G-force for More

Extended Acceleration

increases cruise velocity.

Time	Distance	Velocity
1.0 Yr	.38 LY	.64 LY/Yr
1.2 Yr	.51 LY	.71 LY/Yr
1.4 Yr	.66 LY	.76 LY/Yr

G-force Accelerate for More than a Year

Definitions

• D is total distance from our star, Sol, to destination. This table independently varies value from 1 to 10.
• t_Acc is acceleration duration from departure til start of cruise. This case study proposes a monotonic increase of this duration as shown. This method could shorten lengthy cruise times, but fuel consumption tradeoffs must be carefully considered.
• Δ - Daily difference in spaceship's velocity is due to acceleration caused by constant g-force. We approximate this value: Δ = 86,400 g / c = .2826% c
• V_Fin is final velocity achieved after applying g-force propulsion for t_Acc duration.
• v_Fin is also the maximum velocity achieved during the flight.
• v_Fin is also cruise velocity; for this case study, it increases in correlation with acceleration duration.
• d_Acc is acceleration distance. It also increases in correlation with acceleration duration.
• LY = 63,241 AU
• d_Dec is deceleration distance; it equals acceleration distance.
• d_Cru is cruise distance; it equals total distance minus distances for acceleration and deceleration.
• t_Cru is cruise time as observed from the Earth.
• t_Dec is deceleration time. Assuming consistent g-force, deceleration time equals acceleration time.
• T is total time: acceleration + cruise + deceleration

Total Dist	Accel Time	Final Velocity		Acceleration distance		Cruise distance	Cruise time	Decel time	Total Time
D	tAcc	VFin		dAcc		dCru	tCru	tDec	T
LY	days	AU/day	% c	AU	LY	LY	Years	Years	Years
1	390.8	114.94	66.38%	26,082	0.41	0.18	0.26	1.07	2.37
2	418.2	119.22	68.85%	29,240	0.46	1.08	1.56	1.14	3.82
3	447.5	123.45	71.29%	32,741	0.52	1.96	2.76	1.23	5.17
4	478.8	127.60	73.70%	36,617	0.58	2.84	3.86	1.31	6.44
5	512.3	131.67	76.04%	40,901	0.65	3.71	4.87	1.40	7.64
6	548.2	135.62	78.32%	45,625	0.72	4.56	5.82	1.50	8.78
7	586.5	139.43	80.52%	50,827	0.80	5.39	6.70	1.61	9.86
8	627.6	143.08	82.63%	56,54	0.89	6.21	7.52	1.71	10.90
9	671.5	146.54	84.63	62,816	0.99	7.01	8.29	1.84	11.91
10	718.5	149.81	86.52%	69,683	1.10	7.80	9.01	1.97	12.89
IV	365.26(1.07)D	c[1 - (1 - Δ)tAcc]		ct + v(t) ln(1-Δ)		DTtl - dAcc - dDec	dCru VFin	tAcc 365.26	tAcc + tCru + tDec

AXIOM. Light speed is absolute and puts limits on interstellar travel. Even at light speed, interstellar flights take years for photons, virtually massless particles. Since human spaceships will contain large quantities of mass, the best we can hope for is to approach light speed; we can never attain it and certainly never surpass it.

ASSUMPTION-1. Self Contained Fuel. Prior to departure from Sol, notional spaceship will collect and carry sufficient fuel for planned propulsion phases to destination.

ASSUMPTION-2. Earthlike Gravity. We currently know two methods to achieve Earth like gravity on an interstellar vessel.

• Constant G-force Acceleration. If an onboard propulsion system can increase ship's velocity by 9.80665 m/s for every second of "powered" flight, then ship's contents will feel a force equivalent to Terran gravity in the direction opposite to propulsion vector.
• Centrifugal Force. If ship is not able to maintain g-force for entire flight, then the ship must spin so that contents feel forced against the inside of the outer hull. Thus, ship's shape should be cylindrical and rotate around its longitudinal axis; spin rate (usually given in degrees per second) will be inversely proportional to radius (as cylinder size increases, less spin rate is needed to maintain centripetal acceleration of 9.80665 m/s/s). Other pieces will present further details. (idea: insert figure with two g-force ships)

ASSUMPTION-3. Cruise Phase. TE considers it axiomatic that interstellar distances are so great that any interstellar voyage can easily require fuel consumption greater than 100% of ship's mass to power entire flight. Thus, the powered portions of flight (acceleration and deceleration) must be limited. Thus, an interstellar voyage must include a nonpowered cruise phase. Thus, TE assumes following flight profile.

• Acceleration Phase. Ship starts off trip by accelerating at g-force for a given duration. TE arbitrarily chooses a base line duration of one year, but this acceleration duration can be extended within fuel limitations. During g-force acceleration, ship occupants will feel a gravity like force drawing them back to departure, Solar System; thus, "up" will be toward destination, and "down" will be toward Sol, departure star.
• Cruise Phase. Due to fuel considerations, ship will stop propulsion after a planned duration and will maintain constant velocity. Fortunately, g-force acceleration for a year or more brings the ship to a significant portion of light speed, c, and reduces cruise duration from centuries to just years. Thus, ship will maintain constant velocity for entire cruise phase (majority of voyage). However, the cessation of propulsion will cause the ship to lose g-force from back of ship. To maintain Earth like gravity, occupants will have to reconfigure ship to maintain a controlled longtitudinal spin throughout the cruise phase. Thus, ship's spin will regain Earth like g-force by forcing contents against inside of outer hull.
• Deceleration Phase. Ship will need to end this trip by slowing down from cruise speed to an operational speed. At a predetermined duration prior to arrival, ship will apply propulsion vector against direction of flight. While acceleration phase directed exhaust particles toward Sol, departure; the deceleration propulsion vector will point in opposite direction, toward destination. Now, "up" will now be in the direction of Sol which is retreating from the ship, and "down" will be toward destination, which is getting closer.

Closest Destinations.

Destination		Accel Time	Final Velocity		Acceleration distance		Cruise distance	Cruise time	Decel time	Total Time
Star	D	tAcc	VFin		dAcc		dCru	tCru	tDec	T
Name	LY	days	AU/day	% c	AU	LY	LY	Years	Years	Years
Alpha Centauri	4.365	490.8	129.97	75.06%	39,047	0.62	3.13	4.17	1.34	6.86
Barnard's Star	5.963	546.8	136.30	78.72%	46,512	0.74	4.49	5.71	1.50	8.70
Wolf	7.786	618.6	143.08	82.63%	56,547	0.89	6.00	7.26	1.69	10.65
Lalande	8.291	640.1	144.85	83.66%	59,642	0.94	6.40	7.66	1.75	11.16
Sirius	8.583	652.8	145.86	84.24%	61,499	0.97	6.64	7.88	1.79	11.45
Luyten	8.728	659.3	146.35	84.52%	62,439	0.99	6.75	7.99	1.80	11.60
Ross	9.681	703.2	149.48	86.33%	68,935	1.09	7.50	8.69	1.93	12.54
Observed		Given	c[1 - (1 - Δ)tAcc] c= 173.15 AU/dy		ct + v(t) ln(1-Δ)		DTtl - dAcc - dDec	dCru VFin	tAcc 365.26	tAcc + tCru + tDec

G-force Limitations

1st, TECHNOLOGY. We have yet to design, build and operate a spaceship with a particle accelerator as the propulsion system; thus, the most compelling limit will be the transition from notional to actual. Of the numerous design tasks, an extremely difficult one will involves enormous energy to bring exhaust particles to near light speeds. Once solved, the increased mass and speed of the exhaust fuel flow (ff_Exh) will product an enormous momentum to propel the spaceship at g-force acceleration throughout powered flight. Throughout these volumes, several tables show that the higher the particle exhaust speed, the lower the quantity of original fuel mass (fuel flow per sec, ff_sec) needed to propel the ship at g-force. This means that less fuel needs to exit the spaceship for same distance traveled. HOWEVER, this increased momentum comes at a cost; much more energy is required by spaceship to accelerate the particles to these near light speeds.

2nd, FINITE RANGE. Above g-force requires fuel consumption, and our space vehicle will eventually deplete the fuel supply. Further considerations:

%TOGW Limit is ½ ship’s mass. Percentage of ship’s TakeOff Gross Weight (TOGW is also known as initial ship’s mass) must be used for fuel with the rest needed for infrastructure and payload. Thot exp assumes 50%, but it could range from 10% to 90%.

Return flight mandates a reserve. Cautious planning leads us to assume no refueling at destination or anywhere else along the flight path. Thought experiment assumes another 50% reduction to plan for return flight.

Efficiency factor needs a margin. It's safe to assume that our initial flight design will not be perfect. Even if it was, we still have to consider energy needs for life support, and many other auxilliary energy requirements.

Above factors lead us to determe total propulsion time (tp) from effectively converting 1/8th of the ship’s TOGW to kinetic energy. A further range limitation comes from the flight profile required to maintain g-force throughout the voyage.

Flight Profile. Accelerate for ½ tp. Another range limitation comes from thot exp’s self imposed flight profile where the ship accelerates to half distance, then decelerates for remaining half. We’ve chosen this profile as best way to maintain g-force throughout the trip. We could possibly improve the range by accelerating perhaps 90% of the distance then decelerating at a much greater force for remaining 10% of distance. However, this much greater force would greatly exceed Earth like gravity and thot exp assumes this to be undesireable.

3rd. STELLAR DISTANCES. Our finite range seems to keep getting whacked by above considerations; however, the near light speed of exhaust particles impact so much specific impulse that interplanetary space travel is easily accomplished with considerable margin. Consider above interplanetary table, the most demanding range (Kuiper Belt) is easily covered by the least capable row in the interstellar table (where n= 2).

On the other hand, margin is definitely not there for interstellar travel. Consider the most generous table in the interstellar table (exhaust particle traveling so fast that relativistic effects grow it 11 times mass of same particles at relative rest with the spacecraft). Conservatively, resulting momentum gives spacecraft a range of 329 days of acceleration to take us to 1/3 of one LY; another 329 days of deceleration would take us to .64 LY, the entire distinace is not even close to the Oort Cloud, edge of our Solar System.

Thus far, our notional spacecraft hasn't made any significant progress toward our nearest stellar neighber; yet, our notional spacecraft has already exhausted available fuel. Thus, we must now use reserve fuel to return back to departure point, while still far short of our goal.

4th. RELATIVISTIC PARADOX. Consider an extreme scenario from one of Robert Heinlein's novels, which elaborates on the "twin paradox". Two identical twins grow up together then separate, where one twin accelerates to near light speed, then travels on an interstellar journey for a few years. The traveling twin ages a few years and eventually returns to Earth as still a young man. Upon his return, he's amazed to discover that his meager savings has made him very wealthy and his twin has become an old man; so old, that he marries his twin's great-granddaughter. This fanciful story illustrates that relativistic effects could become very pronounced; thus, this thought experiment assumes that near light speed travel will be accomplished in a carefully controlled manner. For example, initial trips to Alpha Centauri might attain a cruise velocity of perhaps .5c, observing results, then incrementing subsequent trip's cruise speed to perhaps .51c, and so on. copythis

Marsonance Table: 2 Cyclers

For resonance, 

cycler orbit has same period (P) as Mars.

P_Cy = 1.88 yr = 687 days = P_♂

From Kepler’s Third Law, 

P² ∝ a³

thus, the primary orbital element,

 semi-major axis (a),

must be same for both cycler and Mars.

a_Cy = 1.88 AU = a_♂

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For useful rendezvous, 

cycler orbit persistently intercepts Mars orbit.

THEREFORE, orbits must differ,

and all other orbital elements likely differ.

These include: aphelion (Q), perihelion (q), eccentricity (e), semi-latis rectum (ℓ) and respective area (A).

Mars Angle	Mars Radius	Cum Area	Cum Time	Mars Incr. Time	Earth Angle	.Cycler1. Angle	Cycler1 Radius	Incr. Angle	Cycler Incr. Time	Incr. Angle	.Cycler2. Angle	Cycler2 Radius
θ♂	R♂	A♂	T	Δt♂	θꚚ	θC1	RC1	∆θC1	ΔtCy	∆θC2	θC2	RC2
Deg	AU	AU2	days	days	Deg	Deg	AU	Deg	days	Deg	Deg	AU
0 ⁰	1.3814	0.0000	0.0	1.58	0.00 ⁰	124.24 ⁰	1.5156	0.69 ⁰	1.58	0.68 ⁰	235.28 ⁰	1.5243
1 ⁰	1.3814	0.0167	1.6	1.58	1.55 ⁰	124.92 ⁰	1.5281	0.68 ⁰	1.58	0.69 ⁰	235.97 ⁰	1.5117
2 ⁰	1.3815	0.0333	3.2	1.58	3.11 ⁰	125.60 ⁰	1.5406	0.67 ⁰	1.58	0.70 ⁰	236.67 ⁰	1.4990
3 ⁰	1.3816	0.0500	4.7	1.58	4.66 ⁰	126.26 ⁰	1.5529	0.66 ⁰	1.58	0.71 ⁰	237.38 ⁰	1.4862
4 ⁰	1.3817	0.0666	6.3	1.58	6.21 ⁰	126.91 ⁰	1.5652	0.65 ⁰	1.58	0.72 ⁰	238.10 ⁰	1.4733
5 ⁰	1.3818	0.0833	7.9	1.58	7.77 ⁰	127.54 ⁰	1.5773	0.64 ⁰	1.58	0.73 ⁰	238.83 ⁰	1.4603
6 ⁰	1.3820	0.0999	9.5	1.58	9.32 ⁰	128.18 ⁰	1.5893	0.63 ⁰	1.58	0.75 ⁰	239.58 ⁰	1.4473
7 ⁰	1.3823	0.1166	11.0	1.58	10.87 ⁰	128.80 ⁰	1.6013	0.62 ⁰	1.58	0.76 ⁰	240.34 ⁰	1.4341
8 ⁰	1.3825	0.1333	12.6	1.58	12.43 ⁰	129.41 ⁰	1.6131	0.61 ⁰	1.58	0.78 ⁰	241.12 ⁰	1.4208
9 ⁰	1.3829	0.1500	14.2	1.58	13.98 ⁰	130.02 ⁰	1.6249	0.60 ⁰	1.58	0.79 ⁰	241.91 ⁰	1.4074
10 ⁰	1.3832	0.1667	15.8	1.58	15.54 ⁰	130.61 ⁰	1.6365	0.60 ⁰	1.58	0.80 ⁰	242.71 ⁰	1.3939
11 ⁰	1.3836	0.1834	17.3	1.58	17.10 ⁰	131.20 ⁰	1.6481	0.58 ⁰	1.58	0.82 ⁰	243.53 ⁰	1.3803
12 ⁰	1.3840	0.2001	18.9	1.58	18.66 ⁰	131.77 ⁰	1.6595	0.58 ⁰	1.58	0.84 ⁰	244.37 ⁰	1.3666
13 ⁰	1.3844	0.2168	20.5	1.58	20.21 ⁰	132.34 ⁰	1.6708	0.57 ⁰	1.58	0.85 ⁰	245.22 ⁰	1.3528
14 ⁰	1.3849	0.2335	22.1	1.58	21.77 ⁰	132.91 ⁰	1.6820	0.56 ⁰	1.58	0.88 ⁰	246.10 ⁰	1.3389
15 ⁰	1.3854	0.2503	23.7	1.58	23.34 ⁰	133.46 ⁰	1.6931	0.56 ⁰	1.58	0.89 ⁰	246.99 ⁰	1.3249
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
16 ⁰	1.3860	0.2670	25.3	1.59	24.90 ⁰	134.01 ⁰	1.7042	0.55 ⁰	1.59	0.92 ⁰	247.91 ⁰	1.3107
17 ⁰	1.3866	0.2838	26.8	1.59	26.46 ⁰	134.56 ⁰	1.7152	0.55 ⁰	1.59	0.94 ⁰	248.84 ⁰	1.2964
18 ⁰	1.3872	0.3006	28.4	1.59	28.03 ⁰	135.10 ⁰	1.7261	0.54 ⁰	1.59	0.96 ⁰	249.80 ⁰	1.2821
19 ⁰	1.3879	0.3174	30.0	1.59	29.59 ⁰	135.63 ⁰	1.7369	0.53 ⁰	1.59	0.98 ⁰	250.78 ⁰	1.2676
20 ⁰	1.3886	0.3342	31.6	1.59	31.16 ⁰	136.15 ⁰	1.7476	0.53 ⁰	1.59	1.00 ⁰	251.78 ⁰	1.2531
21 ⁰	1.3893	0.3510	33.2	1.59	32.73 ⁰	136.67 ⁰	1.7582	0.52 ⁰	1.59	1.02 ⁰	252.80 ⁰	1.2386
22 ⁰	1.3900	0.3679	34.8	1.59	34.30 ⁰	137.18 ⁰	1.7687	0.51 ⁰	1.59	1.05 ⁰	253.85 ⁰	1.2239
23 ⁰	1.3908	0.3848	36.4	1.60	35.87 ⁰	137.69 ⁰	1.7792	0.51 ⁰	1.60	1.08 ⁰	254.93 ⁰	1.2090
24 ⁰	1.3917	0.4017	38.0	1.60	37.45 ⁰	138.19 ⁰	1.7895	0.50 ⁰	1.60	1.11 ⁰	256.04 ⁰	1.1941
25 ⁰	1.3925	0.4186	39.6	1.60	39.03 ⁰	138.69 ⁰	1.7997	0.50 ⁰	1.60	1.14 ⁰	257.18 ⁰	1.1790
26 ⁰	1.3934	0.4355	41.2	1.60	40.61 ⁰	139.18 ⁰	1.8099	0.49 ⁰	1.60	1.16 ⁰	258.34 ⁰	1.1639
27 ⁰	1.3944	0.4525	42.8	1.60	42.19 ⁰	139.67 ⁰	1.8199	0.48 ⁰	1.60	1.20 ⁰	259.54 ⁰	1.1488
28 ⁰	1.3954	0.4694	44.4	1.61	43.77 ⁰	140.15 ⁰	1.8299	0.49 ⁰	1.61	1.24 ⁰	260.78 ⁰	1.1334
29 ⁰	1.3964	0.4864	46.0	1.61	45.35 ⁰	140.63 ⁰	1.8399	0.48 ⁰	1.61	1.27 ⁰	262.05 ⁰	1.1180
30 ⁰	1.3974	0.5035	47.6	1.61	46.94 ⁰	141.102 ⁰	1.8497	0.47 ⁰	1.61	1.31 ⁰	263.36 ⁰	1.1027
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
31 ⁰	1.3985	0.5205	49.2	1.61	48.53 ⁰	141.57 ⁰	1.8594	0.47 ⁰	1.61	1.35 ⁰	264.70 ⁰	1.0871
32 ⁰	1.3996	0.5376	50.9	1.62	50.12 ⁰	142.04 ⁰	1.8691	0.47 ⁰	1.62	1.40 ⁰	266.10 ⁰	1.0715
33 ⁰	1.4007	0.5547	52.5	1.62	51.72 ⁰	142.50 ⁰	1.8787	0.46 ⁰	1.62	1.44 ⁰	267.53 ⁰	1.0559
34 ⁰	1.4019	0.5718	54.1	1.62	53.32 ⁰	142.96 ⁰	1.8881	0.46 ⁰	1.62	1.48 ⁰	269.01 ⁰	1.0402
35 ⁰	1.4031	0.5890	55.7	1.62	54.92 ⁰	143.41 ⁰	1.8975	0.45 ⁰	1.62	1.52 ⁰	270.53 ⁰	1.0246
36 ⁰	1.4043	0.6062	57.3	1.63	56.52 ⁰	143.86 ⁰	1.9069	0.45 ⁰	1.63	1.58 ⁰	272.11 ⁰	1.0088
37 ⁰	1.4056	0.6234	59.0	1.63	58.13 ⁰	144.31 ⁰	1.9161	0.45 ⁰	1.63	1.63 ⁰	273.74 ⁰	0.9931
38 ⁰	1.4069	0.6407	60.6	1.63	59.74 ⁰	144.75 ⁰	1.9252	0.44 ⁰	1.63	1.68 ⁰	275.42 ⁰	0.9774
39 ⁰	1.4082	0.6580	62.2	1.64	61.35 ⁰	145.19 ⁰	1.9343	0.44 ⁰	1.64	1.74 ⁰	277.17 ⁰	0.9617
40 ⁰	1.4096	0.6753	63.9	1.64	62.96 ⁰	145.63 ⁰	1.9433	0.44 ⁰	1.64	1.80 ⁰	278.97 ⁰	0.9460
41 ⁰	1.4110	0.6927	65.5	1.64	64.58 ⁰	146.06 ⁰	1.9522	0.43 ⁰	1.64	1.86 ⁰	280.83 ⁰	0.9305
42 ⁰	1.4124	0.7100	67.2	1.65	66.20 ⁰	146.49 ⁰	1.9610	0.43 ⁰	1.65	1.94 ⁰	282.77 ⁰	0.9149
43 ⁰	1.4138	0.7275	68.8	1.65	67.83 ⁰	146.92 ⁰	1.9698	0.43 ⁰	1.65	2.01 ⁰	284.78 ⁰	0.8994
44 ⁰	1.4153	0.7449	70.5	1.65	69.46 ⁰	147.34 ⁰	1.9785	0.42 ⁰	1.65	2.08 ⁰	286.86 ⁰	0.8840
45 ⁰	1.4168	0.7624	72.1	1.66	71.09 ⁰	147.77 ⁰	1.9870	0.42 ⁰	1.66	2.16 ⁰	289.02 ⁰	0.8688
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
46 ⁰	1.4184	0.7800	73.8	1.66	72.72 ⁰	148.19 ⁰	1.9955	0.42 ⁰	1.66	2.25 ⁰	291.26 ⁰	0.8537
47 ⁰	1.4200	0.7975	75.4	1.66	74.36 ⁰	148.60 ⁰	2.0040	0.42 ⁰	1.66	2.32 ⁰	293.59 ⁰	0.8389
48 ⁰	1.4216	0.8152	77.1	1.67	76.00 ⁰	149.02 ⁰	2.0123	0.41 ⁰	1.67	2.42 ⁰	296.00 ⁰	0.8243
49 ⁰	1.4232	0.8328	78.8	1.67	77.65 ⁰	149.43 ⁰	2.0206	0.41 ⁰	1.67	2.51 ⁰	298.51 ⁰	0.8099
50 ⁰	1.4249	0.8505	80.5	1.67	79.30 ⁰	149.83 ⁰	2.0287	0.41 ⁰	1.67	2.60 ⁰	301.11 ⁰	0.7959
51 ⁰	1.4266	0.8683	82.1	1.68	80.95 ⁰	150.24 ⁰	2.0368	0.41 ⁰	1.68	2.70 ⁰	303.81 ⁰	0.7822
52 ⁰	1.4283	0.8860	83.8	1.68	82.61 ⁰	150.65 ⁰	2.0448	0.40 ⁰	1.68	2.80 ⁰	306.61 ⁰	0.7689
53 ⁰	1.4300	0.9039	85.5	1.69	84.27 ⁰	151.05 ⁰	2.0528	0.40 ⁰	1.69	2.91 ⁰	309.52 ⁰	0.7560
54 ⁰	1.4318	0.9217	87.2	1.69	85.94 ⁰	151.45 ⁰	2.0606	0.40 ⁰	1.69	3.01 ⁰	312.53 ⁰	0.7437
55 ⁰	1.4336	0.9396	88.9	1.69	87.61 ⁰	151.85 ⁰	2.0684	0.40 ⁰	1.69	3.11 ⁰	315.64 ⁰	0.7320
56 ⁰	1.4355	0.9576	90.6	1.70	89.28 ⁰	152.24 ⁰	2.0761	0.40 ⁰	1.70	3.22 ⁰	318.86 ⁰	0.7209
57 ⁰	1.4373	0.9756	92.3	1.70	90.96 ⁰	152.64 ⁰	2.0837	0.39 ⁰	1.70	3.32 ⁰	322.18 ⁰	0.7105
58 ⁰	1.4392	0.9937	94.0	1.71	92.65 ⁰	153.03 ⁰	2.0912	0.39 ⁰	1.71	3.43 ⁰	325.61 ⁰	0.7007
59 ⁰	1.4411	1.0118	95.7	1.71	94.33 ⁰	153.42 ⁰	2.0986	0.39 ⁰	1.71	3.52 ⁰	329.13 ⁰	0.6919
60 ⁰	1.4430	1.0299	97.4	1.72	96.03 ⁰	153.81 ⁰	2.1060	0.39 ⁰	1.72	3.64 ⁰	332.78 ⁰	0.6838
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
61 ⁰	1.4450	1.0481	99.2	1.72	97.72 ⁰	154.19 ⁰	2.1133	0.39 ⁰	1.72	3.71 ⁰	336.49 ⁰	0.6767
62 ⁰	1.4470	1.0663	100.9	1.73	99.42 ⁰	154.58 ⁰	2.1205	0.39 ⁰	1.73	3.82 ⁰	340.31 ⁰	0.6705
63 ⁰	1.4490	1.0846	102.6	1.73	101.13 ⁰	154.96 ⁰	2.1276	0.38 ⁰	1.73	3.88 ⁰	344.19 ⁰	0.6654
64 ⁰	1.4510	1.1030	104.3	1.74	102.84 ⁰	155.35 ⁰	2.1347	0.38 ⁰	1.74	3.97 ⁰	348.16 ⁰	0.6614
65 ⁰	1.4531	1.1214	106.1	1.74	104.56 ⁰	155.73 ⁰	2.1417	0.38 ⁰	1.74	4.00 ⁰	352.16 ⁰	0.6585
66 ⁰	1.4551	1.1398	107.8	1.75	106.28 ⁰	156.11 ⁰	2.1486	0.38 ⁰	1.75	4.05 ⁰	356.20 ⁰	0.6568
67 ⁰	1.4572	1.1583	109.6	1.75	108.00 ⁰	156.49 ⁰	2.1554	0.38 ⁰	1.75	4.06 ⁰	0.25 ⁰	0.6563
68 ⁰	1.4594	1.1769	111.3	1.76	109.73 ⁰	156.87 ⁰	2.1621	0.38 ⁰	1.76	4.07 ⁰	4.33 ⁰	0.6570
69 ⁰	1.4615	1.1955	113.1	1.76	111.47 ⁰	157.24 ⁰	2.1687	0.38 ⁰	1.76	4.07 ⁰	8.40 ⁰	0.6589
70 ⁰	1.4637	1.2142	114.9	1.77	113.21 ⁰	157.62 ⁰	2.1753	0.38 ⁰	1.77	4.07 ⁰	12.48 ⁰	0.6620
71 ⁰	1.4658	1.2329	116.6	1.77	114.95 ⁰	157.99 ⁰	2.1818	0.37 ⁰	1.77	4.02 ⁰	16.50 ⁰	0.6663
72 ⁰	1.4680	1.2517	118.4	1.78	116.70 ⁰	158.36 ⁰	2.1882	0.37 ⁰	1.78	3.98 ⁰	20.48 ⁰	0.6717
73 ⁰	1.4703	1.2705	120.2	1.78	118.46 ⁰	158.74 ⁰	2.1944	0.37 ⁰	1.78	3.91 ⁰	24.39 ⁰	0.6783
74 ⁰	1.4725	1.2894	122.0	1.79	120.22 ⁰	159.11 ⁰	2.2007	0.37 ⁰	1.79	3.84 ⁰	28.23 ⁰	0.6859
75 ⁰	1.4748	1.3084	123.8	1.79	121.99 ⁰	159.48 ⁰	2.2068	0.37 ⁰	1.79	3.77 ⁰	32.00 ⁰	0.6946
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
76 ⁰	1.4770	1.3274	125.6	1.80	123.76 ⁰	159.84 ⁰	2.2128	0.37 ⁰	1.80	3.68 ⁰	35.68 ⁰	0.7043
77 ⁰	1.4793	1.3464	127.4	1.80	125.54 ⁰	160.21 ⁰	2.2187	0.37 ⁰	1.80	3.58 ⁰	39.26 ⁰	0.7148
78 ⁰	1.4816	1.3656	129.2	1.81	127.32 ⁰	160.58 ⁰	2.2246	0.37 ⁰	1.81	3.49 ⁰	42.74 ⁰	0.7263
79 ⁰	1.4840	1.3848	131.0	1.82	129.11 ⁰	160.94 ⁰	2.2304	0.37 ⁰	1.82	3.39 ⁰	46.13 ⁰	0.7386
80 ⁰	1.4863	1.4040	132.8	1.82	130.91 ⁰	161.31 ⁰	2.2361	0.37 ⁰	1.82	3.29 ⁰	49.42 ⁰	0.7516
81 ⁰	1.4887	1.4233	134.6	1.83	132.71 ⁰	161.68 ⁰	2.2417	0.37 ⁰	1.83	3.19 ⁰	52.61 ⁰	0.7654
82 ⁰	1.4910	1.4427	136.5	1.83	134.51 ⁰	162.04 ⁰	2.2472	0.36 ⁰	1.83	3.06 ⁰	55.67 ⁰	0.7796
83 ⁰	1.4934	1.4621	138.3	1.84	136.32 ⁰	162.40 ⁰	2.2526	0.36 ⁰	1.84	2.98 ⁰	58.64 ⁰	0.7946
84 ⁰	1.4958	1.4816	140.2	1.84	138.14 ⁰	162.77 ⁰	2.2580	0.36 ⁰	1.84	2.86 ⁰	61.50 ⁰	0.8099
85 ⁰	1.4982	1.5012	142.0	1.85	139.97 ⁰	163.13 ⁰	2.2632	0.36 ⁰	1.85	2.77 ⁰	64.27 ⁰	0.8258
86 ⁰	1.5006	1.5208	143.9	1.86	141.79 ⁰	163.49 ⁰	2.2683	0.36 ⁰	1.86	2.68 ⁰	66.94 ⁰	0.8422
87 ⁰	1.5031	1.5405	145.7	1.86	143.63 ⁰	163.85 ⁰	2.2734	0.36 ⁰	1.86	2.58 ⁰	69.52 ⁰	0.8589
88 ⁰	1.5055	1.5602	147.6	1.87	145.47 ⁰	164.21 ⁰	2.2784	0.36 ⁰	1.87	2.49 ⁰	72.01 ⁰	0.8760
89 ⁰	1.5080	1.5800	149.5	1.87	147.32 ⁰	164.57 ⁰	2.2832	0.36 ⁰	1.87	2.39 ⁰	74.40 ⁰	0.8932
90 ⁰	1.5104	1.5999	151.4	1.88	149.17 ⁰	164.93 ⁰	2.2880	0.36 ⁰	1.88	2.31 ⁰	76.71 ⁰	0.9108
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
91 ⁰	1.5129	1.6198	153.2	1.89	151.03 ⁰	165.29 ⁰	2.2927	0.36 ⁰	1.89	2.23 ⁰	78.94 ⁰	0.9286
92 ⁰	1.5154	1.6399	155.1	1.89	152.90 ⁰	165.65 ⁰	2.2973	0.36 ⁰	1.89	2.16 ⁰	81.10 ⁰	0.9466
93 ⁰	1.5178	1.6599	157.0	1.90	154.77 ⁰	166.01 ⁰	2.3017	0.36 ⁰	1.90	2.08 ⁰	83.18 ⁰	0.9648
94 ⁰	1.5203	1.6801	158.9	1.91	156.65 ⁰	166.37 ⁰	2.3061	0.36 ⁰	1.91	2.02 ⁰	85.20 ⁰	0.9831
95 ⁰	1.5228	1.7003	160.8	1.91	158.53 ⁰	166.73 ⁰	2.3104	0.36 ⁰	1.91	1.94 ⁰	87.14 ⁰	1.0015
96 ⁰	1.5253	1.7205	162.8	1.92	160.42 ⁰	167.09 ⁰	2.3146	0.36 ⁰	1.92	1.88 ⁰	89.02 ⁰	1.0200
97 ⁰	1.5278	1.7409	164.7	1.92	162.32 ⁰	167.45 ⁰	2.3187	0.36 ⁰	1.92	1.82 ⁰	90.83 ⁰	1.0386
98 ⁰	1.5303	1.7613	166.6	1.93	164.22 ⁰	167.81 ⁰	2.3227	0.36 ⁰	1.93	1.76 ⁰	92.59 ⁰	1.0572
99 ⁰	1.5328	1.7817	168.6	1.94	166.13 ⁰	168.17 ⁰	2.3266	0.36 ⁰	1.94	1.71 ⁰	94.30 ⁰	1.0759
100 ⁰	1.5353	1.8023	170.5	1.94	168.04 ⁰	168.52 ⁰	2.3304	0.36 ⁰	1.94	1.65 ⁰	95.94 ⁰	1.0945
101 ⁰	1.5378	1.8229	172.4	1.95	169.96 ⁰	168.88 ⁰	2.3341	0.36 ⁰	1.95	1.60 ⁰	97.54 ⁰	1.1132
102 ⁰	1.5403	1.8436	174.4	1.96	171.89 ⁰	169.24 ⁰	2.3377	0.36 ⁰	1.96	1.56 ⁰	99.10 ⁰	1.1319
103 ⁰	1.5428	1.8643	176.4	1.96	173.82 ⁰	169.60 ⁰	2.3412	0.36 ⁰	1.96	1.51 ⁰	100.61 ⁰	1.1506
104 ⁰	1.5453	1.8851	178.3	1.97	175.76 ⁰	169.96 ⁰	2.3445	0.36 ⁰	1.97	1.46 ⁰	102.07 ⁰	1.1692
105 ⁰	1.5478	1.9060	180.3	1.97	177.71 ⁰	170.32 ⁰	2.3478	0.36 ⁰	1.97	1.42 ⁰	103.49 ⁰	1.1877
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
106 ⁰	1.5503	1.9269	182.3	1.98	179.66 ⁰	170.68 ⁰	2.3510	0.36 ⁰	1.98	1.38 ⁰	104.87 ⁰	1.2063
107 ⁰	1.5528	1.9479	184.3	1.99	181.62 ⁰	171.04 ⁰	2.3540	0.36 ⁰	1.99	1.35 ⁰	106.22 ⁰	1.2248
108 ⁰	1.5553	1.9690	186.3	1.99	183.59 ⁰	171.40 ⁰	2.3569	0.36 ⁰	1.99	1.31 ⁰	107.53 ⁰	1.2431
109 ⁰	1.5578	1.9901	188.3	2.00	185.56 ⁰	171.76 ⁰	2.3598	0.36 ⁰	2.00	1.27 ⁰	108.80 ⁰	1.2615
110 ⁰	1.5603	2.0114	190.3	2.01	187.53 ⁰	172.12 ⁰	2.3625	0.36 ⁰	2.01	1.25 ⁰	110.05 ⁰	1.2798
111 ⁰	1.5627	2.0326	192.3	2.01	189.52 ⁰	172.48 ⁰	2.3651	0.36 ⁰	2.01	1.21 ⁰	111.26 ⁰	1.2979
112 ⁰	1.5652	2.0540	194.3	2.02	191.51 ⁰	172.84 ⁰	2.3676	0.36 ⁰	2.02	1.18 ⁰	112.44 ⁰	1.3160
113 ⁰	1.5676	2.0754	196.3	2.03	193.51 ⁰	173.20 ⁰	2.3700	0.36 ⁰	2.03	1.16 ⁰	113.59 ⁰	1.3340
114 ⁰	1.5701	2.0969	198.4	2.03	195.51 ⁰	173.56 ⁰	2.3722	0.36 ⁰	2.03	1.13 ⁰	114.72 ⁰	1.3519
115 ⁰	1.5725	2.1184	200.4	2.04	197.52 ⁰	173.92 ⁰	2.3744	0.36 ⁰	2.04	1.10 ⁰	115.82 ⁰	1.3697
116 ⁰	1.5749	2.1400	202.4	2.04	199.53 ⁰	174.28 ⁰	2.3764	0.36 ⁰	2.04	1.07 ⁰	116.89 ⁰	1.3873
117 ⁰	1.5773	2.1617	204.5	2.05	201.55 ⁰	174.65 ⁰	2.3783	0.36 ⁰	2.05	1.05 ⁰	117.95 ⁰	1.4049
118 ⁰	1.5797	2.1834	206.6	2.06	203.58 ⁰	175.01 ⁰	2.3801	0.37 ⁰	2.06	1.03 ⁰	118.98 ⁰	1.4224
119 ⁰	1.5821	2.2053	208.6	2.06	205.61 ⁰	175.38 ⁰	2.3818	0.36 ⁰	2.06	1.01 ⁰	119.99 ⁰	1.4397
120 ⁰	1.5844	2.2271	210.7	2.07	207.65 ⁰	175.74 ⁰	2.3833	0.37 ⁰	2.07	0.99 ⁰	120.97 ⁰	1.4569
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
121 ⁰	1.5867	2.2491	212.8	2.08	209.70 ⁰	176.11 ⁰	2.3847	0.37 ⁰	2.08	0.97 ⁰	121.94 ⁰	1.4740
122 ⁰	1.5891	2.2711	214.8	2.08	211.75 ⁰	176.47 ⁰	2.3860	0.37 ⁰	2.08	0.95 ⁰	122.89 ⁰	1.4910
123 ⁰	1.5914	2.2931	216.9	2.09	213.81 ⁰	176.84 ⁰	2.3872	0.37 ⁰	2.09	0.93 ⁰	123.82 ⁰	1.5078
124 ⁰	1.5937	2.3153	219.0	2.09	215.87 ⁰	177.21 ⁰	2.3883	0.37 ⁰	2.09	0.91 ⁰	124.73 ⁰	1.5245
125 ⁰	1.5959	2.3375	221.1	2.10	217.94 ⁰	177.58 ⁰	2.3892	0.37 ⁰	2.10	0.89 ⁰	125.62 ⁰	1.5411
126 ⁰	1.5982	2.3597	223.2	2.11	220.02 ⁰	177.95 ⁰	2.3900	0.37 ⁰	2.11	0.88 ⁰	126.50 ⁰	1.5575
127 ⁰	1.6004	2.3820	225.3	2.11	222.10 ⁰	178.31 ⁰	2.3906	0.37 ⁰	2.11	0.86 ⁰	127.36 ⁰	1.5738
128 ⁰	1.6026	2.4044	227.5	2.12	224.18 ⁰	178.69 ⁰	2.3912	0.37 ⁰	2.12	0.85 ⁰	128.21 ⁰	1.5899
129 ⁰	1.6047	2.4269	229.6	2.12	226.28 ⁰	179.06 ⁰	2.3916	0.37 ⁰	2.12	0.79 ⁰	129.00 ⁰	1.6052
130 ⁰	1.6069	2.4494	231.7	2.13	228.37 ⁰	179.43 ⁰	2.3919	0.37 ⁰	2.13	0.81 ⁰	129.82 ⁰	1.6210
131 ⁰	1.6090	2.4719	233.8	2.13	230.48 ⁰	179.80 ⁰	2.3920	0.37 ⁰	2.13	0.80 ⁰	130.62 ⁰	1.6367
132 ⁰	1.6111	2.4946	236.0	2.14	232.59 ⁰	180.17 ⁰	2.3920	0.37 ⁰	2.14	0.79 ⁰	131.41 ⁰	1.6523
133 ⁰	1.6132	2.5172	238.1	2.15	234.70 ⁰	180.55 ⁰	2.3919	0.38 ⁰	2.15	0.78 ⁰	132.19 ⁰	1.6678
134 ⁰	1.6152	2.5400	240.3	2.15	236.82 ⁰	180.93 ⁰	2.3916	0.38 ⁰	2.15	0.77 ⁰	132.96 ⁰	1.6831
135 ⁰	1.6172	2.5628	242.4	2.16	238.95 ⁰	181.30 ⁰	2.3912	0.38 ⁰	2.16	0.75 ⁰	133.72 ⁰	1.6983
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
136 ⁰	1.6192	2.5856	244.6	2.16	241.08 ⁰	181.68 ⁰	2.3906	0.38 ⁰	2.16	0.74 ⁰	134.46 ⁰	1.7132
137 ⁰	1.6212	2.6085	246.8	2.17	243.21 ⁰	182.06 ⁰	2.3900	0.38 ⁰	2.17	0.73 ⁰	135.19 ⁰	1.7281
138 ⁰	1.6231	2.6315	248.9	2.17	245.35 ⁰	182.44 ⁰	2.3891	0.38 ⁰	2.17	0.72 ⁰	135.91 ⁰	1.7427
139 ⁰	1.6250	2.6545	251.1	2.18	247.50 ⁰	182.83 ⁰	2.3882	0.38 ⁰	2.18	0.71 ⁰	136.62 ⁰	1.7573
140 ⁰	1.6268	2.6776	253.3	2.18	249.65 ⁰	183.21 ⁰	2.3871	0.38 ⁰	2.18	0.70 ⁰	137.32 ⁰	1.7716
141 ⁰	1.6286	2.7007	255.5	2.19	251.81 ⁰	183.59 ⁰	2.3858	0.38 ⁰	2.19	0.69 ⁰	138.02 ⁰	1.7859
142 ⁰	1.6304	2.7239	257.7	2.19	253.97 ⁰	183.98 ⁰	2.3844	0.39 ⁰	2.19	0.68 ⁰	138.70 ⁰	1.7999
143 ⁰	1.6322	2.7471	259.9	2.20	256.13 ⁰	184.37 ⁰	2.3829	0.39 ⁰	2.20	0.67 ⁰	139.37 ⁰	1.8138
144 ⁰	1.6339	2.7704	262.1	2.20	258.30 ⁰	184.75 ⁰	2.3812	0.39 ⁰	2.20	0.66 ⁰	140.04 ⁰	1.8276
145 ⁰	1.6356	2.7937	264.3	2.21	260.48 ⁰	185.14 ⁰	2.3793	0.39 ⁰	2.21	0.66 ⁰	140.69 ⁰	1.8412
146 ⁰	1.6372	2.8171	266.5	2.21	262.66 ⁰	185.53 ⁰	2.3774	0.39 ⁰	2.21	0.65 ⁰	141.34 ⁰	1.8546
147 ⁰	1.6388	2.8405	268.7	2.21	264.84 ⁰	185.93 ⁰	2.3752	0.39 ⁰	2.21	0.64 ⁰	141.98 ⁰	1.8678
148 ⁰	1.6403	2.8639	270.9	2.22	267.03 ⁰	186.32 ⁰	2.3729	0.39 ⁰	2.22	0.63 ⁰	142.61 ⁰	1.8809
149 ⁰	1.6419	2.8874	273.2	2.22	269.22 ⁰	186.72 ⁰	2.3705	0.40 ⁰	2.22	0.62 ⁰	143.23 ⁰	1.8938
150 ⁰	1.6433	2.9110	275.4	2.23	271.41 ⁰	187.11 ⁰	2.3679	0.40 ⁰	2.23	0.62 ⁰	143.85 ⁰	1.9066
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
151 ⁰	1.6448	2.9346	277.6	2.23	273.61 ⁰	187.51 ⁰	2.3652	0.40 ⁰	2.23	0.61 ⁰	144.46 ⁰	1.9193
152 ⁰	1.6462	2.9582	279.8	2.24	275.82 ⁰	187.91 ⁰	2.3623	0.40 ⁰	2.24	0.60 ⁰	145.07 ⁰	1.9317
153 ⁰	1.6475	2.9819	282.1	2.24	278.02 ⁰	188.31 ⁰	2.3592	0.40 ⁰	2.24	0.60 ⁰	145.66 ⁰	1.9440
154 ⁰	1.6488	3.0056	284.3	2.24	280.23 ⁰	188.72 ⁰	2.3560	0.40 ⁰	2.24	0.59 ⁰	146.25 ⁰	1.9561
155 ⁰	1.6501	3.0293	286.6	2.25	282.45 ⁰	189.12 ⁰	2.3527	0.41 ⁰	2.25	0.59 ⁰	146.84 ⁰	1.9681
156 ⁰	1.6513	3.0531	288.8	2.25	284.66 ⁰	189.53 ⁰	2.3491	0.41 ⁰	2.25	0.58 ⁰	147.42 ⁰	1.9799
157 ⁰	1.6525	3.0769	291.1	2.25	286.88 ⁰	189.94 ⁰	2.3455	0.41 ⁰	2.25	0.57 ⁰	147.99 ⁰	1.9915
158 ⁰	1.6536	3.1007	293.3	2.26	289.11 ⁰	190.35 ⁰	2.3416	0.41 ⁰	2.26	0.57 ⁰	148.55 ⁰	2.0029
159 ⁰	1.6547	3.1246	295.6	2.26	291.33 ⁰	190.76 ⁰	2.3376	0.41 ⁰	2.26	0.56 ⁰	149.11 ⁰	2.0142
160 ⁰	1.6557	3.1485	297.9	2.26	293.56 ⁰	191.18 ⁰	2.3335	0.41 ⁰	2.26	0.55 ⁰	149.67 ⁰	2.0253
161 ⁰	1.6567	3.1725	300.1	2.26	295.79 ⁰	191.59 ⁰	2.3292	0.42 ⁰	2.26	0.55 ⁰	150.21 ⁰	2.0363
162 ⁰	1.6577	3.1964	302.4	2.27	298.03 ⁰	192.01 ⁰	2.3247	0.42 ⁰	2.27	0.54 ⁰	150.76 ⁰	2.0470
163 ⁰	1.6586	3.2204	304.7	2.27	300.27 ⁰	192.43 ⁰	2.3201	0.42 ⁰	2.27	0.54 ⁰	151.30 ⁰	2.0577
164 ⁰	1.6594	3.2445	306.9	2.27	302.51 ⁰	192.85 ⁰	2.3153	0.42 ⁰	2.27	0.53 ⁰	151.83 ⁰	2.0681
165 ⁰	1.6602	3.2685	309.2	2.27	304.75 ⁰	193.28 ⁰	2.3103	0.42 ⁰	2.27	0.53 ⁰	152.36 ⁰	2.0784
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
166 ⁰	1.6609	3.2926	311.5	2.28	306.99 ⁰	193.71 ⁰	2.3052	0.43 ⁰	2.28	0.53 ⁰	152.89 ⁰	2.0885
167 ⁰	1.6616	3.3166	313.8	2.28	309.24 ⁰	194.14 ⁰	2.2999	0.43 ⁰	2.28	0.52 ⁰	153.41 ⁰	2.0984
168 ⁰	1.6623	3.3407	316.0	2.28	311.48 ⁰	194.57 ⁰	2.2944	0.43 ⁰	2.28	0.52 ⁰	153.92 ⁰	2.1082
169 ⁰	1.6629	3.3649	318.3	2.28	313.73 ⁰	195.01 ⁰	2.2888	0.44 ⁰	2.28	0.51 ⁰	154.43 ⁰	2.1178
170 ⁰	1.6634	3.3890	320.6	2.28	315.98 ⁰	195.44 ⁰	2.2830	0.44 ⁰	2.28	0.51 ⁰	154.94 ⁰	2.1272
171 ⁰	1.6639	3.4132	322.9	2.28	318.24 ⁰	195.88 ⁰	2.2771	0.44 ⁰	2.28	0.50 ⁰	155.44 ⁰	2.1364
172 ⁰	1.6644	3.4373	325.2	2.29	320.49 ⁰	196.32 ⁰	2.2710	0.44 ⁰	2.29	0.50 ⁰	155.94 ⁰	2.1455
173 ⁰	1.6647	3.4615	327.5	2.29	322.74 ⁰	196.77 ⁰	2.2647	0.44 ⁰	2.29	0.50 ⁰	156.43 ⁰	2.1544
174 ⁰	1.6651	3.4857	329.7	2.29	325.00 ⁰	197.22 ⁰	2.2582	0.45 ⁰	2.29	0.49 ⁰	156.93 ⁰	2.1632
175 ⁰	1.6654	3.5099	332.0	2.29	327.25 ⁰	197.67 ⁰	2.2516	0.45 ⁰	2.29	0.49 ⁰	157.41 ⁰	2.1718
176 ⁰	1.6656	3.5341	334.3	2.29	329.51 ⁰	198.12 ⁰	2.2448	0.45 ⁰	2.29	0.49 ⁰	157.90 ⁰	2.1802
177 ⁰	1.6658	3.5583	336.6	2.29	331.77 ⁰	198.58 ⁰	2.2378	0.46 ⁰	2.29	0.48 ⁰	158.38 ⁰	2.1884
178 ⁰	1.6659	3.5825	338.9	2.29	334.03 ⁰	199.04 ⁰	2.2307	0.46 ⁰	2.29	0.48 ⁰	158.86 ⁰	2.1965
179 ⁰	1.6660	3.6068	341.2	2.29	336.29 ⁰	199.50 ⁰	2.2234	0.46 ⁰	2.29	0.47 ⁰	159.33 ⁰	2.2044
180 ⁰	1.6660	3.6310	343.5	2.29	338.54 ⁰	199.96 ⁰	2.2159	0.47 ⁰	2.29	0.47 ⁰	159.80 ⁰	2.2121
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
181 ⁰	1.6660	3.6552	345.8	2.29	340.80 ⁰	200.43 ⁰	2.2083	0.47 ⁰	2.29	0.47 ⁰	160.27 ⁰	2.2196
182 ⁰	1.6659	3.6794	348.1	2.29	343.06 ⁰	200.90 ⁰	2.2005	0.47 ⁰	2.29	0.46 ⁰	160.73 ⁰	2.2270
183 ⁰	1.6658	3.7036	350.4	2.29	345.32 ⁰	201.38 ⁰	2.1925	0.47 ⁰	2.29	0.46 ⁰	161.19 ⁰	2.2342
184 ⁰	1.6656	3.7278	352.7	2.29	347.58 ⁰	201.86 ⁰	2.1844	0.48 ⁰	2.29	0.46 ⁰	161.65 ⁰	2.2413
185 ⁰	1.6654	3.7521	354.9	2.29	349.83 ⁰	202.34 ⁰	2.1760	0.48 ⁰	2.29	0.46 ⁰	162.10 ⁰	2.2482
186 ⁰	1.6651	3.7762	357.2	2.29	352.09 ⁰	202.83 ⁰	2.1676	0.48 ⁰	2.29	0.45 ⁰	162.56 ⁰	2.2549
187 ⁰	1.6647	3.8004	359.5	2.29	354.34 ⁰	203.32 ⁰	2.1589	0.49 ⁰	2.29	0.45 ⁰	163.01 ⁰	2.2614
188 ⁰	1.6644	3.8246	361.8	2.29	356.60 ⁰	203.81 ⁰	2.1501	0.49 ⁰	2.29	0.45 ⁰	163.45 ⁰	2.2678
189 ⁰	1.6639	3.8488	364.1	2.29	358.85 ⁰	204.31 ⁰	2.1410	0.50 ⁰	2.29	0.44 ⁰	163.90 ⁰	2.2740
190 ⁰	1.6634	3.8729	366.4	2.28	1.10 ⁰	204.81 ⁰	2.1319	0.50 ⁰	2.28	0.44 ⁰	164.34 ⁰	2.2800
191 ⁰	1.6629	3.8971	368.7	2.28	3.36 ⁰	205.31 ⁰	2.1226	0.50 ⁰	2.28	0.44 ⁰	164.77 ⁰	2.2859
192 ⁰	1.6623	3.9212	370.9	2.28	5.60 ⁰	205.82 ⁰	2.1131	0.51 ⁰	2.28	0.44 ⁰	165.21 ⁰	2.2916
193 ⁰	1.6616	3.9453	373.2	2.28	7.85 ⁰	206.33 ⁰	2.1034	0.51 ⁰	2.28	0.43 ⁰	165.64 ⁰	2.2971
194 ⁰	1.6609	3.9694	375.5	2.28	10.10 ⁰	206.85 ⁰	2.0935	0.52 ⁰	2.28	0.43 ⁰	166.08 ⁰	2.3025
195 ⁰	1.6602	3.9935	377.8	2.28	12.34 ⁰	207.38 ⁰	2.0835	0.52 ⁰	2.28	0.43 ⁰	166.51 ⁰	2.3078
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
196 ⁰	1.6594	4.0175	380.1	2.27	14.58 ⁰	207.90 ⁰	2.0733	0.53 ⁰	2.27	0.43 ⁰	166.93 ⁰	2.3128
197 ⁰	1.6586	4.0415	382.3	2.27	16.82 ⁰	208.43 ⁰	2.0630	0.53 ⁰	2.27	0.42 ⁰	167.35 ⁰	2.3177
198 ⁰	1.6577	4.0655	384.6	2.27	19.06 ⁰	208.97 ⁰	2.0525	0.54 ⁰	2.27	0.42 ⁰	167.78 ⁰	2.3224
199 ⁰	1.6567	4.0895	386.9	2.27	21.29 ⁰	209.51 ⁰	2.0417	0.54 ⁰	2.27	0.42 ⁰	168.20 ⁰	2.3269
200 ⁰	1.6557	4.1134	389.1	2.26	23.53 ⁰	210.06 ⁰	2.0309	0.55 ⁰	2.26	0.42 ⁰	168.61 ⁰	2.3313
201 ⁰	1.6547	4.1373	391.4	2.26	25.75 ⁰	210.61 ⁰	2.0199	0.55 ⁰	2.26	0.42 ⁰	169.03 ⁰	2.3355
202 ⁰	1.6536	4.1612	393.6	2.26	27.98 ⁰	211.17 ⁰	2.0087	0.56 ⁰	2.26	0.41 ⁰	169.44 ⁰	2.3396
203 ⁰	1.6525	4.1850	395.9	2.26	30.20 ⁰	211.73 ⁰	1.9973	0.56 ⁰	2.26	0.41 ⁰	169.85 ⁰	2.3435
204 ⁰	1.6513	4.2089	398.2	2.25	32.42 ⁰	212.30 ⁰	1.9857	0.57 ⁰	2.25	0.41 ⁰	170.26 ⁰	2.3473
205 ⁰	1.6501	4.2326	400.4	2.25	34.64 ⁰	212.87 ⁰	1.9740	0.57 ⁰	2.25	0.41 ⁰	170.67 ⁰	2.3509
206 ⁰	1.6488	4.2564	402.7	2.25	36.86 ⁰	213.46 ⁰	1.9621	0.58 ⁰	2.25	0.41 ⁰	171.08 ⁰	2.3543
207 ⁰	1.6475	4.2801	404.9	2.24	39.07 ⁰	214.04 ⁰	1.9501	0.59 ⁰	2.24	0.40 ⁰	171.48 ⁰	2.3576
208 ⁰	1.6462	4.3038	407.1	2.24	41.27 ⁰	214.63 ⁰	1.9379	0.59 ⁰	2.24	0.40 ⁰	171.88 ⁰	2.3607
209 ⁰	1.6448	4.3274	409.4	2.24	43.48 ⁰	215.23 ⁰	1.9256	0.60 ⁰	2.24	0.40 ⁰	172.29 ⁰	2.3637
210 ⁰	1.6433	4.3510	411.6	2.23	45.67 ⁰	215.84 ⁰	1.9131	0.61 ⁰	2.23	0.40 ⁰	172.68 ⁰	2.3665
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
211 ⁰	1.6419	4.3745	413.8	2.23	47.87 ⁰	216.45 ⁰	1.9003	0.61 ⁰	2.23	0.40 ⁰	173.08 ⁰	2.3692
212 ⁰	1.6403	4.3980	416.1	2.22	50.06 ⁰	217.07 ⁰	1.8875	0.62 ⁰	2.22	0.40 ⁰	173.48 ⁰	2.3717
213 ⁰	1.6388	4.4215	418.3	2.22	52.25 ⁰	217.70 ⁰	1.8745	0.63 ⁰	2.22	0.40 ⁰	173.87 ⁰	2.3741
214 ⁰	1.6372	4.4449	420.5	2.21	54.43 ⁰	218.33 ⁰	1.8614	0.63 ⁰	2.21	0.39 ⁰	174.26 ⁰	2.3763
215 ⁰	1.6356	4.4683	422.7	2.21	56.61 ⁰	218.97 ⁰	1.8481	0.64 ⁰	2.21	0.39 ⁰	174.66 ⁰	2.3783
216 ⁰	1.6339	4.4916	424.9	2.21	58.78 ⁰	219.63 ⁰	1.8346	0.65 ⁰	2.21	0.39 ⁰	175.05 ⁰	2.3803
217 ⁰	1.6322	4.5148	427.1	2.20	60.95 ⁰	220.28 ⁰	1.8210	0.66 ⁰	2.20	0.39 ⁰	175.43 ⁰	2.3820
218 ⁰	1.6304	4.5381	429.3	2.20	63.12 ⁰	220.95 ⁰	1.8071	0.67 ⁰	2.20	0.39 ⁰	175.82 ⁰	2.3836
219 ⁰	1.6286	4.5612	431.5	2.19	65.28 ⁰	221.63 ⁰	1.7932	0.68 ⁰	2.19	0.38 ⁰	176.21 ⁰	2.3851
220 ⁰	1.6268	4.5844	433.7	2.19	67.44 ⁰	222.32 ⁰	1.7791	0.69 ⁰	2.19	0.39 ⁰	176.59 ⁰	2.3864
221 ⁰	1.6250	4.6074	435.9	2.18	69.59 ⁰	223.01 ⁰	1.7648	0.70 ⁰	2.18	0.38 ⁰	176.98 ⁰	2.3876
222 ⁰	1.6231	4.6304	438.0	2.18	71.73 ⁰	223.72 ⁰	1.7503	0.71 ⁰	2.18	0.38 ⁰	177.36 ⁰	2.3887
223 ⁰	1.6212	4.6534	440.2	2.17	73.87 ⁰	224.43 ⁰	1.7357	0.72 ⁰	2.17	0.38 ⁰	177.74 ⁰	2.3896
224 ⁰	1.6192	4.6763	442.4	2.17	76.01 ⁰	225.16 ⁰	1.7210	0.73 ⁰	2.17	0.38 ⁰	178.12 ⁰	2.3903
225 ⁰	1.6172	4.6992	444.5	2.16	78.14 ⁰	225.90 ⁰	1.7061	0.74 ⁰	2.16	0.38 ⁰	178.50 ⁰	2.3909
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
226 ⁰	1.6152	4.7220	446.7	2.16	80.27 ⁰	226.64 ⁰	1.6911	0.75 ⁰	2.16	0.38 ⁰	178.88 ⁰	2.3914
227 ⁰	1.6132	4.7447	448.8	2.15	82.39 ⁰	227.40 ⁰	1.6759	0.76 ⁰	2.15	0.38 ⁰	179.25 ⁰	2.3917
228 ⁰	1.6111	4.7674	451.0	2.15	84.50 ⁰	228.18 ⁰	1.6605	0.77 ⁰	2.15	0.38 ⁰	179.63 ⁰	2.3919
229 ⁰	1.6090	4.7900	453.1	2.14	86.61 ⁰	228.96 ⁰	1.6450	0.78 ⁰	2.14	0.38 ⁰	180.01 ⁰	2.3920
230 ⁰	1.6069	4.8126	455.3	2.13	88.71 ⁰	229.76 ⁰	1.6294	0.80 ⁰	2.13	0.38 ⁰	180.38 ⁰	2.3919
231 ⁰	1.6047	4.8351	457.4	2.13	90.81 ⁰	231.00 ⁰	1.6052	0.81 ⁰	2.13	0.37 ⁰	180.75 ⁰	2.3917
232 ⁰	1.6026	4.8575	459.5	2.12	92.90 ⁰	231.83 ⁰	1.5892	0.83 ⁰	2.12	0.37 ⁰	181.12 ⁰	2.3914
233 ⁰	1.6004	4.8799	461.6	2.12	94.99 ⁰	232.68 ⁰	1.5730	0.85 ⁰	2.12	0.37 ⁰	181.50 ⁰	2.3909
234 ⁰	1.5982	4.9022	463.8	2.11	97.07 ⁰	233.54 ⁰	1.5567	0.86 ⁰	2.11	0.37 ⁰	181.87 ⁰	2.3903
235 ⁰	1.5959	4.9245	465.9	2.11	99.15 ⁰	234.43 ⁰	1.5402	0.88 ⁰	2.11	0.37 ⁰	182.24 ⁰	2.3896
236 ⁰	1.5937	4.9467	468.0	2.10	101.22 ⁰	235.32 ⁰	1.5236	0.90 ⁰	2.10	0.37 ⁰	182.61 ⁰	2.3887
237 ⁰	1.5914	4.9688	470.0	2.09	103.28 ⁰	236.23 ⁰	1.5069	0.91 ⁰	2.09	0.37 ⁰	182.98 ⁰	2.3878
238 ⁰	1.5891	4.9909	472.1	2.09	105.34 ⁰	237.17 ⁰	1.4900	0.93 ⁰	2.09	0.37 ⁰	183.34 ⁰	2.3866
239 ⁰	1.5867	5.0129	474.2	2.08	107.39 ⁰	238.12 ⁰	1.4730	0.95 ⁰	2.08	0.37 ⁰	183.71 ⁰	2.3854
240 ⁰	1.5844	5.0348	476.3	2.08	109.43 ⁰	239.08 ⁰	1.4559	0.97 ⁰	2.08	0.37 ⁰	184.08 ⁰	2.3840
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
241 ⁰	1.5821	5.0567	478.4	2.07	111.47 ⁰	240.08 ⁰	1.4387	0.99 ⁰	2.07	0.37 ⁰	184.44 ⁰	2.3826
242 ⁰	1.5797	5.0785	480.4	2.06	113.51 ⁰	241.09 ⁰	1.4213	1.01 ⁰	2.06	0.36 ⁰	184.80 ⁰	2.3810
243 ⁰	1.5773	5.1002	482.5	2.06	115.54 ⁰	242.12 ⁰	1.4038	1.04 ⁰	2.06	0.36 ⁰	185.17 ⁰	2.3792
244 ⁰	1.5749	5.1219	484.5	2.05	117.56 ⁰	243.17 ⁰	1.3862	1.05 ⁰	2.05	0.36 ⁰	185.53 ⁰	2.3774
245 ⁰	1.5725	5.1435	486.6	2.04	119.57 ⁰	244.25 ⁰	1.3686	1.08 ⁰	2.04	0.36 ⁰	185.89 ⁰	2.3754
246 ⁰	1.5701	5.1651	488.6	2.04	121.58 ⁰	245.35 ⁰	1.3508	1.10 ⁰	2.04	0.36 ⁰	186.25 ⁰	2.3733
247 ⁰	1.5676	5.1866	490.6	2.03	123.58 ⁰	246.48 ⁰	1.3329	1.13 ⁰	2.03	0.36 ⁰	186.62 ⁰	2.3711
248 ⁰	1.5652	5.2080	492.7	2.03	125.58 ⁰	247.63 ⁰	1.3149	1.16 ⁰	2.03	0.36 ⁰	186.98 ⁰	2.3688
249 ⁰	1.5627	5.2293	494.7	2.02	127.57 ⁰	248.82 ⁰	1.2968	1.18 ⁰	2.02	0.36 ⁰	187.34 ⁰	2.3664
250 ⁰	1.5603	5.2506	496.7	2.01	129.55 ⁰	250.03 ⁰	1.2787	1.21 ⁰	2.01	0.36 ⁰	187.70 ⁰	2.3639
251 ⁰	1.5578	5.2718	498.7	2.01	131.53 ⁰	251.28 ⁰	1.2604	1.25 ⁰	2.01	0.36 ⁰	188.06 ⁰	2.3612
252 ⁰	1.5553	5.2929	500.7	2.00	133.50 ⁰	252.56 ⁰	1.2420	1.28 ⁰	2.00	0.36 ⁰	188.42 ⁰	2.3584
253 ⁰	1.5528	5.3140	502.7	1.99	135.47 ⁰	253.87 ⁰	1.2236	1.31 ⁰	1.99	0.36 ⁰	188.78 ⁰	2.3556
254 ⁰	1.5503	5.3350	504.7	1.99	137.43 ⁰	255.21 ⁰	1.2051	1.35 ⁰	1.99	0.36 ⁰	189.13 ⁰	2.3526
255 ⁰	1.5478	5.3560	506.7	1.98	139.38 ⁰	256.60 ⁰	1.1866	1.39 ⁰	1.98	0.36 ⁰	189.49 ⁰	2.3495
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
256 ⁰	1.5453	5.3768	508.6	1.97	141.32 ⁰	258.02 ⁰	1.1681	1.42 ⁰	1.97	0.36 ⁰	189.85 ⁰	2.3463
257 ⁰	1.5428	5.3976	510.6	1.97	143.26 ⁰	259.49 ⁰	1.1494	1.47 ⁰	1.97	0.36 ⁰	190.21 ⁰	2.3430
258 ⁰	1.5403	5.4184	512.6	1.96	145.20 ⁰	261.00 ⁰	1.1308	1.51 ⁰	1.96	0.36 ⁰	190.57 ⁰	2.3395
259 ⁰	1.5378	5.4391	514.5	1.96	147.13 ⁰	262.56 ⁰	1.1120	1.56 ⁰	1.96	0.36 ⁰	190.93 ⁰	2.3360
260 ⁰	1.5353	5.4597	516.5	1.95	149.05 ⁰	264.16 ⁰	1.0933	1.61 ⁰	1.95	0.36 ⁰	191.28 ⁰	2.3324
261 ⁰	1.5328	5.4802	518.4	1.94	150.96 ⁰	265.81 ⁰	1.0747	1.65 ⁰	1.94	0.36 ⁰	191.64 ⁰	2.3287
262 ⁰	1.5303	5.5007	520.4	1.94	152.87 ⁰	267.52 ⁰	1.0560	1.71 ⁰	1.94	0.36 ⁰	192.00 ⁰	2.3248
263 ⁰	1.5278	5.5211	522.3	1.93	154.77 ⁰	269.29 ⁰	1.0373	1.77 ⁰	1.93	0.36 ⁰	192.36 ⁰	2.3209
264 ⁰	1.5253	5.5414	524.2	1.92	156.67 ⁰	271.11 ⁰	1.0188	1.82 ⁰	1.92	0.36 ⁰	192.72 ⁰	2.3169
265 ⁰	1.5228	5.5617	526.1	1.92	158.56 ⁰	272.99 ⁰	1.0003	1.88 ⁰	1.92	0.36 ⁰	193.07 ⁰	2.3127
266 ⁰	1.5203	5.5819	528.0	1.91	160.44 ⁰	274.94 ⁰	0.9819	1.94 ⁰	1.91	0.36 ⁰	193.43 ⁰	2.3085
267 ⁰	1.5178	5.6020	530.0	1.91	162.32 ⁰	276.96 ⁰	0.9636	2.02 ⁰	1.91	0.36 ⁰	193.79 ⁰	2.3042
268 ⁰	1.5154	5.6221	531.9	1.90	164.19 ⁰	279.04 ⁰	0.9454	2.09 ⁰	1.90	0.36 ⁰	194.15 ⁰	2.2998
269 ⁰	1.5129	5.6421	533.7	1.89	166.06 ⁰	281.20 ⁰	0.9274	2.16 ⁰	1.89	0.36 ⁰	194.51 ⁰	2.2952
270 ⁰	1.5104	5.6620	535.6	1.89	167.92 ⁰	283.44 ⁰	0.9096	2.24 ⁰	1.89	0.36 ⁰	194.87 ⁰	2.2906
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
271 ⁰	1.5080	5.6819	537.5	1.88	169.77 ⁰	285.64 ⁰	0.8929	2.20 ⁰	1.88	0.36 ⁰	195.23 ⁰	2.2859
272 ⁰	1.5055	5.7017	539.4	1.87	171.62 ⁰	287.93 ⁰	0.8764	2.29 ⁰	1.87	0.36 ⁰	195.59 ⁰	2.2811
273 ⁰	1.5031	5.7215	541.3	1.87	173.46 ⁰	290.30 ⁰	0.8601	2.37 ⁰	1.87	0.36 ⁰	195.95 ⁰	2.2762
274 ⁰	1.5006	5.7412	543.1	1.86	175.29 ⁰	292.75 ⁰	0.8441	2.45 ⁰	1.86	0.36 ⁰	196.31 ⁰	2.2712
275 ⁰	1.4982	5.7608	545.0	1.86	177.12 ⁰	295.28 ⁰	0.8286	2.53 ⁰	1.86	0.36 ⁰	196.67 ⁰	2.2661
276 ⁰	1.4958	5.7803	546.8	1.85	178.95 ⁰	297.90 ⁰	0.8133	2.62 ⁰	1.85	0.36 ⁰	197.03 ⁰	2.2609
277 ⁰	1.4934	5.7998	548.7	1.84	180.76 ⁰	300.62 ⁰	0.7984	2.72 ⁰	1.84	0.36 ⁰	197.39 ⁰	2.2557
278 ⁰	1.4910	5.8193	550.5	1.84	182.58 ⁰	303.44 ⁰	0.7840	2.82 ⁰	1.84	0.36 ⁰	197.75 ⁰	2.2503
279 ⁰	1.4887	5.8386	552.3	1.83	184.38 ⁰	306.34 ⁰	0.7701	2.90 ⁰	1.83	0.36 ⁰	198.12 ⁰	2.2449
280 ⁰	1.4863	5.8579	554.2	1.83	186.18 ⁰	309.35 ⁰	0.7568	3.01 ⁰	1.83	0.36 ⁰	198.48 ⁰	2.2393
281 ⁰	1.4840	5.8772	556.0	1.82	187.98 ⁰	312.44 ⁰	0.7441	3.09 ⁰	1.82	0.37 ⁰	198.85 ⁰	2.2337
282 ⁰	1.4816	5.8964	557.8	1.82	189.77 ⁰	315.63 ⁰	0.7320	3.19 ⁰	1.82	0.37 ⁰	199.21 ⁰	2.2280
283 ⁰	1.4793	5.9155	559.6	1.81	191.55 ⁰	318.91 ⁰	0.7207	3.28 ⁰	1.81	0.36 ⁰	199.58 ⁰	2.2222
284 ⁰	1.4770	5.9346	561.4	1.80	193.33 ⁰	322.30 ⁰	0.7101	3.39 ⁰	1.80	0.37 ⁰	199.94 ⁰	2.2163
285 ⁰	1.4748	5.9536	563.2	1.80	195.10 ⁰	325.77 ⁰	0.7003	3.47 ⁰	1.80	0.37 ⁰	200.31 ⁰	2.2103
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
286 ⁰	1.4725	5.9725	565.0	1.79	196.87 ⁰	329.47 ⁰	0.6911	3.70 ⁰	1.79	0.37 ⁰	200.68 ⁰	2.2043
287 ⁰	1.4703	5.9914	566.8	1.79	198.63 ⁰	333.26 ⁰	0.6828	3.79 ⁰	1.79	0.37 ⁰	201.05 ⁰	2.1981
288 ⁰	1.4680	6.0103	568.6	1.78	200.38 ⁰	337.12 ⁰	0.6756	3.87 ⁰	1.78	0.37 ⁰	201.42 ⁰	2.1919
289 ⁰	1.4658	6.0290	570.3	1.78	202.13 ⁰	341.05 ⁰	0.6695	3.93 ⁰	1.78	0.37 ⁰	201.79 ⁰	2.1855
290 ⁰	1.4637	6.0478	572.1	1.77	203.88 ⁰	345.03 ⁰	0.6645	3.98 ⁰	1.77	0.37 ⁰	202.16 ⁰	2.1791
291 ⁰	1.4615	6.0664	573.9	1.77	205.62 ⁰	349.06 ⁰	0.6607	4.03 ⁰	1.77	0.37 ⁰	202.54 ⁰	2.1726
292 ⁰	1.4594	6.0850	575.6	1.76	207.36 ⁰	353.11 ⁰	0.6580	4.06 ⁰	1.76	0.37 ⁰	202.91 ⁰	2.1661
293 ⁰	1.4572	6.1036	577.4	1.76	209.09 ⁰	357.19 ⁰	0.6566	4.08 ⁰	1.76	0.38 ⁰	203.29 ⁰	2.1594
294 ⁰	1.4551	6.1221	579.2	1.75	210.81 ⁰	1.26 ⁰	0.6564	4.07 ⁰	1.75	0.38 ⁰	203.66 ⁰	2.1527
295 ⁰	1.4531	6.1406	580.9	1.75	212.53 ⁰	5.33 ⁰	0.6573	4.07 ⁰	1.75	0.38 ⁰	204.04 ⁰	2.1459
296 ⁰	1.4510	6.1590	582.6	1.74	214.25 ⁰	9.35 ⁰	0.6595	4.02 ⁰	1.74	0.38 ⁰	204.42 ⁰	2.1390
297 ⁰	1.4490	6.1773	584.4	1.74	215.96 ⁰	13.33 ⁰	0.6628	3.98 ⁰	1.74	0.38 ⁰	204.80 ⁰	2.1320
298 ⁰	1.4470	6.1956	586.1	1.73	217.66 ⁰	17.25 ⁰	0.6672	3.92 ⁰	1.73	0.38 ⁰	205.19 ⁰	2.1249
299 ⁰	1.4450	6.2138	587.8	1.73	219.37 ⁰	21.11 ⁰	0.6727	3.86 ⁰	1.73	0.38 ⁰	205.57 ⁰	2.1178
300 ⁰	1.4430	6.2320	589.6	1.72	221.06 ⁰	24.88 ⁰	0.6792	3.77 ⁰	1.72	0.38 ⁰	205.95 ⁰	2.1106
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
301 ⁰	1.4411	6.2502	591.3	1.72	222.75 ⁰	28.58 ⁰	0.6867	3.70 ⁰	1.72	0.39 ⁰	206.34 ⁰	2.1032
302 ⁰	1.4392	6.2683	593.0	1.71	224.44 ⁰	32.17 ⁰	0.6950	3.59 ⁰	1.71	0.39 ⁰	206.73 ⁰	2.0958
303 ⁰	1.4373	6.2863	594.7	1.71	226.12 ⁰	35.66 ⁰	0.7042	3.49 ⁰	1.71	0.39 ⁰	207.12 ⁰	2.0884
304 ⁰	1.4355	6.3043	596.4	1.70	227.80 ⁰	39.05 ⁰	0.7142	3.39 ⁰	1.70	0.39 ⁰	207.51 ⁰	2.0808
305 ⁰	1.4336	6.3223	598.1	1.70	229.48 ⁰	42.33 ⁰	0.7249	3.28 ⁰	1.70	0.39 ⁰	207.91 ⁰	2.0732
306 ⁰	1.4318	6.3402	599.8	1.69	231.15 ⁰	45.50 ⁰	0.7362	3.17 ⁰	1.69	0.39 ⁰	208.30 ⁰	2.0656
307 ⁰	1.4300	6.3581	601.5	1.69	232.81 ⁰	48.57 ⁰	0.7481	3.07 ⁰	1.69	0.40 ⁰	208.70 ⁰	2.0577
308 ⁰	1.4283	6.3759	603.2	1.69	234.48 ⁰	51.55 ⁰	0.7607	2.98 ⁰	1.69	0.40 ⁰	209.10 ⁰	2.0499
309 ⁰	1.4266	6.3937	604.8	1.68	236.13 ⁰	54.40 ⁰	0.7736	2.85 ⁰	1.68	0.40 ⁰	209.50 ⁰	2.0419
310 ⁰	1.4249	6.4114	606.5	1.68	237.79 ⁰	57.16 ⁰	0.7870	2.76 ⁰	1.68	0.40 ⁰	209.91 ⁰	2.0339
311 ⁰	1.4232	6.4291	608.2	1.67	239.44 ⁰	59.80 ⁰	0.8007	2.65 ⁰	1.67	0.41 ⁰	210.31 ⁰	2.0258
312 ⁰	1.4216	6.4468	609.9	1.67	241.08 ⁰	62.36 ⁰	0.8147	2.56 ⁰	1.67	0.41 ⁰	210.72 ⁰	2.0176
313 ⁰	1.4200	6.4644	611.5	1.67	242.73 ⁰	64.83 ⁰	0.8292	2.48 ⁰	1.67	0.41 ⁰	211.13 ⁰	2.0094
314 ⁰	1.4184	6.4820	613.2	1.66	244.37 ⁰	67.21 ⁰	0.8439	2.38 ⁰	1.66	0.41 ⁰	211.54 ⁰	2.0010
315 ⁰	1.4168	6.4995	614.9	1.66	246.00 ⁰	69.50 ⁰	0.8588	2.29 ⁰	1.66	0.42 ⁰	211.96 ⁰	1.9926
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
316 ⁰	1.4153	6.5170	616.5	1.66	247.63 ⁰	71.71 ⁰	0.8738	2.21 ⁰	1.66	0.42 ⁰	212.38 ⁰	1.9841
317 ⁰	1.4138	6.5345	618.2	1.65	249.26 ⁰	73.84 ⁰	0.8891	2.13 ⁰	1.65	0.42 ⁰	212.80 ⁰	1.9755
318 ⁰	1.4124	6.5519	619.8	1.65	250.88 ⁰	75.89 ⁰	0.9045	2.05 ⁰	1.65	0.43 ⁰	213.23 ⁰	1.9668
319 ⁰	1.4110	6.5693	621.5	1.65	252.51 ⁰	77.87 ⁰	0.9199	1.98 ⁰	1.65	0.43 ⁰	213.66 ⁰	1.9580
320 ⁰	1.4096	6.5866	623.1	1.64	254.12 ⁰	79.78 ⁰	0.9355	1.91 ⁰	1.64	0.43 ⁰	214.09 ⁰	1.9492
321 ⁰	1.4082	6.6040	624.7	1.64	255.74 ⁰	81.62 ⁰	0.9511	1.84 ⁰	1.64	0.43 ⁰	214.52 ⁰	1.9403
322 ⁰	1.4069	6.6213	626.4	1.64	257.35 ⁰	83.40 ⁰	0.9667	1.78 ⁰	1.64	0.44 ⁰	214.96 ⁰	1.9313
323 ⁰	1.4056	6.6385	628.0	1.63	258.96 ⁰	85.12 ⁰	0.9824	1.72 ⁰	1.63	0.44 ⁰	215.40 ⁰	1.9222
324 ⁰	1.4043	6.6557	629.6	1.63	260.57 ⁰	86.78 ⁰	0.9981	1.66 ⁰	1.63	0.44 ⁰	215.84 ⁰	1.9130
325 ⁰	1.4031	6.6729	631.3	1.63	262.17 ⁰	88.39 ⁰	1.0138	1.61 ⁰	1.63	0.45 ⁰	216.29 ⁰	1.9038
326 ⁰	1.4019	6.6901	632.9	1.62	263.77 ⁰	89.94 ⁰	1.0294	1.55 ⁰	1.62	0.45 ⁰	216.74 ⁰	1.8945
327 ⁰	1.4007	6.7072	634.5	1.62	265.37 ⁰	91.45 ⁰	1.0450	1.51 ⁰	1.62	0.45 ⁰	217.19 ⁰	1.8851
328 ⁰	1.3996	6.7243	636.1	1.62	266.96 ⁰	92.91 ⁰	1.0607	1.47 ⁰	1.62	0.46 ⁰	217.65 ⁰	1.8756
329 ⁰	1.3985	6.7414	637.7	1.62	268.56 ⁰	94.33 ⁰	1.0762	1.42 ⁰	1.62	0.46 ⁰	218.11 ⁰	1.8660
330 ⁰	1.3974	6.7585	639.4	1.61	270.15 ⁰	95.70 ⁰	1.0917	1.37 ⁰	1.61	0.47 ⁰	218.58 ⁰	1.8563
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
331 ⁰	1.3964	6.7755	641.0	1.61	271.73 ⁰	97.03 ⁰	1.1072	1.33 ⁰	1.61	0.47 ⁰	219.05 ⁰	1.8466
332 ⁰	1.3954	6.7925	642.6	1.61	273.32 ⁰	98.33 ⁰	1.1226	1.30 ⁰	1.61	0.47 ⁰	219.52 ⁰	1.8367
333 ⁰	1.3944	6.8095	644.2	1.61	274.90 ⁰	99.59 ⁰	1.1379	1.26 ⁰	1.61	0.48 ⁰	220.00 ⁰	1.8268
334 ⁰	1.3934	6.8264	645.8	1.60	276.48 ⁰	100.813 ⁰	1.1532	1.22 ⁰	1.60	0.48 ⁰	220.48 ⁰	1.8168
335 ⁰	1.3925	6.8434	647.4	1.60	278.06 ⁰	102.00 ⁰	1.1683	1.19 ⁰	1.60	0.49 ⁰	220.97 ⁰	1.8067
336 ⁰	1.3917	6.8603	649.0	1.60	279.64 ⁰	103.16 ⁰	1.1834	1.16 ⁰	1.60	0.49 ⁰	221.47 ⁰	1.7966
337 ⁰	1.3908	6.8772	650.6	1.60	281.21 ⁰	104.29 ⁰	1.1984	1.13 ⁰	1.60	0.50 ⁰	221.97 ⁰	1.7862
338 ⁰	1.3900	6.8940	652.2	1.60	282.79 ⁰	105.39 ⁰	1.2133	1.10 ⁰	1.60	0.50 ⁰	222.47 ⁰	1.7759
339 ⁰	1.3893	6.9109	653.8	1.59	284.36 ⁰	106.46 ⁰	1.2281	1.07 ⁰	1.59	0.51 ⁰	222.98 ⁰	1.7654
340 ⁰	1.3886	6.9277	655.4	1.59	285.93 ⁰	107.50 ⁰	1.2428	1.04 ⁰	1.59	0.51 ⁰	223.49 ⁰	1.7549
341 ⁰	1.3879	6.9446	657.0	1.59	287.50 ⁰	108.52 ⁰	1.2573	1.02 ⁰	1.59	0.52 ⁰	224.01 ⁰	1.7443
342 ⁰	1.3872	6.9614	658.5	1.59	289.06 ⁰	109.51 ⁰	1.2719	1.00 ⁰	1.59	0.53 ⁰	224.54 ⁰	1.7336
343 ⁰	1.3866	6.9781	660.1	1.59	290.63 ⁰	110.49 ⁰	1.2863	0.97 ⁰	1.59	0.53 ⁰	225.07 ⁰	1.7227
344 ⁰	1.3860	6.9949	661.7	1.59	292.19 ⁰	111.44 ⁰	1.3006	0.95 ⁰	1.59	0.54 ⁰	225.61 ⁰	1.7118
345 ⁰	1.3854	7.0117	663.3	1.59	293.75 ⁰	112.37 ⁰	1.3149	0.93 ⁰	1.59	0.55 ⁰	226.16 ⁰	1.7008
θ♂	R♂(AU)	A♂(AU)2	T (dy)	Δt♂(dy)	θꚚ	θC1	RC1(AU)	∆θC1	ΔtCy(dy)	∆θC2	θC2	RC2(AU)
346 ⁰	1.3849	7.0284	664.9	1.58	295.31 ⁰	113.27 ⁰	1.3289	0.90 ⁰	1.58	0.55 ⁰	226.71 ⁰	1.6898
347 ⁰	1.3844	7.0451	666.5	1.58	296.87 ⁰	114.155 ⁰	1.3429	0.89 ⁰	1.58	0.56 ⁰	227.27 ⁰	1.6786
348 ⁰	1.3840	7.0619	668.1	1.58	298.43 ⁰	115.025 ⁰	1.3568	0.87 ⁰	1.58	0.56 ⁰	227.83 ⁰	1.6673
349 ⁰	1.3836	7.0786	669.6	1.58	299.99 ⁰	115.875 ⁰	1.3706	0.85 ⁰	1.58	0.57 ⁰	228.40 ⁰	1.6560
350 ⁰	1.3832	7.0953	671.2	1.58	301.55 ⁰	116.71 ⁰	1.3843	0.83 ⁰	1.58	0.58 ⁰	228.98 ⁰	1.6445
351 ⁰	1.3829	7.1120	672.8	1.58	303.10 ⁰	117.53 ⁰	1.3978	0.82 ⁰	1.58	0.59 ⁰	229.57 ⁰	1.6330
352 ⁰	1.3825	7.1286	674.4	1.58	304.66 ⁰	118.33 ⁰	1.4113	0.80 ⁰	1.58	0.60 ⁰	230.17 ⁰	1.6213
353 ⁰	1.3823	7.1453	675.9	1.58	306.21 ⁰	119.12 ⁰	1.4247	0.79 ⁰	1.58	0.61 ⁰	230.78 ⁰	1.6095
354 ⁰	1.3820	7.1620	677.5	1.58	307.77 ⁰	119.89 ⁰	1.4380	0.77 ⁰	1.58	0.61 ⁰	231.39 ⁰	1.5977
355 ⁰	1.3818	7.1787	679.1	1.58	309.32 ⁰	120.64 ⁰	1.4512	0.76 ⁰	1.58	0.62 ⁰	232.02 ⁰	1.5857
356 ⁰	1.3817	7.1953	680.7	1.58	310.88 ⁰	121.39 ⁰	1.4642	0.74 ⁰	1.58	0.63 ⁰	232.65 ⁰	1.5736
357 ⁰	1.3816	7.2120	682.3	1.58	312.43 ⁰	122.12 ⁰	1.4772	0.73 ⁰	1.58	0.64 ⁰	233.29 ⁰	1.5615
358 ⁰	1.3815	7.2286	683.8	1.58	313.98 ⁰	122.84 ⁰	1.4901	0.72 ⁰	1.58	0.65 ⁰	233.94 ⁰	1.5492
359 ⁰	1.3814	7.2453	685.4	1.58	315.54 ⁰	123.55 ⁰	1.5029	0.70 ⁰	1.58	0.66 ⁰	234.61 ⁰	1.5368
360 ⁰	1.3814	7.2619	687.0	1.58	317.09 ⁰	124.24 ⁰	1.5156	0.69 ⁰	1.58	0.68 ⁰	235.28 ⁰	1.5243
1° incr.	ℓ♂ 1+e♂cosθ	∫𝑅(θ)²dθ 2	A♂ ∝ T	Ti - Ti-1	0.9856° day	Numerical Methods	ℓC1 1+eC1cosθ	θi - θi-1	∆AC1∝ ∆t ∆tC1=∆tC2 ∆t ∝∆AC2	θi - θi-1	Numerical Methods	ℓC2 1+eC2cosθ

SLIDESHOW

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

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