PARABOLIC FIT TO THE ELEMENTS


semi-major axis


 a

t0

t1

t2

s

r (%)
Chiron
13.706623
0.179347
0.006325
0.00485
82
Pholus
20.275693
0.076649
0.035961
0.00620
17
Nessus
24.581639
-0.146288
-0.075392
0.00995
41
Asbolus
18.090753
0.178621
0.045592
0.01199
22
1994TA
16.777018
0.061370
0.018815
0.00302
8
Hylonome
25.070120
0.013190
0.004680
0.00772
0
Chariklo
15.785757
0.015579
0.005722
0.00196
1
1998QM107
19.994651
-0.049505
-0.006539
0.00455
16
1998SG35
8.436615
0.087621
-0.031693
0.00638
81
1998TF35
26.200257
-0.031258
-0.012325
0.00934
1
1998BU48
33.377974
0.019909
0.005040
0.01773
0
1999OX3
32.323553
0.124515
0.030570
0.01703
10
1999UG5
12.332689
-0.525801
-0.190481
0.02683
45
1999XX143
17.852584
-0.035857
-0.014132
0.00347
4
1999TD10
97.222029
1.773236
0.455569
1.01428
25

 

mean longitude


L

t0

t1

t2

s

r (%)
Chiron
217.082289
711.326272
-6.780558
68.1'
100
Pholus
146.709296
397.676298
0.684955
5.1'
100
Nessus
224.960388
294.446662
-0.517808
8.8'
100
Asbolus
284.722483
470.751331
-1.381175
12.7'
100
1994TA
12.379247
527.118188
-0.040152
5.2'
100
Hylonome
197.661390
287.615459
0.004680
1.7'
100
Chariklo
159.483867
576.026830
0.080862
1.4'
100
1998QM107
309.489540
403.993231
0.609215
3.2'
100
1998SG35
27.870262
1443.290050
-30.381758
1616'
100
1998TF35
20.739157
268.968584
-0.007491
2.1'
100
1998BU48
96.661799
187.372879
0.005040
2.5'
100
1999OX3
356.656394
197.354010
-0.006902
3.3'
100
1999UG5
24.893512
798.128313
-3.221869
800.1'
100
1999XX143
86.237375
477.393757
-0.199600
2.8'
100
1999TD10
357.316946
38.369517
-0.041838
8.6'
100

 

eccentricity


 e

t0

t1

t2

s

r (%)
Chiron
0.382110
0.006499
0.000569
0.0000161
77
Pholus
0.571000
0.001504
0.000661
0.0000041
8
Nessus
0.519093
-0.002952
-0.001573
0.0000055
38
Asbolus
0.621208
0.004681
0.001106
0.0000050
37
1994TA
0.303026
0.000693
0.000296
0.0000050
1
Hylonome
0.246633
0.000644
0.000198
0.0000650
0
Chariklo
0.171256
0.002014
0.000771
0.0000440
8
1998QM107
0.135414
0.003295
0.001013
0.0000064
11
1998SG35
0.321279
0.029112
0.003922
0.0001832
62
1998TF35
0.379113
0.001921
0.000657
0.0000061
4
1998BU48
0.386539
0.000549
0.000157
0.0000071
0
1999OX3
0.458913
0.001289
0.000298
0.0000071
3
1999UG5
0.401273
-0.015488
-0.005167
0.0000315
35
1999XX143
0.459783
-0.001978
-0.000528
0.0000045
8
1999TD10
0.873528
0.002531
0.000684
0.0000043
12

 

longitude of perihelion


P

t0

t1

t2

s

r (%)
Chiron
188.978082
1.387237
0.211044
11.5'
75
Pholus
114.128304
0.160766
0.034619
2.9'
8
Nessus
201.664910
-0.180141
-0.073412
4.6'
5
Asbolus
296.424846
1.241158
0.339161
6.3'
58
1994TA
291.860040
-0.983356
-0.190021
12.4'
49
Hylonome
184.155670
-0.168369
-0.068783
22.9'
1
Chariklo
182.616451
0.120973
-0.010702
28.8'
4
1998QM107
281.606477
-1.406355
-0.513169
74.8'
11
1998SG35
151.117062
-0.046225
0.419331
31.7'
73
1998TF35
353.087423
0.158332
0.052300
8.8'
1
1998BU48
55.006827
0.044217
0.005209
10.3'
0
1999OX3
43.878642
-0.627289
-0.181778
8.2'
19
1999UG5
13.492847
-4.890576
-0.291702
128.6'
87
1999XX143
318.025653
0.163610
0.081665
4.1'
10
1999TD10
357.231978
-0.023257
0.000772
3.0'
1

 

inclination


 i

t0

t1

t2

s

r (%)
Chiron
6.922300
-0.029457
0.000721
0.0'
68
Pholus
24.688225
-0.000649
-0.002205
0.1'
2
Nessus
15.649910
0.013087
0.007094
0.0'
9
Asbolus
17.628798
0.040668
0.018222
0.1'
11
1994TA
5.406527
-0.047043
-0.013089
0.0'
63
Hylonome
4.144816
0.001408
-0.000059
0.0'
9
Chariklo
23.388528
-0.008907
-0.002216
0.0'
2
1998QM107
9.360286
-0.006172
-0.000040
0.0'
28
1998SG35
15.537074
-0.250724
-0.080119
0.6'
31
1998TF35
12.639067
0.017449
0.006860
0.0'
13
1998BU48
14.251233
-0.000864
-0.000509
0.0'
0
1999OX3
2.958177
-0.382252
-0.107336
0.8'
48
1999UG5
5.481785
-0.061301
0.041829
0.7'
73
1999XX143
6.782210
-0.002062
0.000237
0.0'
11
1999TD10
5.959165
0.001060
0.001193
0.1'
0

 

longitude of ascending node


 N

t0

t1

t2

s

r (%)
Chiron
209.220819
-1.041516
-0.120518
2.3'
92
Pholus
119.373516
-0.078957
-0.004461
0.2'
61
Nessus
31.328627
0.016185
0.032722
0.3'
54
Asbolus
6.009580
-0.701053
-0.128971
1.5'
82
1994TA
137.771618
-0.535901
-0.113660
0.5'
86
Hylonome
178.194451
-0.038565
-0.003561
0.2'
16
Chariklo
300.455384
-0.129754
0.002756
0.2'
84
1998QM107
127.096139
-0.608111
-0.114570
0.4'
93
1998SG35
173.244788
-1.010667
0.287056
6.5'
96
1998TF35
51.982065
0.030559
0.038099
0.3'
51
1998BU48
132.772719
-0.016832
-0.000445
0.4'
3
1999OX3
263.297258
-4.612291
-1.290704
119.4'
48
1999UG5
87.230799
-1.515205
0.261968
14.4'
95
1999XX143
103.819189
-0.089098
0.018342
0.2'
85
1999TD10
184.895723
-0.298539
-0.109990
1.1'
44

 
Explanation:

The osculating elements were calculated directly during the numerical integration 1700-2020 at intervals of 400 days, giving a total of 293 dates which were then fitted to a parabola to represent the average orbit.

The elements are for the ecliptic of J2000. "t0"..."t2" are the powers of time measured in Julian centuries from J2000 (JD2451545).

"s" is the standard deviation of the difference between the parabola and the true quantity; it gives a very good idea of the amplitude of the perturbations that deviate the orbit from a smooth curve type of motion.

"r" is the correlation coefficient of the approximation.  It is a measure of how many points are covered by the parabola. A high percentage means a very good fit.

These elements can be used to calculate "mean" positions for 1700-2020 without perturbations. The mean errors in geocentric longitude will be similar to the standard deviation of the mean orbital longitude tabulated above, while the maximum errors will approximate the square of "s".

 
 

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