1. The Orbit Of The Moons Of Uranus
By Paul Nethercott, April 2010 θ
Orbital Inclination
Capture Cross Section z
Area A w
Area B
Angle α
Uranus
Ecliptic - Equator
18 Moons X Y
Eccentricity D
Orbital Radius
R = Radius of Solar System
T = Search time, Seconds
Φ = Nebula Disk thickness
A = Area A
V = planets orbital velocity
Length of W, Triangle θXW
Area B, Triangle θXW
P = Capture Probability
In 5 billion years
Length of Z, Triangle θDZ
Area of Triangle θDZ
M = Mass of spare moons needed
Φ = Nebula Disk thickness
m = Mass of captured moon
Area A

2. N W E Sun S E N S Sun W The Tilt Of Uranus’s Axis
Old Axis
Before Projectile Collision
Projectile
Old Equator W E
Sun
Uranus
18 Moons S
The Tilt Of Uranus’s Axis E
After Projectile Collision
New Equator N
New Axis S
Sun
18 Moons
Uranus W

3. W 18 Moons N S E Ψ = Total orbital configuration probability
Ψ = eccentricity × inclination × clockwise
Prograde/retrograde Probability
Multiply all 18 probabilities W
New Equator
18 Moons
Projectile N
New Axis S
Uranus
18 Moons E
Inclination Probability
Multiply all 18 probabilities
Eccentricity Probability
Multiply all 18 probabilities

4. 5 Billion Year Capture Probabilities Cross Section [Square Km’s]
Moon’s Name
Capture Chance [1/x]
Capture - Years
Area Chance [1/x]
Cross Section [Square Km’s]
Cordelia
E+32
E+42
E+34
476
Ophelia
1.13E+29
E+38
E+31
25,934
Bianca
E+30
E+40
E+32
5,426
Cressida
E+34
E+43
E+36 72
Desdemona
3.0931E+32
E+42
E+34
496
Juliet
E+31
E+41
E+33
1,551
Portia
E+33
E+43
E+35
113
Rosalind
4.428E+31
2.214E+41
E+33
1,310
Cupid
E+30
E+39
E+32
6,350
Belinda
E+33
E+43
E+36
107
Perdita
E+36
E+46
E+38 6
Puck
E+31
E+40
E+33
2,473
Mab
E+28
E+38
E+31
27,831
Miranda
E+26
E+35
E+28
805,571
Ariel
E+27
E+37
E+30
99,389
Umbriel
E+29
E+39
7.4758E+31
12,692
Titania
E+26
E+35
E+28
620,430
Oberon
E+27
E+36
2.0669E+29
241,374

5. Energy = 50,183 Moon X 86.810 1.0000 Planet Mass Moon X, Mass Ratio
T=Orbital Period, Seconds
R= Orbital Radius, metres
M = Mass of planet, kilograms
m = Mass of Moon, kilograms
G= Gravitational constant
T = 3,882,476 seconds
100 Uranus Radii
2,555,900 Kilometres
Uranus
Moon’s Orbital Kinetic Energy
[Units, Sun’s Energy output per second]
Energy = 50,183
Moon X
Planet
Mass
Moon X, Mass Ratio
Ganymede
15.000
5.7873
Titan
13.452
6.4533
Mercury
33.030
2.6282
Mars
64.210
1.3520
Moon X
86.810
1.0000
Venus
0.1783
Earth
0.1453
V=Moon’s Orbital Velocity, metres/second
Velocity = metres/second

6. Average Inclination Velocity
Inclination Period
T= Average Inclination Period, Seconds
M = Mass of Moon X, kg’s
r= Other moon’s orbital radius, metres
G= Gravitational constant
U = Uranus radius, metres
R = Moon D, orbital radius
x = Moon X orbital radius [Number of Uranus Radii]
p = Radius of Moon X
r = Radius of Moon D
A = Average Distance
Average Inclination Velocity
V = Average Inclination Velocity, Metres/Second
M = Mass of Moon X, kg’s
r= Other moon’s orbital radius, metres
G= Gravitational constant
Minimum Inclination Velocity
V=Moon’s Minimum Inclination Velocity, metres/second
Maximum Inclination Velocity
V=Moon’s Maximum Inclination Velocity, metres/second

7. Inclination Times For 18 Moons
Moon X Mass = 0.1 to Times Uranus’ Mass
18 Moons
New Orbital Plane
Inclination
New Equator
Old Equator
Uranus
Old Orbital Plane
Moon X
18 Moons
Moon's
0.1
0.01
0.001
0.005
0.0001
Name
Uranus Mass
Cordelia
7,882
78,815
788,153
157,631
7,881,535
Ophelia
8,519
85,186
851,858
170,372
8,518,576
Bianca
9,376
93,764
937,640
187,528
9,376,402
Cressida
9,790
97,897
978,971
195,794
9,789,711
Desdemona
9,931
99,315
993,148
198,630
9,931,479
Juliet
10,202
102,020
1,020,204
204,041
10,202,039
Portia
10,478
104,782
1,047,823
209,565
10,478,227
Rosalind
11,087
110,874
1,108,739
221,748
11,087,394
Cupid
11,863
118,629
1,186,292
237,258
11,862,923
Belinda
11,935
119,354
1,193,539
238,708
11,935,387
Perdita
12,121
121,209
1,212,087
242,417
12,120,873
Puck
13,648
136,483
1,364,826
272,965
13,648,261
Mab
15,521
155,209
1,552,087
310,417
15,520,866
Miranda
20,597
205,967
2,059,674
411,935
20,596,739
Ariel
30,599
305,991
3,059,910
611,982
30,599,101
Umbriel
43,114
431,142
4,311,421
862,284
43,114,212
Titania
73,156
731,565
7,315,647
1,463,129
73,156,473
Oberon
102,380
1,023,805
10,238,047
2,047,609
102,380,474

8. Minimum Inclination Velocity
Uranus
Moon X r
2 Radii
R = 52 Radii
50 Uranus Radii
Moon a
Maximum Inclination Velocity
Moon X r
Moon a
50 Uranus Radii
Uranus
R=50 Radii

9. Y -X
a, b X R
x, y
Moon D
m, n k
m, n
Moon X -Y

10. Average Gravitational Attraction Moon D, Moon X
Moon D At Four Locations Y
a = 75,559 kilometres
b = 1,277,950 kilometres
d = 75,559 kilometres
f = 75,559 kilometres
b + f + d = 1,379,068 kilometres
b + f = 1,353,509 kilometres
c = 1,305,300 kilometres N d -X W E X a a f S
Moon D, Distance From Moon X
N = x 106 Kilometres
S = x 106 Kilometres
E = x 106 Kilometres
W = x 106 Kilometres c c b
Moon X -Y

11. 360 Degrees Method Average Gravitational Attraction Moon D, Moon X
Four Point Method Y
U = Uranus radius, metres
R = Moon D, orbital radius
x = Moon X orbital radius [Number of Uranus Radii]
p = Radius of Moon X
r = Radius of Moon D
A = Average Distance N R W U -X E X R U R U
Average Gravitational Attraction
Moon D, Moon X U
360 Degrees Method R S
U = Uranus radius, metres
R = Moon D, orbital radius
x = Moon D, x coordinate
y = Moon D, y coordinate
q = Angle 0 to 360
Y = Average Distance
b = Distance from Moon X to Moon D xU
Moon X -Y

12. Saturn Uranus The Moons of Uranus Before Saturn Encounter
Saturn’s Trajectory
Distance = 1,734,848,110 metres
Uranus Axis
Uranus
Uranus Equator
Moon X
Uranus Moons
Force= x 1022 Newtons

13. Saturn Uranus The Moons of Uranus After Saturn Encounter
Saturn’s Trajectory
Uranus Moons
Moon X
Uranus
Uranus Equator
Uranus Axis

14. Encounter Inclination, Kilometres After Saturn Encounter
Uranus
Moons Name
Encounter Inclination, Kilometres
Todays Inclination,
Kilometres
Cordelia
87,962 74
Ophelia
176,425 97
Bianca
265,562
199
Cressida
355,026
6.5
Desdemona
444,602
122
Juliet
534,395 73
Portia
624,408 68
Rosalind
714,914
341
Cupid
806,044
131
Belinda
897,227 41
Perdita
988,562
0.13
Puck
1,081,198
479
Mab
1,175,394
228
Miranda
1,274,058
9,561
Ariel
1,382,309
868
Umbriel
1,504,532
953
Titania
1,669,925
2,588
Oberon
1,882,750
591
The Moons Of Uranus
After Saturn Encounter
Uranus
Moons Name
After Encounter,
Degrees
Todays Inclination,
Ratio
Cordelia
6.59 78
Ophelia
13.21
0.1036
127
Bianca
19.88
0.193
103
Cressida
26.58
0.006
4,430
Desdemona
33.29
299
Juliet
40.01
0.065
616
Portia
46.75
0.059
792
Rosalind
53.52
0.279
192
Cupid
60.35
0.1
603
Belinda
67.17
0.031
2,167
Perdita
74.01
0.0001
740,100
Puck
80.95
0.3192
254
Mab
88.00
0.1335
659
Miranda
95.38
4.232 23
Ariel
103.49
0.26
398
Umbriel
112.64
0.205
549
Titania
125.02
0.34
368
Oberon
140.95
0.058
2,430

15. Uranus Moons, 18 Precise Asteroid Strikes Probabilities
R= Solar Systems radius, metres
r= moons radius
F = Bulls Eye Chance
360= Longitude degrees on the moons surface, asteroid collision location
360= Latitude degrees on the moons surface, asteroid collision location
I = Moons inclination
W = Inclination chance
e= Moon’s Eccentricity
E = Eccentricity chance
S = All Three Probabilities
K = Factorialise All 18 Probabilities

16. Inclination Chance [1/x] Eccentricity Chance [1/x]
Uranus Moons, 18 Precise Asteroid Strikes Probabilities
Name
Inclination
Eccentricity
Bulls Eye Chance [1/x]
Inclination Chance [1/x]
Eccentricity Chance [1/x]
Cordelia
62,499,977,273
1,528,482
3,846.15
Ophelia
0.1036
56,689,321,789
1,250,965
100.81
Bianca
0.193
38,446,737,269
671,503
1,086.96
Cressida
0.006
16,023,067,399
21,600,000
2,777.78
Desdemona
24,414,053,622
1,164,944
7,692.31
Juliet
0.065
11,562,026,088
1,993,846
1,515.15
Portia
0.059
5,486,966,455
2,196,610
20,000.00
Rosalind
0.279
19,290,116,442
464,516
9,090.91
Cupid
0.1
0.0013
308,641,863,075
1,296,000
769.23
Belinda
0.031
12,345,674,523
4,180,645
14,285.71
Perdita
0.0001
0.0012
111,111,070,707
1,296,000,000
833.33
Puck
0.3192
3,810,393,371
406,015
8,333.33
Mab
0.1335
0.0025
159,999,941,818
970,787
400
Miranda
4.232
449,626,862
30,624
Ariel
0.26
74,702,154
498,462
Umbriel
0.205
73,176,363
632,195
10,000.00
Titania
0.34
0.0011
40,210,221
381,176
909.09
Oberon
0.058
0.0014
43,168,856
2,234,483
714.29

17. Combined Factorial Chances
Uranus Moons, 18 Precise Asteroid Strikes Probabilities
Name
All Three Chances
Combined Factorial Chances
Cordelia
3.67E+20
Ophelia
7.15E+18
2.63E+39
Bianca
2.81E+19
7.37E+58
Cressida
9.61E+20
7.09E+79
Desdemona
2.19E+20
1.55E+100
Juliet
3.49E+19
5.42E+119
Portia
2.41E+20
1.31E+140
Rosalind
8.15E+19
1.06E+160
Cupid
3.08E+20
3.27E+180
Belinda
7.37E+20
2.41E+201
Perdita
1.20E+23
2.89E+224
Puck
1.29E+19
3.73E+243
Mab
6.21E+19
2.32E+263
Miranda
1.06E+16
2.46E+279
Ariel
3.10E+16
7.62E+295
Umbriel
4.63E+17
3.52E+312
Titania
1.39E+16
4.90E+328 
Oberon
6.89E+16
3.37E+344 

18. Inclination Times For Uranus’ 18 Moons
Moons X Orbital Radius = 50 x Uranus’ Radius
Moons X Mass = 1% Uranus
Inclination Times = 78,000 to 1,023,000 years

19. Inclination Times For Uranus’ 18 Moons
Moons X Orbital Radius = 50 x Uranus’ Radius
Moons X Mass = Uranus
Inclination Times =788,000 to 10,238,000 years

20. Inclination Times For Uranus’ 18 Moons
Moons X Orbital Radius = 50 x Uranus’ Radius
Moons X Mass = Uranus
Inclination Times = 157,000 to 2,000,000 years

21. Inclination Times For Uranus’ 18 Moons
Moons X Orbital Radius = 50 x Uranus’ Radius
Moons X Mass = Uranus
Inclination Times = 7,800,000 to 102,500,000 years

22. Inclination Times For Uranus’ 18 Moons
Moons X Mass = 0.01 Uranus
Inclination Times = 78,000 to 1,023,000 years

23. Inclination Times For Uranus’ 18 Moons
Moons X Mass = Uranus Mass
Inclination Times = 7.8 to 102 million years

24. Inclination Times For Uranus’ 18 Moons
Moons X Mass = Uranus Mass
Inclination Times = 158,000 to 2,047,000 years

25. Inclination Times For Uranus’ 18 Moons
Moons X Mass = Uranus Mass
Inclination Times = 788,000 to 10,238,000 years

26. Inclination Probability For Pluto’s 3 Moons
Eccentricity Probability For Pluto’s 3 Moons
Clockwise Probability For Pluto’s 3 Moons
Total Probability For Pluto’s 3 Moons

27. Total Probabilities For Pluto’s 3 Moons
Inclination
Eccentricity
Clockwise
Charon
0.001
0.0022
Yes
Nix
0.195
0.003
Hydra
0.212
0.0051
Total Probabilities For Pluto’s 3 Moons
Inclination [1/x]
Eccentric [1/x]
Total Both [1/x]
Clockwise
All Probabilites
180,000
455
81,818,182 2
163,636,364
166,153,846
151,515
25,174,825,174,825 4
100,699,300,699,301
141,074,020,319
29,708,853
4,191,147,365,398,200,000 8
33,529,178,923,185,600,000
Inclination, km's
Eccentricity, Km's
Cross Section Area
0.31
38.58
5.91
165.84
146.12
12,116.59
239.67
330.22
39,572.76
Area Chance [1/x]
Capture - Years
5 Billion Year Chance [1/x]
E+38
E+46
2,178,815,343,528,210,000,000,000,000,000,000,000
E+31
E+39
517,692,240,974,860,000,000,000,000,000
E+30
E+38
48,533,278,657,085,900,000,000,000,000
Moon's Mass ( × 1015 kg)
Capture Mass (Solar Mass)
1,520,000
1,665,895,031,269,050,000,000,000,000,000
2,000
520,817,143,837,887,000,000
48,826,236,073,527,100,000
Total Solar Masses
1,665,895,031,838,700,000,000,000,000,000