Saturday, July 28, 2007

"Let there be light..."


Of course, energy ranks first on the hierarchy of needs. Accordingly, the foremost concern for an asteroidal habitat is energy supply for the builders. Of course, initial builders will be Artificial Intelligence (AI) devices such as robots and nanobots.
AI devices are impervious to the onerous conditions that would devastate humans (lack of water, low temperature, radiation, microgravity, to name a few). They don't need to rest, and they don't originate human error. Thus, AI devices will be the first occupants on the first few asteroids destined to become space habitats for signiificant numbers of humans. Therefore, we'll need Artificial Intelligence (AI) devices, (robots, nanobots, etc.) to do most of the work required to process asteroidal materials into a shell.
Initial construction of the first few habitats will take years to transform raw materials into a a habitat which can provide reasonable acommodations to humans. These tasks are discussed in depth in other blentries, but these tasks will mostly be done by AI devices. They can be monitored and remotely controlled, but since time lags for communications will be constrained by huge distances, these devices will need a certain amoount of automony.
ENERGY NEEDS. These deployed devices to the NEO will need an inexhaustible, consistent supply of energy. Prior to access from solar energy, AI devices will need to use deployed nuclear energy. Nuclear energy can last a long time, but there'll be limitations; these limitations will be easily overcome with solar supplements and eventually solar replacements.
Of course, first task will be to collect minerals from asteroid and start building solar mirror and solar arrays.Subsequent to shell completion, habitat's agriculture as well as extensive flora/fauna will need a consistent source of light. As long as habitats are reasonably close to a star, mirrors will be a good way to collect and distribute light.
Gerald O'Neill describes some ingenious ways to deploy and use mirrors about such habitats.
In the general scheme of things, look for following events:
FIRST, payload of AI devices and a nuclear reactor will gently load on a selected asteroid. As much as possible, these devices will be monitored and controlled from human operators on Earth. It will be impractical to expect continuous contact (due to Earth's rotation and even more so due to asteriodal orbit which will take it long distances away for long periods of time); thus, AI devices will need considerable autonomy. It's possible that human intervention can be supplemented by spaceborne humans.
2ND, AI devices will accomplish considerable time and effort assaying asteroid samples to determine what minerals are available. Hopefully, these minerals will help AI devices manufacture spare parts for themselves and possible even other AI devices.
3RD, hopefully more payloads will arrive to this asteroid. Contents to be determined, but I'd guess more AI devices, and possible minerals determined not to be available at this asteroid. Eventually, we'd want to import needed minerals from other asteroids NOT Earth or other planets/moons.
4TH, start manufacturing solar mirrors and solar arrays for long term energy needs.
5TH, deploy mirror and arrays. Until this point, all energy consumptions must be replenished by nuclear reactor.


Note following references to Gerard O'Neill's classic book: THE HIGH FRONTIER, HUMAN COLONIES IN SPACE. As always, content is fron the original authors, misrakes are mine.

Page 26. On Earth, solar power is attenuated by the atmosphere, uncertain due to weather and cut off every night by Earth's rotation. In free space at 1.0 AU from Sol, average solar energy is available full time at 1.4 kilowatts per square meter, almost ten times higher than average solar energy which reaches Earth's surface.

P. 32-34. It's very likely that solar power will always be cheaper then nuclear power (either fission or fusion). First, to supply heat in space, a simple mirror with no moving parts can locate at the point of use and supply direct heat (i.e., not have to convert via different forms to energy).

Near zero gravity will facilitate manufacture of mirrors in space. Heat material to high temps w/o contamination of confining crucbile walls, form uniform mixtures of heavy and light materials, grow large single crystal, Gentle rotation can maintain very thin surfaces accurately in form of clyinders and cones which may especially useful to make large mirrors made of thin foil.

p. 43 Directly used heat may be obtained from solar power without going through an intermediate stage such as electricity. Even at nighttime, solar powers will always be available, no more the a few feet from the house floor. Reflected by external mirrors, solar heat for cooking can come up through the floor, a window and through a short channel to absorb on the lower side of simple metal cooking surface.

p. 45 To simulate gravity for the humans inhabiting the habitat, they should live on inside of outside cylindrical hull, and the cylindrical habitat should roate about the longitudinal axis as shown. As long as the mass stays constant, the law of conservation of angular momentum should keep continue this this spin in both magnitude and direction. Thus, we'll have a gyroscope with a long axis pointing in same direction regardless of position in orbit.

Thus, if the habitat's longitudinal axis points toward Sagittarius constellation (which happens to be in the same direction as the center of our galaxy, Milky Way), then the habitat will continue pointing to Sagitarius as it orbits Sol, our star. Therefore, different parts of the the habitat will face Sol at different positions in the habitat's orbit around the Sun. In one position, the habitat's tail will face Sol, 3 months later, the left side will face Sol, the next quarter, the front will face Sol, the fourth quarter, the right side. This constantly changing position means the sunlight will hit the habitat and its mirror(s) at different angles throughout the orbit.

Observing figure at left, position of habitat is shown at all four quarters of the annual orbit. Note the long axis at all four positions are all parallel (point same direction.)
One solution to this "precession" problem is to orient the habitat's cylinder axis perpendicular to the habitat's orbit around the sun and to provide a lightweight mirror angled at 45 degress to bring sunshine along that axis. This will ensure sunshine arrives in direction along the cylinder axis.
In CORRECTING PRECESSION figure, same four positions of habitat are shown (a not to scale Earth is shown to idicate that the habitat can share the Earth's orbit if we choose). However, habitat's orientation differs from previous figure in that the long axis of each postion changes to point directly at Sun. To do this, requires adjusting long axis direction about about 1 degree per day. O'Neill suggests a way to do this in his book.
p. 69 L5 is a famous Lagrangian position with respect to Earth and the Sun (there are other Lagrangian points with respect to other two body systems, such as Earth and Luna). It turns out there are multiple L5 positions for habitats to locate, as a matter of fact there might be a multitude of such positions. There are many construction efficiencies at these L5 points and they all depend on constant, dependable solar power.

p. 71 Solar cell array will be much lighter then nuclear plan with same power capacity.

p. 74 Add solar cells as need increases.

p. 77 Asteroidal resources can provide metals and silicon for solar cell arrays.

p. 82-86 Satellite Solar Power Stations (SSPS) will locate in geosynchronous orbit above a fixed point on Earth's surface, a large solar power station. At the orbiting station, solar electric power would convert to microwve energy wheich would travel via a narrow beam to a fixed antenna on the ground.

p. 93 On Luna, a solar power station could locate on a mountain peak at the lunar north or south pole where sunshine would be available fulltime. A transmission line from the pole to the desired location on the lunar surface would allow fulltime operation.

p. 102 It's possible that some interplanetary spacecraft could have engines powered by extensive solar cell arrays like sails on a square rigger. These sails would streech out for several kilometers, but that could easily work for vessels never intended to enter an atmosphere.

p. 115 Need for cheap energy on Earth's surface in form of electricity via microwaves from orbiting SSPS is likely to exist for a long time.

p. 130-132 An unlimited energy source can be designed with the envrionment in mind. perhpas the largest envrionment impact will come from the constructon of the solar panel photovoltaics because of the toxic waste by products. Producing this energy source in space will help decrease or possibly eliminiate this environmental impact.

p. 133 Many mature studies conclude that SSP will:
---be ecologically compatible.
---meet applicable international safety standards.
---be economically viable as global energy supply system.
---comply with international legal and regulatory framework for space operations.
---be acceptable to society.

HABITATS NEEDS ENERGY
Much of following material has been extracted from Wikipedia’s article (http://en.wikipedia.org/wiki/Space_colonization). As always credit for content must go to the original authors, misrakes are all mine.
Solar energy in orbit is abundant, reliable, and powers satellites today. There is no night in space, and no clouds or atmosphere to block sunlight. The solar energy available, in watts per square meter, at any distance, d, from the Sun can be calculated by the formula E = 1366/d², where d is measured in astronomical units.
Particularly in the weightless conditions of space, sunlight can be used directly, using large solar ovens made of lightweight metallic foil so as to generate thousands of degrees of heat at no cost; or reflected onto crops to enable photosynthesis to proceed.
Large structures would be needed to convert sunlight into significant amounts of electrical power for settlers' use. In highly electrified nations on Earth, per-capita electrical consumption can average 1 kilowatt/person (or roughly 10 megawatt-hours per person per year.)
Energy has been suggested as an eventual export item for space settlements, perhaps using microwave beams to send power to Earth or the Moon. This method may have significant drawbacks related to the large area that may be necessary for transmitted energy to be extracted on earth.
The Moon has nights of two Earth weeks in duration and Mars has night, dust, and is farther from the Sun, reducing solar energy available by a factor of about 1/2-1/3, and possibly making nuclear power more attractive on these bodies. Extending this problem to habitats; some habitats may find themselves in highly eccentric orbits (aka "cyclers) or even in interstellar travel (see "migrators") where sunlight will be greatly reduced. This will make nuclear power even more essential.

Thursday, July 26, 2007

7 Days of Creation

Following our Maker's example, let's consider following seven phases of creating a habitat in space. Of course, He started with a plentitude of raw materials. In like matter, we'd need to find a suitable near Earth asteroid (or perhaps a piece of one). If this Near Earth Object (NEO) doesn't have water available already on it, we'd have to find some ingenious way of adding water. Perhaps a stray comet will become available; if all else fails, we could export many tons of seawater from Mother Earth.

1. "Let there be light." Build mirrors to collect and disperse light. Artificial Intelligence (AI) devices, (robots, nanobots, etc.) will precede humans to the NEA to do most of the work required to process asteroidal materials. Before they build an enclosing shell for humans to occupy, they'll need to build a means to resupply their consumed energy. Towards this end, first task will be to collect minerals from asteroid and start building solar mirror and solar arrays.

2. "Separate the waters..." Hopefully, the habitats will be large enough to acommodate clouds which would be the "waters above". Even more important, there should be enough water to form substantial reservoirs, "waters below". Of course, water has many functions and is necessary for life.

3. "Let plants grow." Terraform the habitat with mostly raw materials readily available from the NEO but with necessary traces of life available from a few tons of Terran topsoil. During this phase, the habitat should have achieved enough angular momemtum to simulate gravity. while angular momemtum normally conserves, the habitat will probably need to inject some more energy into its spin because shape and size will likely change during subsequent phases.

4. "Use the lights in the sky ..." essential aids for timekeeping and navigation. Insert lots of AI devices to track celestial objects and keep habitat on track.

5. "Fish and birds" export many life forms from Earth and let them inhabit the habitat. Lots of AI devices to monitor this environment and transmitt lots of video and measurements to Earth-borne scientists.

Notice this habitat still has very few human inhabitatants.

Most of the work for above phases will need to be done by AI devices: specialized robots as well as many nanobots.

If the habitat can't support fishes and birds, it probably can't support mammals. It would be poetic to include canaries in the bird populations (recall that coal miners used to carry canaries with them in the coal mines, when the canary died, coal miners would assume bad air and immediately leave. Similarly, if fish and bird can live in the habitat, it's a good sign that animals and humans can

6. "Animals and lastly, humans"

7. "Rest". Now we enjoy the ride. Please don't equate "rest" with "idleness". The mission really starts here; however, compared to previous 6 phases of construction, daily life will seem very "restful".

Deploy these new constructed habitats into cyclers, orbiters, and migraters.

Start out as spheres to contain NEO raw material as well as breathable atmosphere which will need a solid boundary to contain gases since habitat's gravity won't be nearly enough to do the same job as Terran gravity.

Saturday, July 21, 2007

2nd TABLE: 2 YEAR CYCLER at q≈1 AU.

Annual rendezvous at Earth's perihelion, q.
Insert two cyclers in the 2 year orbit...
... such that each cycler attains its perihelion 
RCy(0⁰) =   0.983 AU   =RCy(360⁰) 
exactly when Terra reaches its perihelion. 
RCy(360⁰) =   0.983 AU   =R(360⁰) 
True
Anom
Cycler
Radius
Cycler
Coordinates
Eccentric
Anomaly (EA)
EA Edge
Area
TA Sect
Area
Incr.
Time
Cum.
Time
Earth
Angle
Mars
Angle
θ R X Y YAC Cumm Incr AEdge ATA Δt T θ θ
Deg AU AU AU AU Deg Deg AU2 AU2 days days Deg Deg
0 ⁰ 0.9829 0.9829 0.0000 0.000 0.0 ⁰ 0.00 ⁰ 0.000000 n/a 0 0 0.00 ⁰ 0.0 ⁰
1 ⁰ 0.9830 0.9828 0.0172 0.019 0.7 ⁰ 0.67 ⁰ 0.000002 0.0084 0.846 0.846 0.83 ⁰ 0.4 ⁰
2 ⁰ 0.9831 0.9825 0.0343 0.037 1.3 ⁰ 0.67 ⁰ 0.000002 0.0084 0.846 1.693 1.67 ⁰ 0.9 ⁰
3 ⁰ 0.9833 0.9819 0.0515 0.056 2.0 ⁰ 0.67 ⁰ 0.000002 0.0084 0.847 2.539 2.50 ⁰ 1.3 ⁰
4 ⁰ 0.9836 0.9812 0.0686 0.075 2.7 ⁰ 0.67 ⁰ 0.000002 0.0084 0.847 3.387 3.34 ⁰ 1.8 ⁰
5 ⁰ 0.9840 0.9802 0.0858 0.093 3.4 ⁰ 0.67 ⁰ 0.000002 0.0084 0.848 4.234 4.17 ⁰ 2.2 ⁰
6 ⁰ 0.9844 0.9790 0.1029 0.112 4.0 ⁰ 0.67 ⁰ 0.000002 0.0085 0.848 5.083 5.01 ⁰ 2.7 ⁰
7 ⁰ 0.9849 0.9776 0.1200 0.130 4.7 ⁰ 0.67 ⁰ 0.000002 0.0085 0.849 5.932 5.85 ⁰ 3.1 ⁰
8 ⁰ 0.9856 0.9760 0.1372 0.149 5.4 ⁰ 0.67 ⁰ 0.000002 0.0085 0.850 6.782 6.68 ⁰ 3.6 ⁰
9 ⁰ 0.9862 0.9741 0.1543 0.168 6.1 ⁰ 0.68 ⁰ 0.000002 0.0085 0.851 7.634 7.52 ⁰ 4.0 ⁰
10 ⁰ 0.9870 0.9720 0.1714 0.186 6.7 ⁰ 0.68 ⁰ 0.000002 0.0085 0.853 8.486 8.36 ⁰ 4.4 ⁰
11 ⁰ 0.9879 0.9697 0.1885 0.205 7.4 ⁰ 0.68 ⁰ 0.000002 0.0085 0.854 9.341 9.21 ⁰ 4.9 ⁰
12 ⁰ 0.9888 0.9672 0.2056 0.223 8.1 ⁰ 0.68 ⁰ 0.000002 0.0085 0.856 10.196 10.05 ⁰ 5.3 ⁰
13 ⁰ 0.9899 0.9645 0.2227 0.242 8.8 ⁰ 0.68 ⁰ 0.000002 0.0085 0.857 11.054 10.89 ⁰ 5.8 ⁰
14 ⁰ 0.9910 0.9615 0.2397 0.261 9.5 ⁰ 0.68 ⁰ 0.000002 0.0086 0.859 11.913 11.74 ⁰ 6.2 ⁰
15 ⁰ 0.9922 0.9584 0.2568 0.279 10.1 ⁰ 0.68 ⁰ 0.000002 0.0086 0.861 12.774 12.59 ⁰ 6.7 ⁰
θ(deg) R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
16 ⁰ 0.9935 0.9550 0.2738 0.298 10.8 ⁰ 0.68 ⁰ 0.000002 0.0086 0.863 13.637 13.44 ⁰ 7.1 ⁰
17 ⁰ 0.9948 0.9513 0.2909 0.316 11.5 ⁰ 0.68 ⁰ 0.000002 0.0086 0.866 14.503 14.29 ⁰ 7.6 ⁰
18 ⁰ 0.9963 0.9475 0.3079 0.335 12.2 ⁰ 0.68 ⁰ 0.000002 0.0087 0.868 15.371 15.15 ⁰ 8.1 ⁰
19 ⁰ 0.9978 0.9434 0.3249 0.353 12.9 ⁰ 0.68 ⁰ 0.000002 0.0087 0.871 16.242 16.01 ⁰ 8.5 ⁰
20 ⁰ 0.9994 0.9391 0.3418 0.372 13.5 ⁰ 0.68 ⁰ 0.000002 0.0087 0.873 17.115 16.87 ⁰ 9.0 ⁰
21 ⁰ 1.0011 0.9346 0.3588 0.390 14.2 ⁰ 0.69 ⁰ 0.000002 0.0087 0.876 17.992 17.73 ⁰ 9.4 ⁰
22 ⁰ 1.0029 0.9299 0.3757 0.408 14.9 ⁰ 0.69 ⁰ 0.000002 0.0088 0.879 18.871 18.60 ⁰ 9.9 ⁰
23 ⁰ 1.0048 0.9249 0.3926 0.427 15.6 ⁰ 0.69 ⁰ 0.000002 0.0088 0.883 19.754 19.47 ⁰ 10.4 ⁰
24 ⁰ 1.0067 0.9197 0.4095 0.445 16.3 ⁰ 0.69 ⁰ 0.000002 0.0088 0.886 20.640 20.34 ⁰ 10.8 ⁰
25 ⁰ 1.0088 0.9143 0.4263 0.463 17.0 ⁰ 0.69 ⁰ 0.000002 0.0089 0.890 21.530 21.22 ⁰ 11.3 ⁰
26 ⁰ 1.0109 0.9086 0.4432 0.482 17.7 ⁰ 0.69 ⁰ 0.000002 0.0089 0.893 22.423 22.10 ⁰ 11.7 ⁰
27 ⁰ 1.0131 0.9027 0.4600 0.500 18.4 ⁰ 0.69 ⁰ 0.000002 0.0089 0.897 23.320 22.98 ⁰ 12.2 ⁰
28 ⁰ 1.0154 0.8966 0.4767 0.518 19.1 ⁰ 0.69 ⁰ 0.000002 0.0090 0.901 24.221 23.87 ⁰ 12.7 ⁰
29 ⁰ 1.0178 0.8902 0.4935 0.536 19.8 ⁰ 0.70 ⁰ 0.000002 0.0090 0.905 25.126 24.76 ⁰ 13.2 ⁰
30 ⁰ 1.0203 0.8836 0.5102 0.555 20.5 ⁰ 0.70 ⁰ 0.000002 0.0091 0.910 26.036 25.66 ⁰ 13.6 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
31 ⁰ 1.0229 0.8768 0.5268 0.573 21.2 ⁰ 0.70 ⁰ 0.000002 0.0091 0.914 26.950 26.56 ⁰ 14.1 ⁰
32 ⁰ 1.0256 0.8697 0.5435 0.591 21.9 ⁰ 0.70 ⁰ 0.000002 0.0092 0.919 27.869 27.47 ⁰ 14.6 ⁰
33 ⁰ 1.0283 0.8624 0.5601 0.609 22.6 ⁰ 0.70 ⁰ 0.000002 0.0092 0.924 28.793 28.38 ⁰ 15.1 ⁰
34 ⁰ 1.0311 0.8549 0.5766 0.627 23.3 ⁰ 0.71 ⁰ 0.000002 0.0093 0.929 29.722 29.29 ⁰ 15.6 ⁰
35 ⁰ 1.0341 0.8471 0.5931 0.645 24.0 ⁰ 0.71 ⁰ 0.000003 0.0093 0.934 30.656 30.21 ⁰ 16.1 ⁰
36 ⁰ 1.0371 0.8390 0.6096 0.663 24.7 ⁰ 0.71 ⁰ 0.000003 0.0094 0.939 31.595 31.14 ⁰ 16.6 ⁰
37 ⁰ 1.0402 0.8308 0.6260 0.680 25.4 ⁰ 0.71 ⁰ 0.000003 0.0094 0.945 32.540 32.07 ⁰ 17.1 ⁰
38 ⁰ 1.0434 0.8222 0.6424 0.698 26.1 ⁰ 0.71 ⁰ 0.000003 0.0095 0.951 33.491 33.01 ⁰ 17.5 ⁰
39 ⁰ 1.0467 0.8135 0.6587 0.716 26.8 ⁰ 0.72 ⁰ 0.000003 0.0095 0.957 34.448 33.95 ⁰ 18.1 ⁰
40 ⁰ 1.0501 0.8044 0.6750 0.734 27.5 ⁰ 0.72 ⁰ 0.000003 0.0096 0.963 35.410 34.90 ⁰ 18.6 ⁰
41 ⁰ 1.0536 0.7952 0.6912 0.751 28.3 ⁰ 0.72 ⁰ 0.000003 0.0097 0.969 36.380 35.86 ⁰ 19.1 ⁰
42 ⁰ 1.0572 0.7857 0.7074 0.769 29.0 ⁰ 0.72 ⁰ 0.000003 0.0097 0.976 37.355 36.82 ⁰ 19.6 ⁰
43 ⁰ 1.0609 0.7759 0.7235 0.786 29.7 ⁰ 0.73 ⁰ 0.000003 0.0098 0.982 38.338 37.79 ⁰ 20.1 ⁰
44 ⁰ 1.0647 0.7659 0.7396 0.804 30.4 ⁰ 0.73 ⁰ 0.000003 0.0099 0.989 39.327 38.76 ⁰ 20.6 ⁰
45 ⁰ 1.0685 0.7556 0.7556 0.821 31.2 ⁰ 0.73 ⁰ 0.000003 0.0099 0.996 40.323 39.74 ⁰ 21.1 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
46 ⁰ 1.0725 0.7450 0.7715 0.839 31.9 ⁰ 0.73 ⁰ 0.000003 0.0100 1.004 41.327 40.73 ⁰ 21.7 ⁰
47 ⁰ 1.0766 0.7342 0.7874 0.856 32.6 ⁰ 0.74 ⁰ 0.000003 0.0101 1.011 42.339 41.73 ⁰ 22.2 ⁰
48 ⁰ 1.0807 0.7232 0.8031 0.873 33.4 ⁰ 0.74 ⁰ 0.000003 0.0102 1.019 43.358 42.73 ⁰ 22.7 ⁰
49 ⁰ 1.0850 0.7118 0.8189 0.890 34.1 ⁰ 0.74 ⁰ 0.000003 0.0102 1.027 44.385 43.75 ⁰ 23.3 ⁰
50 ⁰ 1.0894 0.7002 0.8345 0.907 34.9 ⁰ 0.74 ⁰ 0.000003 0.0103 1.035 45.420 44.77 ⁰ 23.8 ⁰
51 ⁰ 1.0938 0.6884 0.8501 0.924 35.6 ⁰ 0.75 ⁰ 0.000003 0.0104 1.044 46.464 45.80 ⁰ 24.3 ⁰
52 ⁰ 1.0984 0.6762 0.8655 0.941 36.4 ⁰ 0.75 ⁰ 0.000003 0.0105 1.052 47.517 46.83 ⁰ 24.9 ⁰
53 ⁰ 1.1031 0.6638 0.8809 0.958 37.1 ⁰ 0.75 ⁰ 0.000003 0.0106 1.061 48.578 47.88 ⁰ 25.5 ⁰
54 ⁰ 1.1078 0.6512 0.8963 0.974 37.9 ⁰ 0.76 ⁰ 0.000003 0.0107 1.070 49.648 48.93 ⁰ 26.0 ⁰
55 ⁰ 1.1127 0.6382 0.9115 0.991 38.6 ⁰ 0.76 ⁰ 0.000003 0.0108 1.080 50.728 50.00 ⁰ 26.6 ⁰
56 ⁰ 1.1177 0.6250 0.9266 1.007 39.4 ⁰ 0.76 ⁰ 0.000003 0.0109 1.089 51.817 51.07 ⁰ 27.2 ⁰
57 ⁰ 1.1228 0.6115 0.9416 1.024 40.2 ⁰ 0.77 ⁰ 0.000003 0.0110 1.099 52.917 52.15 ⁰ 27.7 ⁰
58 ⁰ 1.1280 0.5977 0.9566 1.040 40.9 ⁰ 0.77 ⁰ 0.000003 0.0111 1.109 54.026 53.25 ⁰ 28.3 ⁰
59 ⁰ 1.1332 0.5837 0.9714 1.056 41.7 ⁰ 0.77 ⁰ 0.000003 0.0112 1.120 55.146 54.35 ⁰ 28.9 ⁰
60 ⁰ 1.1386 0.5693 0.9861 1.072 42.5 ⁰ 0.78 ⁰ 0.000003 0.0113 1.130 56.276 55.47 ⁰ 29.5 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
61 ⁰ 1.1442 0.5547 1.0007 1.088 43.3 ⁰ 0.78 ⁰ 0.000003 0.0114 1.141 57.417 56.59 ⁰ 30.1 ⁰
62 ⁰ 1.1498 0.5398 1.0152 1.104 44.1 ⁰ 0.79 ⁰ 0.000003 0.0115 1.152 58.570 57.73 ⁰ 30.7 ⁰
63 ⁰ 1.1555 0.5246 1.0296 1.119 44.8 ⁰ 0.79 ⁰ 0.000003 0.0116 1.164 59.733 58.87 ⁰ 31.3 ⁰
64 ⁰ 1.1613 0.5091 1.0438 1.135 45.6 ⁰ 0.79 ⁰ 0.000004 0.0117 1.175 60.909 60.03 ⁰ 31.9 ⁰
65 ⁰ 1.1673 0.4933 1.0579 1.150 46.4 ⁰ 0.80 ⁰ 0.000004 0.0118 1.187 62.096 61.20 ⁰ 32.5 ⁰
66 ⁰ 1.1733 0.4772 1.0719 1.165 47.2 ⁰ 0.80 ⁰ 0.000004 0.0120 1.200 63.296 62.38 ⁰ 33.2 ⁰
67 ⁰ 1.1795 0.4609 1.0857 1.180 48.0 ⁰ 0.81 ⁰ 0.000004 0.0121 1.212 64.508 63.58 ⁰ 33.8 ⁰
68 ⁰ 1.1858 0.4442 1.0994 1.195 48.9 ⁰ 0.81 ⁰ 0.000004 0.0122 1.225 65.733 64.79 ⁰ 34.4 ⁰
69 ⁰ 1.1921 0.4272 1.1130 1.210 49.7 ⁰ 0.81 ⁰ 0.000004 0.0123 1.238 66.972 66.01 ⁰ 35.1 ⁰
70 ⁰ 1.1986 0.4100 1.1264 1.224 50.5 ⁰ 0.82 ⁰ 0.000004 0.0125 1.252 68.223 67.24 ⁰ 35.7 ⁰
71 ⁰ 1.2053 0.3924 1.1396 1.239 51.3 ⁰ 0.82 ⁰ 0.000004 0.0126 1.266 69.489 68.49 ⁰ 36.4 ⁰
72 ⁰ 1.2120 0.3745 1.1527 1.253 52.1 ⁰ 0.83 ⁰ 0.000004 0.0128 1.280 70.768 69.75 ⁰ 37.1 ⁰
73 ⁰ 1.2188 0.3564 1.1656 1.267 53.0 ⁰ 0.83 ⁰ 0.000004 0.0129 1.294 72.062 71.02 ⁰ 37.8 ⁰
74 ⁰ 1.2258 0.3379 1.1783 1.281 53.8 ⁰ 0.84 ⁰ 0.000004 0.0130 1.309 73.371 72.31 ⁰ 38.4 ⁰
75 ⁰ 1.2329 0.3191 1.1909 1.294 54.7 ⁰ 0.84 ⁰ 0.000004 0.0132 1.324 74.695 73.62 ⁰ 39.1 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
76 ⁰ 1.2401 0.3000 1.2032 1.308 55.5 ⁰ 0.85 ⁰ 0.000004 0.0133 1.339 76.034 74.94 ⁰ 39.8 ⁰
77 ⁰ 1.2474 0.2806 1.2154 1.321 56.4 ⁰ 0.85 ⁰ 0.000004 0.0135 1.355 77.389 76.27 ⁰ 40.6 ⁰
78 ⁰ 1.2548 0.2609 1.2274 1.334 57.2 ⁰ 0.86 ⁰ 0.000004 0.0137 1.371 78.760 77.63 ⁰ 41.3 ⁰
79 ⁰ 1.2623 0.2409 1.2391 1.347 58.1 ⁰ 0.86 ⁰ 0.000005 0.0138 1.387 80.148 78.99 ⁰ 42.0 ⁰
80 ⁰ 1.2700 0.2205 1.2507 1.359 58.9 ⁰ 0.87 ⁰ 0.000005 0.0140 1.404 81.552 80.38 ⁰ 42.7 ⁰
81 ⁰ 1.2777 0.1999 1.2620 1.372 59.8 ⁰ 0.87 ⁰ 0.000005 0.0142 1.421 82.973 81.78 ⁰ 43.5 ⁰
82 ⁰ 1.2856 0.1789 1.2731 1.384 60.7 ⁰ 0.88 ⁰ 0.000005 0.0143 1.439 84.412 83.20 ⁰ 44.2 ⁰
83 ⁰ 1.2936 0.1577 1.2840 1.396 61.6 ⁰ 0.88 ⁰ 0.000005 0.0145 1.457 85.869 84.63 ⁰ 45.0 ⁰
84 ⁰ 1.3018 0.1361 1.2946 1.407 62.5 ⁰ 0.89 ⁰ 0.000005 0.0147 1.475 87.345 86.09 ⁰ 45.8 ⁰
85 ⁰ 1.3100 0.1142 1.3050 1.419 63.4 ⁰ 0.90 ⁰ 0.000005 0.0149 1.494 88.838 87.56 ⁰ 46.6 ⁰
86 ⁰ 1.3184 0.0920 1.3152 1.430 64.3 ⁰ 0.90 ⁰ 0.000005 0.0151 1.513 90.351 89.05 ⁰ 47.3 ⁰
87 ⁰ 1.3269 0.0694 1.3250 1.440 65.2 ⁰ 0.91 ⁰ 0.000005 0.0153 1.532 91.884 90.56 ⁰ 48.1 ⁰
88 ⁰ 1.3355 0.0466 1.3346 1.451 66.1 ⁰ 0.91 ⁰ 0.000005 0.0155 1.552 93.436 92.09 ⁰ 49.0 ⁰
89 ⁰ 1.3442 0.0235 1.3440 1.461 67.0 ⁰ 0.92 ⁰ 0.000005 0.0157 1.572 95.008 93.64 ⁰ 49.8 ⁰
90 ⁰ 1.3530 0.0000 1.3530 1.471 67.9 ⁰ 0.93 ⁰ 0.000006 0.0159 1.593 96.602 95.21 ⁰ 50.6 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
91 ⁰ 1.3619 -0.0238 1.3617 1.480 68.9 ⁰ 0.93 ⁰ 0.000006 0.0161 1.614 98.216 96.80 ⁰ 51.5 ⁰
92 ⁰ 1.3710 -0.0478 1.3702 1.489 69.8 ⁰ 0.94 ⁰ 0.000006 0.0163 1.636 99.852 98.41 ⁰ 52.3 ⁰
93 ⁰ 1.3802 -0.0722 1.3783 1.498 70.7 ⁰ 0.94 ⁰ 0.000006 0.0165 1.658 101.509 100.05 ⁰ 53.2 ⁰
94 ⁰ 1.3895 -0.0969 1.3861 1.507 71.7 ⁰ 0.95 ⁰ 0.000006 0.0167 1.680 103.189 101.70 ⁰ 54.1 ⁰
95 ⁰ 1.3989 -0.1219 1.3936 1.515 72.7 ⁰ 0.96 ⁰ 0.000006 0.0170 1.703 104.892 103.38 ⁰ 55.0 ⁰
96 ⁰ 1.4084 -0.1472 1.4007 1.523 73.6 ⁰ 0.96 ⁰ 0.000006 0.0172 1.726 106.618 105.08 ⁰ 55.9 ⁰
97 ⁰ 1.4181 -0.1728 1.4075 1.530 74.6 ⁰ 0.97 ⁰ 0.000006 0.0174 1.750 108.368 106.81 ⁰ 56.8 ⁰
98 ⁰ 1.4278 -0.1987 1.4139 1.537 75.6 ⁰ 0.98 ⁰ 0.000007 0.0177 1.774 110.141 108.56 ⁰ 57.7 ⁰
99 ⁰ 1.4377 -0.2249 1.4200 1.544 76.6 ⁰ 0.99 ⁰ 0.000007 0.0179 1.798 111.940 110.33 ⁰ 58.7 ⁰
100 ⁰ 1.4476 -0.2514 1.4257 1.550 77.6 ⁰ 0.99 ⁰ 0.000007 0.0182 1.823 113.763 112.12 ⁰ 59.6 ⁰
101 ⁰ 1.4577 -0.2781 1.4309 1.555 78.6 ⁰ 1.00 ⁰ 0.000007 0.0184 1.849 115.612 113.95 ⁰ 60.6 ⁰
102 ⁰ 1.4679 -0.3052 1.4358 1.561 79.6 ⁰ 1.01 ⁰ 0.000007 0.0187 1.875 117.486 115.79 ⁰ 61.6 ⁰
103 ⁰ 1.4782 -0.3325 1.4403 1.566 80.6 ⁰ 1.02 ⁰ 0.000008 0.0189 1.901 119.387 117.67 ⁰ 62.6 ⁰
104 ⁰ 1.4886 -0.3601 1.4444 1.570 81.6 ⁰ 1.03 ⁰ 0.000008 0.0192 1.928 121.315 119.57 ⁰ 63.6 ⁰
105 ⁰ 1.4991 -0.3880 1.4480 1.574 82.7 ⁰ 1.04 ⁰ 0.000008 0.0195 1.955 123.270 121.49 ⁰ 64.6 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
106 ⁰ 1.5097 -0.4161 1.4512 1.577 83.7 ⁰ 1.05 ⁰ 0.000008 0.0198 1.983 125.252 123.45 ⁰ 65.6 ⁰
107 ⁰ 1.5204 -0.4445 1.4539 1.580 84.8 ⁰ 1.07 ⁰ 0.000009 0.0200 2.011 127.263 125.43 ⁰ 66.7 ⁰
108 ⁰ 1.5311 -0.4731 1.4562 1.583 85.9 ⁰ 1.10 ⁰ 0.000009 0.0203 2.039 129.302 127.44 ⁰ 67.8 ⁰
109 ⁰ 1.5420 -0.5020 1.4580 1.585 87.0 ⁰ 1.14 ⁰ 0.000011 0.0206 2.069 131.371 129.48 ⁰ 68.8 ⁰
110 ⁰ 1.5530 -0.5311 1.4593 1.586 88.3 ⁰ 1.26 ⁰ 0.000014 0.0209 2.098 133.469 131.55 ⁰ 69.9 ⁰
111 ⁰ 1.5640 -0.5605 1.4601 1.587 89.7 ⁰ 1.42 ⁰ 0.000020 0.0212 2.129 135.598 133.65 ⁰ 71.1 ⁰
112 ⁰ 1.5752 -0.5901 1.4605 1.588 89.9 ⁰ 0.20 ⁰ 0.000000 0.0215 2.157 137.756 135.77 ⁰ 72.2 ⁰
113 ⁰ 1.5864 -0.6198 1.4603 1.587 90.1 ⁰ 0.20 ⁰ 0.000000 0.0218 2.188 139.944 137.93 ⁰ 73.3 ⁰
114 ⁰ 1.5977 -0.6498 1.4595 1.587 91.4 ⁰ 1.32 ⁰ 0.000016 0.0221 2.221 142.165 140.12 ⁰ 74.5 ⁰
115 ⁰ 1.6090 -0.6800 1.4583 1.585 92.8 ⁰ 1.36 ⁰ 0.000018 0.0224 2.253 144.418 142.34 ⁰ 75.7 ⁰
116 ⁰ 1.6204 -0.7104 1.4565 1.583 94.0 ⁰ 1.21 ⁰ 0.000013 0.0228 2.284 146.702 144.59 ⁰ 76.9 ⁰
117 ⁰ 1.6319 -0.7409 1.4541 1.581 95.2 ⁰ 1.17 ⁰ 0.000011 0.0231 2.317 149.019 146.87 ⁰ 78.1 ⁰
118 ⁰ 1.6435 -0.7716 1.4511 1.577 96.3 ⁰ 1.16 ⁰ 0.000011 0.0234 2.350 151.369 149.19 ⁰ 79.3 ⁰
119 ⁰ 1.6551 -0.8024 1.4476 1.574 97.5 ⁰ 1.16 ⁰ 0.000011 0.0237 2.383 153.752 151.54 ⁰ 80.6 ⁰
120 ⁰ 1.6668 -0.8334 1.4435 1.569 98.6 ⁰ 1.16 ⁰ 0.000011 0.0241 2.417 156.169 153.92 ⁰ 81.8 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
121 ⁰ 1.6785 -0.8645 1.4387 1.564 99.8 ⁰ 1.16 ⁰ 0.000011 0.0244 2.451 158.620 156.34 ⁰ 83.1 ⁰
122 ⁰ 1.6902 -0.8957 1.4334 1.558 101.0 ⁰ 1.17 ⁰ 0.000011 0.0248 2.485 161.105 158.79 ⁰ 84.4 ⁰
123 ⁰ 1.7020 -0.9270 1.4274 1.552 102.1 ⁰ 1.17 ⁰ 0.000011 0.0251 2.520 163.626 161.27 ⁰ 85.7 ⁰
124 ⁰ 1.7138 -0.9584 1.4208 1.544 103.3 ⁰ 1.18 ⁰ 0.000012 0.0255 2.555 166.181 163.79 ⁰ 87.1 ⁰
125 ⁰ 1.7257 -0.9898 1.4136 1.537 104.5 ⁰ 1.18 ⁰ 0.000012 0.0258 2.591 168.772 166.34 ⁰ 88.4 ⁰
126 ⁰ 1.7375 -1.0213 1.4057 1.528 105.7 ⁰ 1.19 ⁰ 0.000012 0.0262 2.627 171.399 168.93 ⁰ 89.8 ⁰
127 ⁰ 1.7494 -1.0528 1.3971 1.519 106.9 ⁰ 1.20 ⁰ 0.000012 0.0265 2.663 174.062 171.56 ⁰ 91.2 ⁰
128 ⁰ 1.7613 -1.0843 1.3879 1.509 108.1 ⁰ 1.21 ⁰ 0.000012 0.0269 2.699 176.761 174.22 ⁰ 92.6 ⁰
129 ⁰ 1.7731 -1.1159 1.3780 1.498 109.3 ⁰ 1.21 ⁰ 0.000013 0.0273 2.736 179.497 176.91 ⁰ 94.1 ⁰
130 ⁰ 1.7850 -1.1474 1.3674 1.486 110.5 ⁰ 1.22 ⁰ 0.000013 0.0276 2.773 182.270 179.65 ⁰ 95.5 ⁰
131 ⁰ 1.7968 -1.1788 1.3561 1.474 111.7 ⁰ 1.23 ⁰ 0.000013 0.0280 2.810 185.080 182.41 ⁰ 97.0 ⁰
132 ⁰ 1.8086 -1.2102 1.3441 1.461 113.0 ⁰ 1.24 ⁰ 0.000013 0.0284 2.847 187.927 185.22 ⁰ 98.5 ⁰
133 ⁰ 1.8204 -1.2415 1.3314 1.447 114.2 ⁰ 1.25 ⁰ 0.000014 0.0287 2.885 190.812 188.06 ⁰ 100.0 ⁰
134 ⁰ 1.8322 -1.2727 1.3180 1.433 115.5 ⁰ 1.25 ⁰ 0.000014 0.0291 2.922 193.734 190.94 ⁰ 101.5 ⁰
135 ⁰ 1.8439 -1.3038 1.3038 1.417 116.7 ⁰ 1.26 ⁰ 0.000014 0.0295 2.960 196.694 193.86 ⁰ 103.1 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
136 ⁰ 1.8555 -1.3348 1.2890 1.401 118.0 ⁰ 1.27 ⁰ 0.000014 0.0299 2.998 199.691 196.82 ⁰ 104.6 ⁰
137 ⁰ 1.8671 -1.3655 1.2734 1.384 119.3 ⁰ 1.28 ⁰ 0.000015 0.0302 3.035 202.726 199.81 ⁰ 106.2 ⁰
138 ⁰ 1.8786 -1.3961 1.2570 1.366 120.6 ⁰ 1.28 ⁰ 0.000015 0.0306 3.073 205.800 202.84 ⁰ 107.8 ⁰
139 ⁰ 1.8901 -1.4264 1.2400 1.348 121.9 ⁰ 1.29 ⁰ 0.000015 0.0310 3.111 208.910 205.90 ⁰ 109.5 ⁰
140 ⁰ 1.9014 -1.4566 1.2222 1.329 123.2 ⁰ 1.30 ⁰ 0.000016 0.0314 3.149 212.059 209.01 ⁰ 111.1 ⁰
141 ⁰ 1.9126 -1.4864 1.2037 1.308 124.5 ⁰ 1.31 ⁰ 0.000016 0.0317 3.186 215.245 212.15 ⁰ 112.8 ⁰
142 ⁰ 1.9237 -1.5159 1.1844 1.287 125.8 ⁰ 1.31 ⁰ 0.000016 0.0321 3.224 218.469 215.32 ⁰ 114.5 ⁰
143 ⁰ 1.9348 -1.5452 1.1644 1.266 127.1 ⁰ 1.32 ⁰ 0.000016 0.0325 3.261 221.730 218.54 ⁰ 116.2 ⁰
144 ⁰ 1.9456 -1.5740 1.1436 1.243 128.4 ⁰ 1.33 ⁰ 0.000017 0.0329 3.298 225.028 221.79 ⁰ 117.9 ⁰
145 ⁰ 1.9564 -1.6026 1.1221 1.220 129.8 ⁰ 1.34 ⁰ 0.000017 0.0332 3.335 228.363 225.07 ⁰ 119.7 ⁰
146 ⁰ 1.9669 -1.6307 1.0999 1.196 131.1 ⁰ 1.34 ⁰ 0.000017 0.0336 3.371 231.734 228.40 ⁰ 121.4 ⁰
147 ⁰ 1.9774 -1.6584 1.0770 1.171 132.5 ⁰ 1.35 ⁰ 0.000017 0.0340 3.408 235.142 231.76 ⁰ 123.2 ⁰
148 ⁰ 1.9876 -1.6856 1.0533 1.145 133.8 ⁰ 1.36 ⁰ 0.000018 0.0343 3.443 238.585 235.15 ⁰ 125.0 ⁰
149 ⁰ 1.9977 -1.7124 1.0289 1.118 135.2 ⁰ 1.37 ⁰ 0.000018 0.0347 3.479 242.064 238.58 ⁰ 126.8 ⁰
150 ⁰ 2.0076 -1.7386 1.0038 1.091 136.6 ⁰ 1.37 ⁰ 0.000018 0.0350 3.514 245.578 242.04 ⁰ 128.7 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
151 ⁰ 2.0173 -1.7644 0.9780 1.063 137.9 ⁰ 1.38 ⁰ 0.000019 0.0354 3.548 249.126 245.54 ⁰ 130.5 ⁰
152 ⁰ 2.0268 -1.7895 0.9515 1.034 139.3 ⁰ 1.39 ⁰ 0.000019 0.0357 3.582 252.708 249.07 ⁰ 132.4 ⁰
153 ⁰ 2.0360 -1.8141 0.9243 1.005 140.7 ⁰ 1.39 ⁰ 0.000019 0.0360 3.615 256.324 252.63 ⁰ 134.3 ⁰
154 ⁰ 2.0450 -1.8381 0.8965 0.974 142.1 ⁰ 1.40 ⁰ 0.000019 0.0364 3.648 259.972 256.23 ⁰ 136.2 ⁰
155 ⁰ 2.0538 -1.8614 0.8680 0.943 143.5 ⁰ 1.40 ⁰ 0.000020 0.0367 3.680 263.652 259.86 ⁰ 138.2 ⁰
156 ⁰ 2.0623 -1.8840 0.8388 0.912 144.9 ⁰ 1.41 ⁰ 0.000020 0.0370 3.711 267.363 263.51 ⁰ 140.1 ⁰
157 ⁰ 2.0706 -1.9060 0.8091 0.879 146.3 ⁰ 1.42 ⁰ 0.000020 0.0373 3.741 271.104 267.20 ⁰ 142.1 ⁰
158 ⁰ 2.0786 -1.9273 0.7787 0.846 147.8 ⁰ 1.42 ⁰ 0.000020 0.0376 3.771 274.875 270.92 ⁰ 144.0 ⁰
159 ⁰ 2.0863 -1.9478 0.7477 0.813 149.2 ⁰ 1.43 ⁰ 0.000021 0.0379 3.800 278.675 274.66 ⁰ 146.0 ⁰
160 ⁰ 2.0938 -1.9675 0.7161 0.778 150.6 ⁰ 1.43 ⁰ 0.000021 0.0381 3.827 282.502 278.43 ⁰ 148.0 ⁰
161 ⁰ 2.1009 -1.9864 0.6840 0.743 152.1 ⁰ 1.44 ⁰ 0.000021 0.0384 3.854 286.356 282.23 ⁰ 150.1 ⁰
162 ⁰ 2.1077 -2.0046 0.6513 0.708 153.5 ⁰ 1.44 ⁰ 0.000021 0.0387 3.880 290.236 286.06 ⁰ 152.1 ⁰
163 ⁰ 2.1142 -2.0218 0.6181 0.672 155.0 ⁰ 1.45 ⁰ 0.000021 0.0389 3.904 294.140 289.90 ⁰ 154.1 ⁰
164 ⁰ 2.1204 -2.0383 0.5845 0.635 156.4 ⁰ 1.45 ⁰ 0.000022 0.0391 3.928 298.068 293.78 ⁰ 156.2 ⁰
165 ⁰ 2.1263 -2.0538 0.5503 0.598 157.9 ⁰ 1.45 ⁰ 0.000022 0.0394 3.950 302.018 297.67 ⁰ 158.3 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
166 ⁰ 2.1318 -2.0684 0.5157 0.561 159.3 ⁰ 1.46 ⁰ 0.000022 0.0396 3.971 305.990 301.58 ⁰ 160.3 ⁰
167 ⁰ 2.1369 -2.0822 0.4807 0.523 160.8 ⁰ 1.46 ⁰ 0.000022 0.0398 3.991 309.981 305.52 ⁰ 162.4 ⁰
168 ⁰ 2.1417 -2.0949 0.4453 0.484 162.2 ⁰ 1.47 ⁰ 0.000022 0.0400 4.010 313.991 309.47 ⁰ 164.5 ⁰
169 ⁰ 2.1462 -2.1068 0.4095 0.445 163.7 ⁰ 1.47 ⁰ 0.000022 0.0401 4.027 318.018 313.44 ⁰ 166.6 ⁰
170 ⁰ 2.1503 -2.1176 0.3734 0.406 165.2 ⁰ 1.47 ⁰ 0.000023 0.0403 4.043 322.062 317.42 ⁰ 168.8 ⁰
171 ⁰ 2.1540 -2.1275 0.3370 0.366 166.7 ⁰ 1.47 ⁰ 0.000023 0.0404 4.058 326.120 321.42 ⁰ 170.9 ⁰
172 ⁰ 2.1573 -2.1363 0.3002 0.326 168.1 ⁰ 1.48 ⁰ 0.000023 0.0406 4.071 330.192 325.44 ⁰ 173.0 ⁰
173 ⁰ 2.1603 -2.1442 0.2633 0.286 169.6 ⁰ 1.48 ⁰ 0.000023 0.0407 4.083 334.275 329.46 ⁰ 175.2 ⁰
174 ⁰ 2.1629 -2.1510 0.2261 0.246 171.1 ⁰ 1.48 ⁰ 0.000023 0.0408 4.094 338.369 333.50 ⁰ 177.3 ⁰
175 ⁰ 2.1650 -2.1568 0.1887 0.205 172.6 ⁰ 1.48 ⁰ 0.000023 0.0409 4.103 342.472 337.54 ⁰ 179.5 ⁰
176 ⁰ 2.1668 -2.1615 0.1511 0.164 174.1 ⁰ 1.48 ⁰ 0.000023 0.0410 4.110 346.582 341.59 ⁰ 181.6 ⁰
177 ⁰ 2.1682 -2.1652 0.1135 0.123 175.5 ⁰ 1.48 ⁰ 0.000023 0.0410 4.116 350.698 345.65 ⁰ 183.8 ⁰
178 ⁰ 2.1692 -2.1679 0.0757 0.082 177.0 ⁰ 1.49 ⁰ 0.000023 0.0411 4.121 354.819 349.71 ⁰ 185.9 ⁰
179 ⁰ 2.1698 -2.1695 0.0379 0.041 178.5 ⁰ 1.49 ⁰ 0.000023 0.0411 4.124 358.943 353.77 ⁰ 188.1 ⁰
180 ⁰ 2.1700 -2.1700 0.0000 0.000 180.0 ⁰ 1.49 ⁰ 0.000023 0.0411 4.125 363.069 357.84 ⁰ 190.2 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
181 ⁰ 2.1698 -2.1695 -0.0379 -0.041 181.5 ⁰ 1.49 ⁰ 0.000023 0.0411 4.125 367.194 1.91 ⁰ 192.4 ⁰
182 ⁰ 2.1692 -2.1679 -0.0757 -0.082 183.0 ⁰ 1.49 ⁰ 0.000023 0.0411 4.124 371.318 5.97 ⁰ 194.6 ⁰
183 ⁰ 2.1682 -2.1652 -0.1135 -0.123 184.5 ⁰ 1.49 ⁰ 0.000023 0.0411 4.121 375.439 10.03 ⁰ 196.7 ⁰
184 ⁰ 2.1668 -2.1615 -0.1511 -0.164 185.9 ⁰ 1.48 ⁰ 0.000023 0.0410 4.116 379.555 14.09 ⁰ 198.9 ⁰
185 ⁰ 2.1650 -2.1568 -0.1887 -0.205 187.4 ⁰ 1.48 ⁰ 0.000023 0.0410 4.110 383.666 18.14 ⁰ 201.0 ⁰
186 ⁰ 2.1629 -2.1510 -0.2261 -0.246 188.9 ⁰ 1.48 ⁰ 0.000023 0.0409 4.103 387.769 22.18 ⁰ 203.2 ⁰
187 ⁰ 2.1603 -2.1442 -0.2633 -0.286 190.4 ⁰ 1.48 ⁰ 0.000023 0.0408 4.094 391.862 26.22 ⁰ 205.3 ⁰
188 ⁰ 2.1573 -2.1363 -0.3002 -0.326 191.9 ⁰ 1.48 ⁰ 0.000023 0.0407 4.083 395.946 30.24 ⁰ 207.5 ⁰
189 ⁰ 2.1540 -2.1275 -0.3370 -0.366 193.3 ⁰ 1.48 ⁰ 0.000023 0.0406 4.071 400.017 34.26 ⁰ 209.6 ⁰
190 ⁰ 2.1503 -2.1176 -0.3734 -0.406 194.8 ⁰ 1.47 ⁰ 0.000023 0.0404 4.058 404.075 38.26 ⁰ 211.7 ⁰
191 ⁰ 2.1462 -2.1068 -0.4095 -0.445 196.3 ⁰ 1.47 ⁰ 0.000023 0.0403 4.043 408.119 42.24 ⁰ 213.9 ⁰
192 ⁰ 2.1417 -2.0949 -0.4453 -0.484 197.8 ⁰ 1.47 ⁰ 0.000022 0.0401 4.027 412.146 46.21 ⁰ 216.0 ⁰
193 ⁰ 2.1369 -2.0822 -0.4807 -0.523 199.2 ⁰ 1.47 ⁰ 0.000022 0.0400 4.010 416.156 50.16 ⁰ 218.1 ⁰
194 ⁰ 2.1318 -2.0684 -0.5157 -0.561 200.7 ⁰ 1.46 ⁰ 0.000022 0.0398 3.991 420.148 54.10 ⁰ 220.2 ⁰
195 ⁰ 2.1263 -2.0538 -0.5503 -0.598 202.1 ⁰ 1.46 ⁰ 0.000022 0.0396 3.971 424.119 58.01 ⁰ 222.2 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
196 ⁰ 2.1204 -2.0383 -0.5845 -0.635 203.6 ⁰ 1.45 ⁰ 0.000022 0.0394 3.950 428.069 61.91 ⁰ 224.3 ⁰
197 ⁰ 2.1142 -2.0218 -0.6181 -0.672 205.0 ⁰ 1.45 ⁰ 0.000022 0.0391 3.928 431.997 65.78 ⁰ 226.4 ⁰
198 ⁰ 2.1077 -2.0046 -0.6513 -0.708 206.5 ⁰ 1.45 ⁰ 0.000021 0.0389 3.904 435.902 69.62 ⁰ 228.4 ⁰
199 ⁰ 2.1009 -1.9864 -0.6840 -0.743 207.9 ⁰ 1.44 ⁰ 0.000021 0.0387 3.880 439.781 73.45 ⁰ 230.4 ⁰
200 ⁰ 2.0938 -1.9675 -0.7161 -0.778 209.4 ⁰ 1.44 ⁰ 0.000021 0.0384 3.854 443.635 77.25 ⁰ 232.5 ⁰
201 ⁰ 2.0863 -1.9478 -0.7477 -0.813 210.8 ⁰ 1.43 ⁰ 0.000021 0.0381 3.827 447.463 81.02 ⁰ 234.5 ⁰
202 ⁰ 2.0786 -1.9273 -0.7787 -0.846 212.2 ⁰ 1.43 ⁰ 0.000021 0.0379 3.800 451.262 84.76 ⁰ 236.5 ⁰
203 ⁰ 2.0706 -1.9060 -0.8091 -0.879 213.7 ⁰ 1.42 ⁰ 0.000020 0.0376 3.771 455.033 88.48 ⁰ 238.4 ⁰
204 ⁰ 2.0623 -1.8840 -0.8388 -0.912 215.1 ⁰ 1.42 ⁰ 0.000020 0.0373 3.741 458.775 92.17 ⁰ 240.4 ⁰
205 ⁰ 2.0538 -1.8614 -0.8680 -0.943 216.5 ⁰ 1.41 ⁰ 0.000020 0.0370 3.711 462.486 95.83 ⁰ 242.3 ⁰
206 ⁰ 2.0450 -1.8381 -0.8965 -0.974 217.9 ⁰ 1.40 ⁰ 0.000020 0.0367 3.680 466.166 99.45 ⁰ 244.3 ⁰
207 ⁰ 2.0360 -1.8141 -0.9243 -1.005 219.3 ⁰ 1.40 ⁰ 0.000019 0.0364 3.648 469.814 103.05 ⁰ 246.2 ⁰
208 ⁰ 2.0268 -1.7895 -0.9515 -1.034 220.7 ⁰ 1.39 ⁰ 0.000019 0.0360 3.615 473.429 106.61 ⁰ 248.1 ⁰
209 ⁰ 2.0173 -1.7644 -0.9780 -1.063 222.1 ⁰ 1.39 ⁰ 0.000019 0.0357 3.582 477.011 110.14 ⁰ 250.0 ⁰
210 ⁰ 2.0076 -1.7386 -1.0038 -1.091 223.4 ⁰ 1.38 ⁰ 0.000019 0.0354 3.548 480.560 113.64 ⁰ 251.8 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
211 ⁰ 1.9977 -1.7124 -1.0289 -1.118 224.8 ⁰ 1.37 ⁰ 0.000018 0.0350 3.514 484.073 117.10 ⁰ 253.7 ⁰
212 ⁰ 1.9876 -1.6856 -1.0533 -1.145 226.2 ⁰ 1.37 ⁰ 0.000018 0.0347 3.479 487.552 120.53 ⁰ 255.5 ⁰
213 ⁰ 1.9774 -1.6584 -1.0770 -1.171 227.5 ⁰ 1.36 ⁰ 0.000018 0.0343 3.443 490.996 123.93 ⁰ 257.3 ⁰
214 ⁰ 1.9669 -1.6307 -1.0999 -1.196 228.9 ⁰ 1.35 ⁰ 0.000017 0.0340 3.408 494.403 127.28 ⁰ 259.1 ⁰
215 ⁰ 1.9564 -1.6026 -1.1221 -1.220 230.2 ⁰ 1.34 ⁰ 0.000017 0.0336 3.371 497.775 130.61 ⁰ 260.8 ⁰
216 ⁰ 1.9456 -1.5740 -1.1436 -1.243 231.6 ⁰ 1.34 ⁰ 0.000017 0.0332 3.335 501.110 133.89 ⁰ 262.6 ⁰
217 ⁰ 1.9348 -1.5452 -1.1644 -1.266 232.9 ⁰ 1.33 ⁰ 0.000017 0.0329 3.298 504.408 137.14 ⁰ 264.3 ⁰
218 ⁰ 1.9237 -1.5159 -1.1844 -1.287 234.2 ⁰ 1.32 ⁰ 0.000016 0.0325 3.261 507.669 140.36 ⁰ 266.0 ⁰
219 ⁰ 1.9126 -1.4864 -1.2037 -1.308 235.5 ⁰ 1.31 ⁰ 0.000016 0.0321 3.224 510.892 143.54 ⁰ 267.7 ⁰
220 ⁰ 1.9014 -1.4566 -1.2222 -1.329 236.8 ⁰ 1.31 ⁰ 0.000016 0.0317 3.186 514.078 146.68 ⁰ 269.4 ⁰
221 ⁰ 1.8901 -1.4264 -1.2400 -1.348 238.1 ⁰ 1.30 ⁰ 0.000016 0.0314 3.149 517.227 149.78 ⁰ 271.0 ⁰
222 ⁰ 1.8786 -1.3961 -1.2570 -1.366 239.4 ⁰ 1.29 ⁰ 0.000015 0.0310 3.111 520.338 152.84 ⁰ 272.7 ⁰
223 ⁰ 1.8671 -1.3655 -1.2734 -1.384 240.7 ⁰ 1.28 ⁰ 0.000015 0.0306 3.073 523.411 155.87 ⁰ 274.3 ⁰
224 ⁰ 1.8555 -1.3348 -1.2890 -1.401 242.0 ⁰ 1.28 ⁰ 0.000015 0.0302 3.035 526.446 158.87 ⁰ 275.9 ⁰
225 ⁰ 1.8439 -1.3038 -1.3038 -1.417 243.3 ⁰ 1.27 ⁰ 0.000014 0.0299 2.998 529.444 161.82 ⁰ 277.4 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
226 ⁰ 1.8322 -1.2727 -1.3180 -1.433 244.5 ⁰ 1.26 ⁰ 0.000014 0.0295 2.960 532.404 164.74 ⁰ 279.0 ⁰
227 ⁰ 1.8204 -1.2415 -1.3314 -1.447 245.8 ⁰ 1.25 ⁰ 0.000014 0.0291 2.922 535.326 167.62 ⁰ 280.5 ⁰
228 ⁰ 1.8086 -1.2102 -1.3441 -1.461 247.0 ⁰ 1.25 ⁰ 0.000014 0.0287 2.885 538.210 170.46 ⁰ 282.0 ⁰
229 ⁰ 1.7968 -1.1788 -1.3561 -1.474 248.3 ⁰ 1.24 ⁰ 0.000013 0.0284 2.847 541.058 173.27 ⁰ 283.5 ⁰
230 ⁰ 1.7850 -1.1474 -1.3674 -1.486 249.5 ⁰ 1.23 ⁰ 0.000013 0.0280 2.810 543.867 176.04 ⁰ 285.0 ⁰
231 ⁰ 1.7731 -1.1159 -1.3780 -1.498 250.7 ⁰ 1.22 ⁰ 0.000013 0.0276 2.773 546.640 178.77 ⁰ 286.4 ⁰
232 ⁰ 1.7613 -1.0843 -1.3879 -1.509 251.9 ⁰ 1.21 ⁰ 0.000013 0.0273 2.736 549.376 181.47 ⁰ 287.9 ⁰
233 ⁰ 1.7494 -1.0528 -1.3971 -1.519 253.1 ⁰ 1.21 ⁰ 0.000012 0.0269 2.699 552.076 184.13 ⁰ 289.3 ⁰
234 ⁰ 1.7375 -1.0213 -1.4057 -1.528 254.3 ⁰ 1.20 ⁰ 0.000012 0.0265 2.663 554.739 186.75 ⁰ 290.7 ⁰
235 ⁰ 1.7257 -0.9898 -1.4136 -1.537 255.5 ⁰ 1.19 ⁰ 0.000012 0.0262 2.627 557.365 189.34 ⁰ 292.1 ⁰
236 ⁰ 1.7138 -0.9584 -1.4208 -1.544 256.7 ⁰ 1.18 ⁰ 0.000012 0.0258 2.591 559.956 191.89 ⁰ 293.4 ⁰
237 ⁰ 1.7020 -0.9270 -1.4274 -1.552 257.9 ⁰ 1.18 ⁰ 0.000012 0.0255 2.555 562.512 194.41 ⁰ 294.8 ⁰
238 ⁰ 1.6902 -0.8957 -1.4334 -1.558 259.0 ⁰ 1.17 ⁰ 0.000011 0.0251 2.520 565.032 196.90 ⁰ 296.1 ⁰
239 ⁰ 1.6785 -0.8645 -1.4387 -1.564 260.2 ⁰ 1.17 ⁰ 0.000011 0.0248 2.485 567.518 199.35 ⁰ 297.4 ⁰
240 ⁰ 1.6668 -0.8334 -1.4435 -1.569 261.4 ⁰ 1.16 ⁰ 0.000011 0.0244 2.451 569.969 201.76 ⁰ 298.7 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
241 ⁰ 1.6551 -0.8024 -1.4476 -1.574 262.5 ⁰ 1.16 ⁰ 0.000011 0.0241 2.417 572.385 204.14 ⁰ 299.9 ⁰
242 ⁰ 1.6435 -0.7716 -1.4511 -1.577 263.7 ⁰ 1.16 ⁰ 0.000011 0.0237 2.383 574.769 206.49 ⁰ 301.2 ⁰
243 ⁰ 1.6319 -0.7409 -1.4541 -1.581 264.8 ⁰ 1.16 ⁰ 0.000011 0.0234 2.350 577.118 208.81 ⁰ 302.4 ⁰
244 ⁰ 1.6204 -0.7104 -1.4565 -1.583 266.0 ⁰ 1.17 ⁰ 0.000011 0.0231 2.317 579.435 211.09 ⁰ 303.6 ⁰
245 ⁰ 1.6090 -0.6800 -1.4583 -1.585 267.2 ⁰ 1.21 ⁰ 0.000013 0.0228 2.284 581.720 213.34 ⁰ 304.8 ⁰
246 ⁰ 1.5977 -0.6498 -1.4595 -1.587 268.6 ⁰ 1.36 ⁰ 0.000018 0.0224 2.253 583.972 215.56 ⁰ 306.0 ⁰
247 ⁰ 1.5864 -0.6198 -1.4603 -1.587 269.9 ⁰ 1.32 ⁰ 0.000016 0.0221 2.221 586.193 217.75 ⁰ 307.2 ⁰
248 ⁰ 1.5752 -0.5901 -1.4605 -1.588 270.2 ⁰ 0.25 ⁰ 0.000000 0.0218 2.188 588.382 219.91 ⁰ 308.3 ⁰
249 ⁰ 1.5640 -0.5605 -1.4601 -1.587 270.4 ⁰ 0.25 ⁰ 0.000000 0.0215 2.157 590.539 222.04 ⁰ 309.4 ⁰
250 ⁰ 1.5530 -0.5311 -1.4593 -1.586 271.7 ⁰ 1.32 ⁰ 0.000016 0.0212 2.129 592.668 224.13 ⁰ 310.6 ⁰
251 ⁰ 1.5420 -0.5020 -1.4580 -1.585 273.0 ⁰ 1.26 ⁰ 0.000014 0.0209 2.098 594.766 226.20 ⁰ 311.7 ⁰
252 ⁰ 1.5311 -0.4731 -1.4562 -1.583 274.1 ⁰ 1.14 ⁰ 0.000011 0.0206 2.069 596.835 228.24 ⁰ 312.7 ⁰
253 ⁰ 1.5204 -0.4445 -1.4539 -1.580 275.2 ⁰ 1.10 ⁰ 0.000009 0.0203 2.039 598.874 230.25 ⁰ 313.8 ⁰
254 ⁰ 1.5097 -0.4161 -1.4512 -1.577 276.3 ⁰ 1.07 ⁰ 0.000009 0.0200 2.011 600.885 232.23 ⁰ 314.9 ⁰
255 ⁰ 1.4991 -0.3880 -1.4480 -1.574 277.3 ⁰ 1.05 ⁰ 0.000008 0.0198 1.983 602.868 234.19 ⁰ 315.9 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
256 ⁰ 1.4886 -0.3601 -1.4444 -1.570 278.4 ⁰ 1.04 ⁰ 0.000008 0.0195 1.955 604.822 236.11 ⁰ 316.9 ⁰
257 ⁰ 1.4782 -0.3325 -1.4403 -1.566 279.4 ⁰ 1.03 ⁰ 0.000008 0.0192 1.928 606.750 238.01 ⁰ 317.9 ⁰
258 ⁰ 1.4679 -0.3052 -1.4358 -1.561 280.4 ⁰ 1.02 ⁰ 0.000008 0.0189 1.901 608.651 239.89 ⁰ 318.9 ⁰
259 ⁰ 1.4577 -0.2781 -1.4309 -1.555 281.4 ⁰ 1.01 ⁰ 0.000007 0.0187 1.875 610.526 241.73 ⁰ 319.9 ⁰
260 ⁰ 1.4476 -0.2514 -1.4257 -1.550 282.4 ⁰ 1.00 ⁰ 0.000007 0.0184 1.849 612.374 243.56 ⁰ 320.9 ⁰
261 ⁰ 1.4377 -0.2249 -1.4200 -1.544 283.4 ⁰ 0.99 ⁰ 0.000007 0.0182 1.823 614.197 245.35 ⁰ 321.8 ⁰
262 ⁰ 1.4278 -0.1987 -1.4139 -1.537 284.4 ⁰ 0.99 ⁰ 0.000007 0.0179 1.798 615.996 247.13 ⁰ 322.8 ⁰
263 ⁰ 1.4181 -0.1728 -1.4075 -1.530 285.4 ⁰ 0.98 ⁰ 0.000007 0.0177 1.774 617.769 248.87 ⁰ 323.7 ⁰
264 ⁰ 1.4084 -0.1472 -1.4007 -1.523 286.4 ⁰ 0.97 ⁰ 0.000006 0.0174 1.750 619.519 250.60 ⁰ 324.6 ⁰
265 ⁰ 1.3989 -0.1219 -1.3936 -1.515 287.3 ⁰ 0.96 ⁰ 0.000006 0.0172 1.726 621.245 252.30 ⁰ 325.5 ⁰
266 ⁰ 1.3895 -0.0969 -1.3861 -1.507 288.3 ⁰ 0.96 ⁰ 0.000006 0.0170 1.703 622.948 253.98 ⁰ 326.4 ⁰
267 ⁰ 1.3802 -0.0722 -1.3783 -1.498 289.3 ⁰ 0.95 ⁰ 0.000006 0.0167 1.680 624.628 255.63 ⁰ 327.3 ⁰
268 ⁰ 1.3710 -0.0478 -1.3702 -1.489 290.2 ⁰ 0.94 ⁰ 0.000006 0.0165 1.658 626.285 257.27 ⁰ 328.2 ⁰
269 ⁰ 1.3619 -0.0238 -1.3617 -1.480 291.1 ⁰ 0.94 ⁰ 0.000006 0.0163 1.636 627.921 258.88 ⁰ 329.0 ⁰
270 ⁰ 1.3530 0.0000 -1.3530 -1.471 292.1 ⁰ 0.93 ⁰ 0.000006 0.0161 1.614 629.535 260.47 ⁰ 329.9 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
271 ⁰ 1.3442 0.0235 -1.3440 -1.461 293.0 ⁰ 0.93 ⁰ 0.000006 0.0159 1.593 631.129 262.04 ⁰ 330.7 ⁰
272 ⁰ 1.3355 0.0466 -1.3346 -1.451 293.9 ⁰ 0.92 ⁰ 0.000005 0.0157 1.572 632.701 263.59 ⁰ 331.5 ⁰
273 ⁰ 1.3269 0.0694 -1.3250 -1.440 294.8 ⁰ 0.91 ⁰ 0.000005 0.0155 1.552 634.253 265.12 ⁰ 332.3 ⁰
274 ⁰ 1.3184 0.0920 -1.3152 -1.430 295.7 ⁰ 0.91 ⁰ 0.000005 0.0153 1.532 635.786 266.63 ⁰ 333.2 ⁰
275 ⁰ 1.3100 0.1142 -1.3050 -1.419 296.6 ⁰ 0.90 ⁰ 0.000005 0.0151 1.513 637.299 268.12 ⁰ 333.9 ⁰
276 ⁰ 1.3018 0.1361 -1.2946 -1.407 297.5 ⁰ 0.90 ⁰ 0.000005 0.0149 1.494 638.792 269.59 ⁰ 334.7 ⁰
277 ⁰ 1.2936 0.1577 -1.2840 -1.396 298.4 ⁰ 0.89 ⁰ 0.000005 0.0147 1.475 640.268 271.05 ⁰ 335.5 ⁰
278 ⁰ 1.2856 0.1789 -1.2731 -1.384 299.3 ⁰ 0.88 ⁰ 0.000005 0.0145 1.457 641.725 272.48 ⁰ 336.3 ⁰
279 ⁰ 1.2777 0.1999 -1.2620 -1.372 300.2 ⁰ 0.88 ⁰ 0.000005 0.0143 1.439 643.164 273.90 ⁰ 337.0 ⁰
280 ⁰ 1.2700 0.2205 -1.2507 -1.359 301.1 ⁰ 0.87 ⁰ 0.000005 0.0142 1.421 644.585 275.30 ⁰ 337.8 ⁰
281 ⁰ 1.2623 0.2409 -1.2391 -1.347 301.9 ⁰ 0.87 ⁰ 0.000005 0.0140 1.404 645.989 276.69 ⁰ 338.5 ⁰
282 ⁰ 1.2548 0.2609 -1.2274 -1.334 302.8 ⁰ 0.86 ⁰ 0.000005 0.0138 1.387 647.377 278.05 ⁰ 339.2 ⁰
283 ⁰ 1.2474 0.2806 -1.2154 -1.321 303.6 ⁰ 0.86 ⁰ 0.000004 0.0137 1.371 648.748 279.41 ⁰ 339.9 ⁰
284 ⁰ 1.2401 0.3000 -1.2032 -1.308 304.5 ⁰ 0.85 ⁰ 0.000004 0.0135 1.355 650.103 280.74 ⁰ 340.7 ⁰
285 ⁰ 1.2329 0.3191 -1.1909 -1.294 305.3 ⁰ 0.85 ⁰ 0.000004 0.0133 1.339 651.442 282.06 ⁰ 341.4 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
286 ⁰ 1.2258 0.3379 -1.1783 -1.281 306.2 ⁰ 0.84 ⁰ 0.000004 0.0132 1.324 652.766 283.37 ⁰ 342.0 ⁰
287 ⁰ 1.2188 0.3564 -1.1656 -1.267 307.0 ⁰ 0.84 ⁰ 0.000004 0.0130 1.309 654.075 284.66 ⁰ 342.7 ⁰
288 ⁰ 1.2120 0.3745 -1.1527 -1.253 307.9 ⁰ 0.83 ⁰ 0.000004 0.0129 1.294 655.369 285.93 ⁰ 343.4 ⁰
289 ⁰ 1.2053 0.3924 -1.1396 -1.239 308.7 ⁰ 0.83 ⁰ 0.000004 0.0128 1.280 656.648 287.19 ⁰ 344.1 ⁰
290 ⁰ 1.1986 0.4100 -1.1264 -1.224 309.5 ⁰ 0.82 ⁰ 0.000004 0.0126 1.266 657.914 288.44 ⁰ 344.7 ⁰
291 ⁰ 1.1921 0.4272 -1.1130 -1.210 310.3 ⁰ 0.82 ⁰ 0.000004 0.0125 1.252 659.165 289.67 ⁰ 345.4 ⁰
292 ⁰ 1.1858 0.4442 -1.0994 -1.195 311.1 ⁰ 0.81 ⁰ 0.000004 0.0123 1.238 660.404 290.89 ⁰ 346.1 ⁰
293 ⁰ 1.1795 0.4609 -1.0857 -1.180 312.0 ⁰ 0.81 ⁰ 0.000004 0.0122 1.225 661.629 292.10 ⁰ 346.7 ⁰
294 ⁰ 1.1733 0.4772 -1.0719 -1.165 312.8 ⁰ 0.81 ⁰ 0.000004 0.0121 1.212 662.841 293.30 ⁰ 347.3 ⁰
295 ⁰ 1.1673 0.4933 -1.0579 -1.150 313.6 ⁰ 0.80 ⁰ 0.000004 0.0120 1.200 664.041 294.48 ⁰ 348.0 ⁰
296 ⁰ 1.1613 0.5091 -1.0438 -1.135 314.4 ⁰ 0.80 ⁰ 0.000004 0.0118 1.187 665.228 295.65 ⁰ 348.6 ⁰
297 ⁰ 1.1555 0.5246 -1.0296 -1.119 315.2 ⁰ 0.79 ⁰ 0.000004 0.0117 1.175 666.404 296.81 ⁰ 349.2 ⁰
298 ⁰ 1.1498 0.5398 -1.0152 -1.104 315.9 ⁰ 0.79 ⁰ 0.000003 0.0116 1.164 667.567 297.95 ⁰ 349.8 ⁰
299 ⁰ 1.1442 0.5547 -1.0007 -1.088 316.7 ⁰ 0.79 ⁰ 0.000003 0.0115 1.152 668.720 299.09 ⁰ 350.4 ⁰
300 ⁰ 1.1386 0.5693 -0.9861 -1.072 317.5 ⁰ 0.78 ⁰ 0.000003 0.0114 1.141 669.861 300.22 ⁰ 351.0 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
301 ⁰ 1.1332 0.5837 -0.9714 -1.056 318.3 ⁰ 0.78 ⁰ 0.000003 0.0113 1.130 670.991 301.33 ⁰ 351.6 ⁰
302 ⁰ 1.1280 0.5977 -0.9566 -1.040 319.1 ⁰ 0.77 ⁰ 0.000003 0.0112 1.120 672.111 302.43 ⁰ 352.2 ⁰
303 ⁰ 1.1228 0.6115 -0.9416 -1.024 319.8 ⁰ 0.77 ⁰ 0.000003 0.0111 1.109 673.220 303.53 ⁰ 352.8 ⁰
304 ⁰ 1.1177 0.6250 -0.9266 -1.007 320.6 ⁰ 0.77 ⁰ 0.000003 0.0110 1.099 674.320 304.61 ⁰ 353.3 ⁰
305 ⁰ 1.1127 0.6382 -0.9115 -0.991 321.4 ⁰ 0.76 ⁰ 0.000003 0.0109 1.089 675.409 305.68 ⁰ 353.9 ⁰
306 ⁰ 1.1078 0.6512 -0.8963 -0.974 322.1 ⁰ 0.76 ⁰ 0.000003 0.0108 1.080 676.489 306.75 ⁰ 354.5 ⁰
307 ⁰ 1.1031 0.6638 -0.8809 -0.958 322.9 ⁰ 0.76 ⁰ 0.000003 0.0107 1.070 677.559 307.80 ⁰ 355.0 ⁰
308 ⁰ 1.0984 0.6762 -0.8655 -0.941 323.6 ⁰ 0.75 ⁰ 0.000003 0.0106 1.061 678.621 308.85 ⁰ 355.6 ⁰
309 ⁰ 1.0938 0.6884 -0.8501 -0.924 324.4 ⁰ 0.75 ⁰ 0.000003 0.0105 1.052 679.673 309.89 ⁰ 356.1 ⁰
310 ⁰ 1.0894 0.7002 -0.8345 -0.907 325.1 ⁰ 0.75 ⁰ 0.000003 0.0104 1.044 680.717 310.91 ⁰ 356.7 ⁰
311 ⁰ 1.0850 0.7118 -0.8189 -0.890 325.9 ⁰ 0.74 ⁰ 0.000003 0.0103 1.035 681.752 311.93 ⁰ 357.2 ⁰
312 ⁰ 1.0807 0.7232 -0.8031 -0.873 326.6 ⁰ 0.74 ⁰ 0.000003 0.0102 1.027 682.779 312.95 ⁰ 357.8 ⁰
313 ⁰ 1.0766 0.7342 -0.7874 -0.856 327.4 ⁰ 0.74 ⁰ 0.000003 0.0102 1.019 683.798 313.95 ⁰ 358.3 ⁰
314 ⁰ 1.0725 0.7450 -0.7715 -0.839 328.1 ⁰ 0.74 ⁰ 0.000003 0.0101 1.011 684.810 314.95 ⁰ 358.8 ⁰
315 ⁰ 1.0685 0.7556 -0.7556 -0.821 328.8 ⁰ 0.73 ⁰ 0.000003 0.0100 1.004 685.814 315.94 ⁰ 359.4 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
316 ⁰ 1.0647 0.7659 -0.7396 -0.804 329.6 ⁰ 0.73 ⁰ 0.000003 0.0099 0.996 686.810 316.92 ⁰ 359.9 ⁰
317 ⁰ 1.0609 0.7759 -0.7235 -0.786 330.3 ⁰ 0.73 ⁰ 0.000003 0.0099 0.989 687.799 317.90 ⁰ 0.4 ⁰
318 ⁰ 1.0572 0.7857 -0.7074 -0.769 331.0 ⁰ 0.73 ⁰ 0.000003 0.0098 0.982 688.782 318.86 ⁰ 0.9 ⁰
319 ⁰ 1.0536 0.7952 -0.6912 -0.751 331.7 ⁰ 0.72 ⁰ 0.000003 0.0097 0.976 689.758 319.83 ⁰ 1.4 ⁰
320 ⁰ 1.0501 0.8044 -0.6750 -0.734 332.5 ⁰ 0.72 ⁰ 0.000003 0.0097 0.969 690.727 320.78 ⁰ 1.9 ⁰
321 ⁰ 1.0467 0.8135 -0.6587 -0.716 333.2 ⁰ 0.72 ⁰ 0.000003 0.0096 0.963 691.690 321.73 ⁰ 2.4 ⁰
322 ⁰ 1.0434 0.8222 -0.6424 -0.698 333.9 ⁰ 0.72 ⁰ 0.000003 0.0095 0.957 692.646 322.67 ⁰ 2.9 ⁰
323 ⁰ 1.0402 0.8308 -0.6260 -0.680 334.6 ⁰ 0.71 ⁰ 0.000003 0.0095 0.951 693.597 323.61 ⁰ 3.4 ⁰
324 ⁰ 1.0371 0.8390 -0.6096 -0.663 335.3 ⁰ 0.71 ⁰ 0.000003 0.0094 0.945 694.542 324.54 ⁰ 3.9 ⁰
325 ⁰ 1.0341 0.8471 -0.5931 -0.645 336.0 ⁰ 0.71 ⁰ 0.000003 0.0094 0.939 695.481 325.47 ⁰ 4.4 ⁰
326 ⁰ 1.0311 0.8549 -0.5766 -0.627 336.7 ⁰ 0.71 ⁰ 0.000003 0.0093 0.934 696.415 326.39 ⁰ 4.9 ⁰
327 ⁰ 1.0283 0.8624 -0.5601 -0.609 337.4 ⁰ 0.71 ⁰ 0.000002 0.0093 0.929 697.344 327.30 ⁰ 5.4 ⁰
328 ⁰ 1.0256 0.8697 -0.5435 -0.591 338.1 ⁰ 0.70 ⁰ 0.000002 0.0092 0.924 698.268 328.21 ⁰ 5.9 ⁰
329 ⁰ 1.0229 0.8768 -0.5268 -0.573 338.8 ⁰ 0.70 ⁰ 0.000002 0.0092 0.919 699.187 329.12 ⁰ 6.4 ⁰
330 ⁰ 1.0203 0.8836 -0.5102 -0.555 339.5 ⁰ 0.70 ⁰ 0.000002 0.0091 0.914 700.101 330.02 ⁰ 6.9 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
331 ⁰ 1.0178 0.8902 -0.4935 -0.536 340.2 ⁰ 0.70 ⁰ 0.000002 0.0091 0.910 701.011 330.92 ⁰ 7.3 ⁰
332 ⁰ 1.0154 0.8966 -0.4767 -0.518 340.9 ⁰ 0.70 ⁰ 0.000002 0.0090 0.905 701.916 331.81 ⁰ 7.8 ⁰
333 ⁰ 1.0131 0.9027 -0.4600 -0.500 341.6 ⁰ 0.69 ⁰ 0.000002 0.0090 0.901 702.817 332.70 ⁰ 8.3 ⁰
334 ⁰ 1.0109 0.9086 -0.4432 -0.482 342.3 ⁰ 0.69 ⁰ 0.000002 0.0089 0.897 703.714 333.58 ⁰ 8.7 ⁰
335 ⁰ 1.0088 0.9143 -0.4263 -0.463 343.0 ⁰ 0.69 ⁰ 0.000002 0.0089 0.893 704.607 334.46 ⁰ 9.2 ⁰
336 ⁰ 1.0067 0.9197 -0.4095 -0.445 343.7 ⁰ 0.69 ⁰ 0.000002 0.0089 0.890 705.497 335.34 ⁰ 9.7 ⁰
337 ⁰ 1.0048 0.9249 -0.3926 -0.427 344.4 ⁰ 0.69 ⁰ 0.000002 0.0088 0.886 706.383 336.21 ⁰ 10.1 ⁰
338 ⁰ 1.0029 0.9299 -0.3757 -0.408 345.1 ⁰ 0.69 ⁰ 0.000002 0.0088 0.883 707.266 337.08 ⁰ 10.6 ⁰
339 ⁰ 1.0011 0.9346 -0.3588 -0.390 345.8 ⁰ 0.69 ⁰ 0.000002 0.0088 0.879 708.145 337.95 ⁰ 11.1 ⁰
340 ⁰ 0.9994 0.9391 -0.3418 -0.372 346.5 ⁰ 0.69 ⁰ 0.000002 0.0087 0.876 709.022 338.81 ⁰ 11.5 ⁰
341 ⁰ 0.9978 0.9434 -0.3249 -0.353 347.1 ⁰ 0.68 ⁰ 0.000002 0.0087 0.873 709.895 339.67 ⁰ 12.0 ⁰
342 ⁰ 0.9963 0.9475 -0.3079 -0.335 347.8 ⁰ 0.68 ⁰ 0.000002 0.0087 0.871 710.766 340.53 ⁰ 12.4 ⁰
343 ⁰ 0.9948 0.9513 -0.2909 -0.316 348.5 ⁰ 0.68 ⁰ 0.000002 0.0087 0.868 711.634 341.39 ⁰ 12.9 ⁰
344 ⁰ 0.9935 0.9550 -0.2738 -0.298 349.2 ⁰ 0.68 ⁰ 0.000002 0.0086 0.866 712.500 342.24 ⁰ 13.3 ⁰
345 ⁰ 0.9922 0.9584 -0.2568 -0.279 349.9 ⁰ 0.68 ⁰ 0.000002 0.0086 0.863 713.363 343.09 ⁰ 13.8 ⁰
θ R(AU) X (AU) Y (AU) YAC(AU) ECumm EIncr AEdge(AU2) ATA(AU2) t(dy) T(dy) θ θ
346 ⁰ 0.9910 0.9615 -0.2397 -0.261 350.5 ⁰ 0.68 ⁰ 0.000002 0.0086 0.861 714.224 343.94 ⁰ 14.3 ⁰
347 ⁰ 0.9899 0.9645 -0.2227 -0.242 351.2 ⁰ 0.68 ⁰ 0.000002 0.0086 0.859 715.083 344.79 ⁰ 14.7 ⁰
348 ⁰ 0.9888 0.9672 -0.2056 -0.223 351.9 ⁰ 0.68 ⁰ 0.000002 0.0085 0.857 715.941 345.63 ⁰ 15.2 ⁰
349 ⁰ 0.9879 0.9697 -0.1885 -0.205 352.6 ⁰ 0.68 ⁰ 0.000002 0.0085 0.856 716.797 346.47 ⁰ 15.6 ⁰
350 ⁰ 0.9870 0.9720 -0.1714 -0.186 353.3 ⁰ 0.68 ⁰ 0.000002 0.0085 0.854 717.651 347.32 ⁰ 16.0 ⁰
351 ⁰ 0.9862 0.9741 -0.1543 -0.168 353.9 ⁰ 0.68 ⁰ 0.000002 0.0085 0.853 718.503 348.16 ⁰ 16.5 ⁰
352 ⁰ 0.9856 0.9760 -0.1372 -0.149 354.6 ⁰ 0.68 ⁰ 0.000002 0.0085 0.851 719.355 349.00 ⁰ 16.9 ⁰
353 ⁰ 0.9849 0.9776 -0.1200 -0.130 355.3 ⁰ 0.67 ⁰ 0.000002 0.0085 0.850 720.205 349.83 ⁰ 17.4 ⁰
354 ⁰ 0.9844 0.9790 -0.1029 -0.112 356.0 ⁰ 0.67 ⁰ 0.000002 0.0085 0.849 721.054 350.67 ⁰ 17.8 ⁰
355 ⁰ 0.9840 0.9802 -0.0858 -0.093 356.6 ⁰ 0.67 ⁰ 0.000002 0.0085 0.848 721.903 351.51 ⁰ 18.3 ⁰
356 ⁰ 0.9836 0.9812 -0.0686 -0.075 357.3 ⁰ 0.67 ⁰ 0.000002 0.0084 0.848 722.750 352.34 ⁰ 18.7 ⁰
357 ⁰ 0.9833 0.9819 -0.0515 -0.056 358.0 ⁰ 0.67 ⁰ 0.000002 0.0084 0.847 723.598 353.18 ⁰ 19.2 ⁰
358 ⁰ 0.9831 0.9825 -0.0343 -0.037 358.7 ⁰ 0.67 ⁰ 0.000002 0.0084 0.847 724.444 354.01 ⁰ 19.6 ⁰
359 ⁰ 0.9830 0.9828 -0.0172 -0.019 359.3 ⁰ 0.67 ⁰ 0.000002 0.0084 0.846 725.291 354.85 ⁰ 20.1 ⁰
360 ⁰ 0.9829 0.9829 0.0000 0.000 360.0 ⁰ 0.67 ⁰ 0.000002 0.0084 0.846 726.137 355.68 ⁰ 20.5 ⁰
Given C

1+e×cos(θ)
R×Cos(θ) R×Sin(θ) Y × a/b
sin-1
(YAC/a)
EAi-EAi-1
EA Sect
minus
EA Trian
TA Edge
plus
TA Trian
ATA:πab

Δt : P
Σt 0.9856°

day
0.5240°

day
2 Year OrbitCompute semi-major axis: a = T2/3 = 1.587 AU 
        For q, choose EARTH ORBIT perihelion: 
 q=  0.983 AU. 
 Sol's farthest point from 2 yr  ORBIT: Q = 2.191 AU.
R =

1 + e × Cos(θ)
e = Q-q

Q+q
= 0.380
ℓ =2×Q×q

Q + q
= 1.353 AU
Terran OrbitObserve semi-major axis: a = 1.0 AU
          OBSERVE:  Sol's nearest point to EARTH ORBIT:  
q=  0.983 AU 
 Sol's farthest point from EARTH  ORBIT: Q=1.017 AU
R =

1 + e × Cos(θ)
e =Q-q

Q+q
= 0.017
ℓ =2×Q×q

Q + q
= 0.9997 AU
Mars OrbitObserve Semi-major axis: a = 1.52 AU.
         OBSERVE: Sol's nearest point to MARS ORBIT:  
q=  1.37 AU 
 Sol's farthest point from MARS ORBIT: Q=1.67 AU
R =

1 + e × Cos(θ)
e =Q-q

Q+q
= 0.0987
ℓ =2×Q×q

Q + q
= 1.5052 AU




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