aD + 1).
THT2 ∝ aHT3 = [(aD+1)/2]3




Hohman Transfer Examples
Destination OrbitTransfer Orbit
Eccen-
tricity
Semi-Major
Axis
Orbital
Period
Eccen-tricity **time  
e (ratio)aD (AU) T (Yrs) e (ratio) t (Yrs)
*Earth0.016711.00n/an/a
Mars0.09341.521.87.21.71 yr
Jupiter0.04835.2011.86.682.73 yr
Saturn0.05609.5429.47.816.05 yr
Uranus0.046119.1884.00.9116.03 yr
Neptune0.009730.06164.81.9430.61 yr
ObservedObserved
2π a3/2

(G×MS)
aD - 1

aD + 1
(1+aD)3/2

5.656
*   Assume departure from Earth's orbit.
**Time from Earth Orbit to Destination. See A. E. Roy, On Motion, pg. 354.
Universal
Gravitation
Constant
G=6.673x10-11


kg sec
Sol's Mass
MSol=
1.99x1030 kg
Standard
Gravitational
Parameter
μSol=13.28x1019

sec2
= G×MSol
Convert to
AUs and Yrs
μSol=39.5 AU³

year2
= G×MSol
Orbital
Period
T=

μSol
×(aD +1)3/2

23/2
Transit
Time
tt = .5 T=(aD +1)3/2

5.656
year
Quicker and more flexible transfer orbits can be accomplished; however, Hohman Transfers are the most energy efficient and are easily calculated.
  1. HT transit times give us a rough order of magnitude of required travel times for constant velocity flights between planets.
  2. Orbital flights can be extremely complicated. Flight planners has used "flybys" and "gravity assists". (Recall: Pioneer and Voyager missions.)
SUMMARY: Transfer orbits are very fuel efficient, but they are too limited and too slow.
(Analogy: Consider today's maritime environment. Sailships are certainly much more energy efficient then a modern powered vessel. However, there are about 165,000 ocean going vessels (over 100,000 tons); virtually every single one is powered; owners clearly prefer greater control versus energy efficiency.)
Traveling 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.